myctr

# NETWORK ANALYSIS OF THE KYIV BYLYNY CYCLE
– EAST SLAVIC EPIC NARRATIVES

PETRO SARKANYCH  Institute for Condensed Matter Physics, National Acad. Sci.
of Ukraine, Lviv, 79011, Ukraine
$\mathbb{L}^{4}$ Collaboration & Doctoral College for the Statistical Physics
of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe  NAZAR FEDORAK
Ivan Franko National University of Lviv, Lviv, 79000, Ukraine
Ukrainian Catholic University, Lviv, 79011, Ukraine  YURIJ HOLOVATCH
Institute for Condensed Matter Physics, National Acad. Sci. of Ukraine, Lviv,
79011, Ukraine
$\mathbb{L}^{4}$ Collaboration & Doctoral College for the Statistical Physics
of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe
Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB,
United Kingdom
Complexity Science Hub Vienna, 1080 Vienna, Austria  PÁDRAIG MACCARRON  MACSI,
Department of Mathematics and Statistics, University of Limerick,
Limerick V94 T9PX, Ireland  JOSEPH YOSE  Centre for Fluid and Complex Systems,
Coventry University, Coventry, CV1 5FB, United Kingdom
$\mathbb{L}^{4}$ Collaboration & Doctoral College for the Statistical Physics
of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe  RALPH KENNA
Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB,
United Kingdom
$\mathbb{L}^{4}$ Collaboration & Doctoral College for the Statistical Physics
of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, Europe

((March 19, 2022))

###### Abstract

In recent times, the advent of network science permitted new quantitative
approaches to literary studies. Here we bring the Kyiv bylyny cycle into the
field — East Slavic epic narratives originating in modern-day Ukraine. By
comparing them to other prominent European epics, we identify universal and
distinguishing properties of the social networks in bylyny. We analyse
community structures and rank most important characters. The method allows to
bolster hypotheses from humanities literature — such as the position of Prince
Volodymyr — and to generate new ones We show how the Kyiv cycle of bylyny fits
very well with narrative networks from other nations — especially heroic ones.
We anticipate that, besides delivering new narratological insights, this study
will aid future scholars and interested public to navigate their way through
Ukraine’s epic story and identify its heroes.

###### keywords:

digital humanities, comparative mythology, bylyny, Ukraine, Kyiv cycle,
Volodymyr, complex networks, social networks, comparative literature, heroes

##  1 Introduction

Over the past decade, quantitative methods have been developed to compare
social networks depicted in mythological narratives. In Refs.[35] and other
studies [31], these have been applied to prominent European epics 111For
comparative purposes, by ”epic” in this paper we loosely mean an extensive
narrative, that appears to describe events that happened far in the past,
without demanding all scholastic hallmarks of epic (e.g. poetic form,
formulaic composition, attested as an oral tradition, etc) are met. For the
reader interested in authoritative explanations of the traditional oral epic,
we refer to John Miles Foley’s Ref.[17] and related literature.  such as in
early Irish literature; the Anglo-Saxon Beowulf; the ancient Greek Iliad; as
well as a collection of sagas of the Icelanders [36]. Here we bring bylyny —
heroic epics of eastern Slavs — into the fold of network narratology. We
consider epics from the heyday of Kyivan Rus’ — the end of the ninth century
to the middle of the eleventh century. While narrative analysis is
traditionally the prerogative of the humanities [7], and while societal-
structure analysis is traditionally the subject of social sciences, the
involvement of methods and concepts imported from the natural sciences is now
broadly accepted in academia [18].

Actually, applications of quantitative methods to folklore and classical
literature have a long tradition. Historic-geographical approaches have been
used to identify different types of folk tales, depending on topics, events
and characters [30]. The famous Aarne-Thompson-Uther catalogue includes more
than two thousand such categories [10]. A very different approach is the usage
of principal-component analysis. This allows each text to be presented in the
form of a vector, with elements representing certain motifs [6].
Identification of similarity between texts is reduced to the measurement of
similarities of vectors. Another different, but equally innovative approach,
is that of phylogenetics. This was developed for the study of evolutionary
relationships between biological species and adapted to search for connections
between various narratives [60, 14]. A popular quantitative approach is to
involve complex networks. E.g. in an analysis of the Egils saga, Ref. [59]
allowed sub-classifications of internodal relationships include geneaology,
friendship, enmity interactions, gifts and inheritance. Another approach
analyses how adjectives are used with certain body parts in classic fairy
tales [65]. Network approaches can also be used to categorise tales [1] and a
review of applications of networks to analyse fictional texts can be found in
Ref. [32].

In the comparative approach used here, social networks are quantified by a set
of observables such as node-degree distribution, clustering coefficients,
assortativity, and other standard measures. Each of these is not unique to
social network, but can be used to characteristic and compare them [44]. By
using these measures, it is by now well established that social networks, in
the main, have a number of common characteristics: they are mostly small-world
[3, 64, 38, 40]; have heavy-tailed (right skewed) nodal degree distributions
[3, 5, 45]; and their clustering coefficients are higher than would be
expected for other (such as randomly constructed) network types [44]. The
social-balance hypothesis often holds for such networks too (‘‘the enemy of my
enemy is my friend’’) [22, 21, 58]; they have hierarchical structures [52];
and are assortatively mixed by node degree [44, 42]. The program set up in
[35, 36, 34, 66, 54] quantifies the extent to which networks of characters of
mythological narratives that belong to different cultures exhibit these and
other unifying and distinguishing features. Here we analyze bylyny - the
heroic epic of Eastern Slavs. Continuing our studies initiated in Refs. [55,
24], our goal is to find universal quantitative characteristics and to place
bylyny in a larger context of mythological narratives of other cultures. We
also wish to identify the most important characters and their placement in the
narrative, both amongst their immediate community and the broader society —
‘‘the secrets to their success’’, so to speak. The rest of the paper is
organized as follows. In Section 2, we briefly discuss bylyny, their content,
as well as the period and place of their origins. We present the complex
network of bylyny society in Section 3 and rank most prominent characters. We
discuss network properties in Section 4, where we compare bylyny with network
properties of other mythological narratives. We end with a conclusion and
outlook in Section 5.

##  2 Bylyny

Bylyny (or staryny, as they are sometimes called) are short, melodious,
recitative epic songs of the Eastern Slavs. (The word ‘‘bylyny’’ is plural and
its singular form is ‘‘bylyna’’.) One of the first researchers of bylyny in
the context of the Ukrainian medieval tradition was prominent historian and
literary critic Mykhailo Hrushevsky who proposed the division of bylyny into
heroic-epic and religious-legendary parts [25]. The first of these are older
and are associated primarily with areas around Kyiv and Halych in modern-day
Ukraine. They centre on characters such as Dobrynya, Illya Muromets’, and
Oleksiy (Oleshko, Alyosha) Popovych, as well as the so-called bylyny of the
‘‘Halych-and-Volhynian group’’ [25]. These bylyny form the main focus of this
paper.

The second group was created later are associated with Novgorod and Moscow.
These are social (not heroic) bylyny. Plots of the Novgorod cycle are grouped
around ordinary people: merchants, moneylenders, musicians, etc. Novgorod was
an important (primarily naval) trade centre and, due to its geographical
remoteness from land-based military and commercial routes, it evaded the
Tatar-Mongol invasion in the 13th century. In contrast, Moscow was rapidly
subordinated into the Golden Horde and for several centuries the city was one
of the western Mongolian ulus. These historical and geographical details are
reflected in bylyny local to different areas [25].

Given the thematic heterogeneity and striking differences in the geographic
and political orientation of bylyny, it is not sensible to analyse the whole
corpus as one here. We focus our attention only on the Kyiv cycle, which
covers the period of the highest prosperity of Kyivan Rus’ (the end of the 9th
to the the middle of the 11th century). Part of this epic tradition includes
the songs of skomorokhs (a typological analogue of Western European singer-
minstrels) and the story of matchmaking. These epic works are not heroic, and
therefore we also omit them from our analysis. The subject of our study is
therefore 39 texts of epic tradition which we take from Ref. [50].

Bylyny were passed from generation to generation in oral form. Although the
first recording was of the Moscow cycle by Englishman Richard James, for his
diary, in 1619 [33], it is believed that Kirsha Danilov was the first to
publish a collection of bylyny in the middle of 18th century [13]. 222This
collection shows signs of edits and corrections from the collector [47]. These
describe events that happened in Kyiv, but they had been transmitted and
migrated by oral tradition, and were collected and documented in the northern
eastern Slavic lands in the 18th-19th centuries. Vasyl Avenarius explained
this by the fact that, at that time, the majority of the population of Ukraine
(south-western Eastern Slavic territory) was already literate, in contrast to
the inhabitants of the remote villages of the empire. In Ukraine, therefore,
knowledge and testimony of historical memory were passed in writing [4]. Also,
for Ukrainians at that time, more recent (originating in the 15th-18th
centuries) recitative lyric epics about Cossacks (the so-called dumas) became
popular [56]. Also, the characters of bylyny in Ukraine ‘‘migrated’’ to other
folklore genres, such as folk tales or folk songs. Interestingly, there are
dumas about Illya Muromets’, one of the most popular of the bylyny characters.

Approximately 100 years after Danilov’s collection, the topic of bylyny was
brought to attention of scholars again. This was due to the fact, that Pavel
Rybnikov discovered an active bylyny tradition in the Olonets region of
northern Russia [53]. At first, this was received with a fair share of
scepticism similar of that shown towards Ossian [67]. However, subsequent
expeditions verified its authenticity [47].333As it was pointed by Oinas,
during the Soviet time folklore research was heavily affected by ideology and
propaganda [48]. His work on Kalevipoeg [46], the Estonian epic cycle, is a
good example of epic poetry in which the bylyny are considered part of the
broader traditional genre.

Despite temporal, geographic and thematic differences, bylyny have a lot in
common and different stories have common characters. Bylyny of the Kyiv cycle
include a series of works related to the exploits of the most famous heroes:
Illya Muromets’, Dobrynya and Oleksiy Popovych. It is this feature of bylyny
that allows us to interpret the characters of this epic tradition as a social
network. The main character of bylyny of the Kyivan cycle is Prince Volodymyr,
who performs the classical function of ‘‘epic king’’ in the manner of many
medieval heroic epics (like Charlemagne in the so-called ‘‘royal cycle’’ of
the French ‘‘chansons de geste’’). His wife is Opraksiya (Apraksiya, Eupraxia)
and she never appears in the epics separately from her husband. Three main
battle heroes are Illya Muromets’, Dobrynya and Oleksiy Popovych. Each are
vassals of Prince Volodymyr and are in military service to him. The main
antagonists of the three heroes are the Soloviy The Robber, the Tatars and
various bandits. In addition to concrete historical references, the words
‘‘Tatar’’ or ‘‘Tatars’’ may refer to an enemy in a more general sense.

A most interesting ‘‘epic hero’’ from a literary point of view is Illya, an
old experienced warrior who does not always blindly perform the orders of
Prince Volodymyr and sometimes transforms them or even resists them. In
contrast, Oleksiy is young and hot-tempered. This pair are reminiscent of the
characters of the German epic ‘‘Hildebrandslied’’, only there the old hero
Hildebrand was the father of his young antagonist Gadubranda. Dobrynya is the
guardian (perhaps an uncle) of Grand Prince Volodymyr-Vasyl the Great, the
baptist of Rus’, and in bylyny he is depicted as Volodymyr’s nephew [25].
According to some scholars, Dobrynya may have been the main protagonist of the
whole epic cycle in the period when it started to be created [25]. We give
some more information about the character(s) of Dobrynya in Appendix A.

Bylyny feature the usual epic hyperbole. For example, characters may show
superhuman abilities: Illya, Dobrynya, or Oleksiy is able to defeat several
thousand troops alone; Soloviy The Robber is able to demolish houses with his
piercing whistle, and so on (compare Cuchulain from Táin Bó Cúailnge and the
Ulster cycle in Ireland, for example). An interesting and controversial issue
is the link between characters of bylyny and their likely historical
prototypes.

Historians, folklorists and literary scholars tried to get past distortion in
the tales to a historical basis, especially for the Kyiv cycle [29, 62, 49,
25]. The key character is Prince Volodymyr himself. His mental, ideological
and geographical connection with the Baptist of the Kyivan Rus’ Volodymyr-
Vasyl the Great (958-1015) is indisputable. Historical sources are primarily
medieval works such as ‘‘The Tale of Bygone Years’’ [12], ‘‘The Lives of SS.
Borys and Hlib’’ [2], as well as the life of Volodymyr the Great himself [61].
The life of Prince Volodymyr the Great gradually idealized in the memory of
people and became an example of the Christian way of life in the context of
the ancient Ukrainian chronicle tradition. Later rulers of Rus’ - mostly
Volodymyr’s descendants – were compared to his example. It can be assumed that
the gradual transition from the oral to the written transfer of the most
important events in the history of people - that is, the gradual transition
from folklorization to fiction of history - began with the Kyiv chronicles.
This transition became systematic after 988, when, through baptism, Rus’ was
adsorbed into other European states and cultures. Chronicle history knows many
glorious princes, but after the death of the Baptist of Rus’, the name
‘‘Volodymyr’’ bore a special royal responsibility giving rise to special
expectations of his actions. Examples of the ‘‘worthy Volodymyrs’’, whose
images are detailed and vividly written in the chronicle tradition and in
memory, are Volodymyr Monomakh (1053-1125, initially the Prince of Chernihiv
and Pereyaslavl, later - the Grand Prince of Kyiv, the great-grandson of
Volodymyr the Great) and Volodymyr Vasylkovych (1249-1288, Prince of Volhyn’,
the great-grandson of the Grand Prince of Kyiv Mstyslav Izyaslavych, who
himself was the great-grandson of Volodymyr Monomakh).

Each of these two princes — Volodymyr Monomakh and Volodymyr Vasylkovych — is
depicted only positively in the Ukrainian chronicle tradition. The first,
besides becoming a positive character of the Tale of Bygone Years [12], the
Kyiv Chronicle (12th century)[23] and even the Halych-and-Volhynian Chronicle
(13th century)[63], was the only Ukrainian prince-writer. His works
(‘‘Testament of Volodymyr Monomakh’’, a fragment ‘‘Letter to Prince Oleh’’ and
‘‘Prayer’’) were placed in the Laurentian edition of the Tale of Bygone Years
under the annalistic year 1096 (the year according to the chronicles) [12].
The main human characteristics of Volodymyr Monomakh in literary and national
memory were justice, Christian zeal, enlightenment, wisdom, charity and he is
also remembered for tireless and invincible military campaigns, political
strength and statesmanly thinking, aimed at uniting the Rus’ lands and their
rulers. As for Volodymyr Vasylkovych, the Halych-and-Volhynian chronicle
presents an extremely touching portrait of this prince — ‘‘a philosopher never
seen in the land of Rus’’ and who suffered an incurable illness [37].
Volodymyr Vasylkovych did not have children, but took care of his people as a
father. He distributed much of his property to churches and monasteries, and
was the embodiment of wisdom, humility and mercy. According to the chronicles,
when, four months after his death, his tomb was opened (at the command of his
widow), Volodymyr Vasylkovych’s body was found uncorrupted: ‘‘the fragrance
was from the grave, and the smell is similar to the expensive scents’’ [37].

Thus, Volodymyr the Great, Volodymyr Monomakh, and Volodymyr Vasylkovych
together carry a whole complex of positive features. These were implicitly
approved in the public consciousness and merged into an epic manifestation as
the unified ‘‘epic ruler’’, Volodymyr. Still, local temporal and thematic
differences in bylyny of different cycles suggest corresponding temporal,
territorial and ideological personifications. Volodymyr the Great is
associated with bylyny of the 10th-11th centuries; Volodymyr Monomakh with
stories of the 12th-13th centuries; and Volodymyr Vasylkovych for the stories
in the 13th-14th centuries (especially of Halych-and-Volhynian cycle). One of
the schemes outlined below for the distribution of the epicenter of bylyny
suggests this triple division of Prince Volodymyr. Whether Prince Volodymyr is
part-amalgam of these historic characters or not is an interesting question,
and one that has been addressed exhaustively using traditional philological
and historical methods. Complex networks cannot resolve such issues, of
course. Still, very similar roles of ‘‘superheroes’’ are interesting to
explore in network terms, not least to gain insight into how people in
medieval times sought to present their heroic icons, real or imaginary [35,
18].

##  3 The Kyiv Bylyny Network

The extraction and analysis of networks of interacting characters from epic
narratives is a recent quantitative approach to comparative narratology; see
Ref.[31] for an extensive survey up to 2019 and Ref.[18] for more recent
developments. In it, individual characters in a text are represented by nodes
and interactions between them are represented by edges. In the approach
introduced in Refs.[35], and in subsequent literature [36, 27], two characters
are deemed linked if they know or interact with each other in some way.
Multiple meticulous human readings are required to construct a reliable
network — e.g. to infer whether characters have met before and or whether they
present together in a small group or, indeed, if the interactions between them
are hostile or not. The manual method of Ref.[35] and attempts at automation
form two (of four) focal points for extraction and analysis of character
networks in Ref.[31]. In Ref. [15] the authors suggest a method to construct a
network of characters automatically by allowing a computer to detect points in
the text where two characters communicate directly. Despite this method
showing good precision, it captures only one of our conditions for a
friendship connection to be made — namely when two characters are in
conversation. There are other methods to analyse the text with the help of
modern data science approaches, like the one presented in Ref. [26] where the
ranked list of characters is obtained automatically using named entity
recognition. Despite this method showing high accuracy, it does not allow to
extract the interactions between the characters. Thus, it is not yet possible
to extract the full, nuanced network using automated means and we use the
manual approach here. Therefore we use human reading to construct a friendly
link between two characters if they talk to each other, from the text it is
obvious that they have met before or they are present in a small group. In
contrast, the hostile link is added if two characters either fight each other
or are in a state of war.

From the 39 bylyny texts that form the basis of this study, we extracted a
dataset comprising 153 individual characters connected by friendly and hostile
links. This social network is depicted in Figure 1. Each character there is
represented by a number and some of the most important ones in network terms
are listed in Table 1. The most prominent of these have already been mentioned
and we encounter others in the sequel as well as in Appendix A where we
provide more background information to the Kyiv bylyny. Isolated nodes are
omitted as they do not form part of a network. The terms used to rank
characters are explained in the next section.

Character Name |  # |  $R_{k}$ |  $R_{C}$ |  $R_{B}$
---|---|---|---|---
Prince Volodymyr |  52 |  1 |  1 |  1
Illya Muromets’ |  46 |  2 |  2 |  2
Dobrynya |  28 |  3 |  3 |  3
Oleksiy Popovych |  1 |  5 |  4 |  10
Mykhailo Potyk |  87 |  9 |  7 |  5
Princeess Opraksiya |  104 |  4 |  5 |  13
Duke |  33 |  7 |  6 |  15
Vasyl |  8 |  10 |  13 |  7
Churylo |  153 |  6 |  12 |  16
Soloviy the Robber |  126 |  11 |  15 |  23
Tatar |  138 |  15 |  14 |  24
Kudrevanko |  65 |  10 |  8 |  37
Dunai |  32 |  18 |  11 |  31
Ivan Hostynyi Syn |  43 |  19 |  37 |  4
Mykhailo |  85 |  16 |  25 |  28
Kalyn |  49 |  17 |  16 |  36
Matviy |  77 |  12 |  9 |  49
Luka |  71 |  13 |  10 |  50
Hoten |  146 |  24 |  40 |  11
Soloviy |  125 |  25 |  42 |  14
Table 1: List of most important characters of bylyny, ranked by three commonly
used network measures. Character names are listed in the first column and
their numeric identifiers (using the symbol # in the text) are listed in the
second. These numbers are sorted by the Cyrylic alphabet and used to locate
the corresponding character in Figure 1. The three remaining columns give how
each character is ranked in terms of node degree ($R_{k}$), closeness
($R_{C}$) and betweenness ($R_{B}$) centralities.

In Figure 1, friendly and hostile links are represented by solid blue lines
and dotted red lines, respectively. Of the 320 edges, 223 are friendly and 105
hostile. The aggregate amount of friendly and hostile bonds is larger than the
total number of edges because the same characters can interact in different
ways (friendly and hostile) in different bylyny — and even within the same
text [36].

Figure 1: Social network of characters of Kyiv cycle bylyny. Red dashed lines
corresponds to the hostile links, while blue solid to the friendly ones. Each
node has its own code number. The most important characters and the
corresponding numbers are listed in Table 2. The largest connected component
is in the left top corner of the figure. Smaller graphs represent characters
of separate stories. For example, graph consisting of nodes 143 and 144 is two
bulls observing troops who do not interact with other characters. The star
shaped graph in the second row from the bottom describes stories about Vavilo
(node number 9). Characters of this part of the epics do not appear in any
other story.

The network in Figure 1 consists of several separate pieces. The top left
cluster is called the giant connected component. No individual bylyna has this
many characters with some 10-20 characters in the biggest individual bylyna.
Similar ‘‘subtle narrational tricks’’ were used in modern narratives to mirror
natural social networks [18]. The size of the giant component reflects the
spread of characters across different tales. This is not least because in the
Kyiv epic cycle bylyny are united by the presence of hero-protagonist, Prince
Volodymyr. He is identified in the network as node number 52 (we henceforth
refer to node numbers using the symbol #, so that Prince Volodymyr is
identified as #52). In relative terms, the giant component comprises 76.5 % of
the bylyny network. This is smaller than for the epics of many other nations,
but similar to that of the Old English epic poem Beowulf. This comparison is
not to suggest there is a connection between bylyny and Beowulf. Rather it is
but one measure to position the complexity of bylyny relative to other epics.
Our aim here is to quantify and document network features of bylyny and we do
this using standard network indices — precisely in order to compare to other
epic narratives from other nations. The results are gathered in Table 2 where
giant components are represented by $G_{c}$ in the penultimate column.

The other components of Figure 1 correspond to individual or smaller groups of
stories. These also belong to Kyiv cycle, but they don’t share characters with
the largest connected component. For example the star shaped cluster in the
second row from the bottom comes from the story about Vavilo (#9). That tale
relates how Vavilo overwhelms an antagonist king and takes his place (hence
the high degree of hostility represented by dotted red edges). Characters in
this story do not appear anywhere else, so they form isolated fragment of the
full social network. Thus, besides illustrating the cohesion and fragmentation
of bylyny, Figure 1 also offers an aide to navigating one’s way through the
complex world it depicts.

The number of vertices is denoted by $N$ in Table 2 and the number of edges is
$L$. We explain the meaning of the other indices in Section 4 where we use
them for comparative purposes. The first row of the table contains statistics
for the full social network of bylyny and results for the friendly and hostile
networks are listed in the second and third rows. The hostile network has 98
nodes 51% (50) of which are in the largest connected component. Bylyny have a
higher proportion of hostile edges than the other narrative networks, data for
which are also listed in Table 2. Hostility for most epic tales tends to be
between 10% and 20% in terms of edge count. The difference between bylyny and
other tales can be explained by the fact that bylyny are 39 individual stories
about heroes. Each of the stories describes heroic exploits, they require an
antagonist or even a couple of them for the hero to defeat. And with heroes
being common for most of the stories, one may expect the portion of hostile
links to be greater than in many other epics.

Different regions of the Kyivan Rus’ had their own heroes, and these are not
necessarily connected to the giant component. E.g., the connected component
involving Vasyl’ Okulovych (#11), in a right upper corner of Figure 1, has a
large proportion of hostility.

Network |  $N$ |  $L$ |  $\langle k\rangle$ |  $k_{\rm max}$ |  $l$ |  $l_{\rm rand}$ |  $l_{\rm max}$ |  $C$ |  $C_{\rm rand}$ |  $G_{c}$ |  $r_{k}$
---|---|---|---|---|---|---|---|---|---|---|---
Bylyny (all) |  153 |  320 |  4.18 |  52 |  2.9 |  3.61 |  6 |  0.57 |  0.03 |  76.5 |  -0.15
Bylyny (hostile) |  98 |  102 |  2.14 |  17 |  3.63 |  5.76 |  8 |  0.06 |  0.022 |  51 |  -0.11
Bylyny (friendly) |  142 |  223 |  3.16 |  41 |  2.76 |  4.33 |  6 |  0.42 |  0.022 |  57 |  -0.11
Beowulf (all) |  72 |  167 |  4.45 |  27 |  2.38 |  2.91 |  6 |  0.7 |  0.06 |  67.5 |  -0.10
Beowulf (hostile) |  31 |  26 |  1.67 |  - |  2.08 |  3.25 |  4 |  0 |  0.05 |  32.2 |  -0.20
Beowulf (friendly) |  68 |  141 |  4.12 |  - |  2.45 |  2.98 |  6 |  0.69 |  0.06 |  66.1 |  -0.03
Táin (all) |  422 |  1200 |  6.10 |  168 |  2.8 |  3.3 |  7 |  0.8 |  0.02 |  98.5 |  -0.33
Táin (hostile) |  144 |  168 |  2.33 |  - |  2.93 |  5.88 |  7 |  0.17 |  0.02 |  90.9 |  -0.36
Táin (friendly) |  385 |  1091 |  5.67 |  - |  2.84 |  3.43 |  7 |  0.84 |  0.01 |  90.9 |  -0.32
Iliad (all) |  716 |  2084 |  7.40 |  106 |  3.5 |  3.3 |  11 |  0.6 |  0.01 |  98.7 |  -0.08
Iliad (hostile) |  321 |  361 |  2.25 |  - |  4.10 |  7.12 |  9 |  0 |  0.01 |  89.4 |  -0.39
Iliad (friendly) |  664 |  2317 |  6.98 |  - |  3.83 |  3.34 |  12 |  0.62 |  0.01 |  82.3 |  0.10
Odyssey |  301 |  1019 |  6.77 |  112 |  3.29 |  3.18 |  8 |  0.45 |  0.02 |  98.3 |  -0.08
Gísla Saga |  103 |  254 |  4.9 |  44 |  3.4 |  2.9 |  11 |  0.6 |  0.05 |  98 |  -0.15
Egils Saga |  293 |  769 |  5.3 |  59 |  4.2 |  3.4 |  12 |  0.6 |  0.02 |  97 |  -0.07
Laxdæla Saga |  332 |  894 |  5.4 |  45 |  5.0 |  3.5 |  16 |  0.5 |  0.02 |  99 |  0.19
Njáls Saga |  575 |  1612 |  5.6 |  83 |  5.1 |  3.7 |  24 |  0.4 |  0.01 |  100 |  0.01
Mabinogion |  666 |  2427 |  7.29 |  135 |  3.83 |  3.48 |  11 |  0.48 |  0.01 |  76 |  0.19
Table 2: Characteristics of the social network of bylyny compared to those of
other epics (from Refs. [35, 36, 27]). Here $N$ and $L$ indicate the number of
characters and edges respectively. Other measures are the average and maximum
degrees ($\langle k\rangle$ and $k_{\rm max}$); the average shortest path
length of the complex network ($l$) and the counterpart for random graphs of
the same size ($l_{\rm rand}$); the diameter of the giant component ($l_{\rm
max}$); the average clustering coefficient of the complex network and that of
the corresponding random graphs ($C$ and $C_{\rm rand}$); the size of the
largest connected component ($G_{c}$): and the assortativity by degree
($r_{k}$). Identifiers in brackets (‘‘all’’, ‘‘hostile’’, ‘‘friendly’’)
specify types of relationships used to construct the network.

For comparative purposes, Table 2 also contains network statistics for epics
from other nations. Besides Ireland’s Táin Bó Cuailnge and the Anglo Saxon
Beowulf, mentioned previously, these include the Iliad and Oddysey from Greece
and the Icelandic Gísli Saga, Egils Saga, Njáls Saga, Laxdæla Saga and the
Welsh Mabinogion. The data for these texts come from previous publications
[34]. When the information is available, we present data separately for
friendly and hostile links as well as for the full networks. Comparison of the
quantitative characteristics of social network of bylyny with those listed
above enables a search for universal and differentiating characteristics of
societal aspects of epic narratives.

In Ref. [34], different categories of networks are identified for different
genres based on the shape of their degree distributions and their
assortativity. There it is observed that stories centred on a single
protagonist that travels to many locations, such as Beowulf, the Odyssey or
Gísla saga all are disassorative and the main characters having exceptionally
high degrees (relative to both system size and the rest of the characters). On
the other hand narratives such as Laxdæla saga, Njáls saga and the Mabinogion
(which, after the first four chapters mostly deals with Arthurian Romances)
are set in one location, and while they have protagonists, they are still
stories of a people. These have faster decaying degree distributions and are
assortative. (We present a plot the cumulative degree distribution in Appendix
B.) Between these extremes we find the Iliad and Egils saga, both of these
have a few protagonists who are highly active in the hostile network, these
networks have assortative friendly networks. Similar to these is the Táin Bó
Cuailnge, however in this case we identify 6 characters with extremely large
degrees in both hostile and freindly networks (for further discussion see Ref.
[35]) placing it between these first and last categories. From the network
measures in table 1, we see that bylyny is more similar to that of Beowulf,
the Odyssey and Gísla saga. We discuss its individual properties and this
result in more detail over the following sections.

##  4 Network Statistics

###  4.1 Node degree

The degree of a node is the number of connections it has and, as such, it is
one measure of a character’s importance for the story. The node with the
largest degree is Prince Volodymyr (#52) who, mentioned in almost every
bylyna, is connected to roughly half of all other characters. At $k_{\rm
max}=52$, his degree is much higher than the average degree $\langle
k\rangle=4.18$. These maximal and average values are entered in Table 1 to
give a feeling for how the central hero compares with central heroes of other
texts. These include Ireland’s Cuchulain, England’s Beowulf and Greece’s
Achilles. While absolute values (of degree) are not meaningful comparative
measures across different texts, rankings are, and Prince Volodymyr is highest
ranked in Ukraine in the same way as Cuchulain is in Ireland and other
national heroes are in their respective countries. But Prince Volodymyr is not
the only hero in Ukraine and Illya Muromets’ (#46), Dobrynya (#28) and Oleksiy
Popovych (#1) are also prominent (see Appendix A) and ranked accordingly. In
Appendix A we present the giant component of Fig. 1 with nodes sized
proportionate to node degrees. Like Fig. 1, this is similar to a star graph,
or rather to several star graphs fused together; it draws out how leaders are
directly linked to each other and also attached to greater numbers of low
degree characters. (We also present a plot of the degree distribution in
Appendix B.)

As discussed in Section 2, some researchers believe Prince Volodymyr to be a
collective character - a fusion of three distinct entities. We will return to
this issue in Subsection 4.6 where we discuss the assortativity of the network
[56, 11].

###  4.2 Distances between characters

Real social networks — even those with large numbers of nodes — are
characterized by small average distances between them. This is the famous
small-world effect [38]. Since the 1960’s the term ‘‘six degrees of
separation’’ or ‘‘six handshakes’’ entered the public domain [20] and it is
widely known that the average distance between randomly selected members of
society is about six. More recently it was established that a similar value
occurs in an equivalently sized Erdős-Rényi random graph [64]. Distance, in
this sense, is the shortest length of a path or sequence of edges, which have
to be traversed to get from one node to another. We denote it by $l$ and refer
to such paths as geodesics. The longest geodesic is called the diameter of a
network and represented by $l_{\rm max}$. We now check the typical distances
(paths) between nodes in bylyny social network and compare to other stories
from other countries. In the case of disconnected graphs like that of bylyny,
we use only the giant connected component to determine diameters.

In order to find the average shortest path $l$ and diameter $l_{\rm max}$, all
geodesics in all connected components are taken into account and the resulting
values of $l$ and $l_{\rm max}$ are listed in Table 2. For bylyny the average
path length is $l=2.9$. Again this is most similar to the Irish Táin Bó
Cuailnge, for which $l=2.8$. The same can be said about the diameter of the
network; for bylyny the maximum path length between characters is 6 (for all
and friendly networks) while for the Táin Bó Cuailnge it is 7. The value of
the diameter $l_{\rm max}=8$ for the hostile network of bylyny is higher,
which means that this network is ‘stretched’ relative to the friendly one. A
similar feature is observed for other epics in Table 2.

It is usual to compare the average geodesic length $l$ to the corresponding
value $l_{\rm rand}$ calculated for an Erdős-Rényi random graph [16] of the
same size. An Erdős-Rényi graph is an example of the small world network for
which average path length grows logarithmically with the number of nodes [8].
Average values of $l_{\rm rand}$ are given in Table 2 for random networks of
appropriate sizes. As one can see from the table, the average shortest
distance for bylyny networks are lower than for random graphs with relevant
number of edges and nodes. This is similar to the Irish Táin Bó Cuailnge and
the Angle Saxon Beowulf Interestingly, however, the Icelandic sagas and Greek
classics, do not share this quality.

###  4.3 Closeness centrality

We are also interested in the concept of distance between characters. One
relevant measure is the closeness centrality [39, 9]. For each node, this is
the inverse of the sum of the distances to all the other nodes within the
connected component. Therefore, the higher the closeness centrality $C_{C}$
is, the closer the given node is to all other nodes. See Appendix B for a
visual depiction of the giant component weighted according to this measure.
The top five characters ranked according to closeness centrality are Prince
Volodymyr (#52); Illya Muromets’ (#46); Dobrynya (#28); Oleksiy Popovich (#1)
and Princess Opraksiya (#104).

Immediately after these are Duke (#33) and Mykhailo Potyk (#87). ‘‘Duke’’ here
is a name and not a title. The famous Ukrainian historian Mykhailo Hrushevsky,
who specialised in the history of literature, identified them as part of the
Halicia–Volhynia character group [25]. According to bylyny, Duke is a Halician
prince and Mykhailo Potyk is considered to be borrowed from Western Ukraine,
where he, in turn, came from Bulgaria, with a history of St. Michael from
Potuka [25]. In the texts, he is a hero fighting on the side of Prince
Volodymyr and against King Lyahetskiy (#60). We find it interesting that
closeness centrality has identified the importance of characters of the
Halych-and-Volhynian region, which once was a successor of the Kyivan Rus’.
These characters have relatively low degrees. It is also interesting that,
without Volodymyr and Opraksiya, the highest ranked character by closeness
centrality is Dobrynya who outranks Illya Muromets’. This may be a reflection
of the fact that in several texts Illya opposes Prince Volodymyr, while
Dobrynya is always on the side of the ruler, and, therefore, closer to him.

Thus, besides a simple ranking of network nodes, individual metrics may
inspire us to look deeper into individual characters, questioning the roles
they play in the story and how they are represented. We continue in this vein
with other measures of centrality.

###  4.4 Betweenness centrality

Another local characteristic that can give an insight onto the importance of
individual nodes is the betweenness centrality $C_{B}$. This measures how
important the node is in maintaining communications between other nodes.
Betweenness centrality is the fraction of geodesics passing through a given
node. Like the closeness centrality, betweenness makes sense only within
connected components. Accordingly, a value $C_{B}=1$ corresponds to the case
when all the geodesics of the network pass through the given node. The lead
characters according to in betweenness terms are again Prince Volodymyr (#52),
Illya Muromets’ (#46) and Dobrynya (#28). Oleksiy Popovych (#1) is ranked
significantly lower according to this measure. Interestingly, Ivan Hostynyi
Syn (#43) is ranked fourth although he appears just once, in a story which
only has five unique characters. However, because Ivan has a direct connection
to Prince Volodymyr (Figure 1 ) these five unique characters are connected to
the rest of the network.

In ways like this, nodes with high betweenness centrality are important for
maintaining the integrity of the network. For example, if one removes the
three characters of bylyny social network with the highest values of $C_{B}$,
the network splits into 24 pieces, the largest of which contains only 72
nodes.

###  4.5  Clustering coefficient

The clustering coefficient measures the probability that neighbours of a
particular node in a network are themselves connected [64]. In a fully
connected graph, the clustering coefficient of a node is equal to 1. In a tree
graph (one without loops) it is 0. For bylyny, and in complex networks in
general [52], nodes with high degree tend to have small clustering
coefficients; the larger the degree of the node is, the less likely that its
neighbours are connected to each other. This is due to the fact that heroes
[Illya (#46), Dobrynya (#28), Oleksiy Popovych (#1)] each have several
different enemies independent of each other.

While clustering coefficient is a local (nodal) characteristic, its average
value tells us something about the nature of the whole network. In contrast to
the manner in which complex networks tend to have similar average path lengths
to that of Erdős-Rényi graph, their average clustering coefficients tend to
not to be so aligned. We denote the clustering coefficient of random
counterparts as $C_{\rm rand}$. For epic narratives, clustering coefficient
for friendly and full networks can be an order of magnitude greater than those
of random graphs of the same size and this is not the case for hostile
network. Bylyny social networks are no different and values are given in Table
2. These observations may serve as an evidence of the structural balance
hypothesis for epics social networks: if two characters are connected through
friendly links with a third one, it is likely that the first two are
positively linked. Likewise, if two characters are connected through hostile
links with a third, it is unlikely that they are also hostile to each other.

###  4.6 Degree assortativity

In real social networks, individual nodes tend to be connected to vertices of
similar degree; (‘‘birds of a feather flock together’’) [44]. In fictional
social networks (such as the Marvel universe [19]), however, high-degree
vertices are mostly connected to low-degree ones (‘‘not everyone can be a
superhero’’). Social networks of epic narratives tend to occupy an
intermediate position. A measure for correlation between neighbouring nodes is
the degree assortativity $r_{k}$ [41, 44]. By definition, degree assortativity
is bounded so that $-1<r_{k}<1$. Positive values characterise assortative
networks whereby high-degree nodes connect to each other and nodes with low
degrees are interconnected as well. Negative values, on the other hand,
indicate that the network is disassortative, i.e. that high-degree nodes are
joined to nodes with a low degree and vice versa.

Assortativity values for bylyny social networks are listed in Table 1, along
with those of other epics. For the full network, a value $r_{k}=-0.15$
indicates that the network is disassortative. This result is consistent with
the fact that bylyny are epic tales about heroes: parts of networks are star-
shaped structures (Figure 1) where heroes associate with less significant
characters. A different behaviour is found for some Icelandic sagas; they are
stories about people and for them the assortativity is positive. In a previous
network study of the Icelandic sagas we concluded that network analysis allows
to quantitatively compare societies from epic narratives with a real-world
social networks [36].

In epic networks, the hero is sometimes brought into contact with lower-degree
characters through conflict. This results in a greater degree of negativity in
the degree assortativity of the hostile networks than the friendly one. This
tendency is evident in Beowulf and the Iliad. It does not occur in bylyny,
however – or in Ireland’s Táin Bó Cúailnge. In this sense, again, bylyny find
similarities with Ireland’s iconic tale. It should be noted, however, that the
negativity of assortativity can sometimes be caused by the structure of the
story itself. For example, events described in the epic Beowulf occur in two
different places and are also divided by time intervals. They are connected
only through a common protagonist. As shown in Refs.[35, 27], removal of the
protagonist changes the nature of network connections from disassortative to
(weakly) assortative. A similar effect is present in the bylyny social
network. Removal of the node corresponding to Prince Volodymyr increases the
degree assortativity to $r_{k}=0.01$, which is indeed a positive value, albeit
a very small one.

As discussed in Section 2, many researchers believe that Prince Volodymyr is a
collective character [56] — an amalgamation of historical figures Volodymyr
the Great, Yaroslav the Wise, and Volodymyr Monomakh [11]. We split Prince
Volodymyr’s node into three distinct vertices and randomly distributed his
edges amongst them. We did this multiple times and find that the bylyny
network assortativity increases assortativity to $r_{k}=0.004$. In this way,
the network becomes more similar to a real-world social networks. Division
into four makes the network even more assortative with $r_{k}=0.03$. Thus, we
see that dividing the superheroic main character into more ‘‘human’’ (less
connected) individuals makes the network more akin to a real social network.
Of course, disassortativity is necessarily driven by high-degree characters
interacting with low degree ones and reducing the degree of the most connected
characters necessarily increases the value of $r_{k}$. In a sense this
procedure ‘‘de-mythicises’’ the hero, so it is up to the reader to make what
they will of it. Certainly, and as always, we advise that any conclusion
cannot be drawn from a single metric and has to involve holistic input from
humanities.

###  4.7 Communities

Even from Figure 1 it is obvious that the bylyny network comprises distinct
communities. While this visualisation depicts interacting characters, it hides
a more subtle community structure — for, even in the giant component many
vertices are more heavily connected certain others than with the rest of the
network. The standard approach to detecting communities uses a specially
tailored algorithm created by Girvan and Newman [43]. Application to the
bylyny social network (taking into account both types of links) yields an
interesting result: the largest connected components is divided into 15
communities. We depict these in Figure 2. The largest such community has 36
nodes (coloured red in the center of the figure). These include Prince
Volodymyr (#52), his wife Opraksiya (#104), Oleksiy Popovych (#1) and Dobrynya
(#28). The second largest community has 22 characters. This is the large group
of yellow nodes concentrated around Illya Muromets’ (#46) to the right side of
the figure. This demonstrates that Illya Muromets’ (#46) and Dobrynya (#28)
with Oleksiy Popovych (#1) represent a different generations of heroes [50,
4]. Illya is from the older heroes, whereas Oleksiy and Dobrynya are from the
younger ones.

Figure 2: Community structure of the bylyny social network (with both hostile
and friendly links). The largest of 15 communities is centered around Prince
Volodymyr (#52 in the center of the picture), while that around Illya
Muromets’ is second biggest (#46 on the right side of the figure). The next
two communities by size are concentrated around Churylo (#153) and Mykhailo
Potyk (#87).

The analysis also identifies a community concentrated around Churylo (#153)
and another around Mykhailo Potyk (#87). Both of these characters, along with
Duke (#33) are associated with Halicia–Volhynia [25]. This Principality or
Kingdom was a medieval state and vassal of the Golden Horde that existed from
1199 to 1349. The appearance of these characters in the epic describing the
Kyivan Rus’, can be explained by the fact that after the destruction of Kyiv
by the Mongols, cultural heritage passed to Western land in the
Halicia–Volhynia kingdom and it has absorbed part of the local heritage. As
one can see, the quantitative analysis of bylyny social network also provides
separate communities centred around these characters, as shown in Figure 2.

##  5 Conclusions and Outlook for the Future

To what extent do epic narratives belonging to different cultures share common
and differentiating characteristics, and to what extent can we quantify them?
This was the question asked 10 years ago in Ref.[35]. In the interim years,
the approach has been developed, extended, improved and applied to an
increasing corpus of (mostly medieval) literature [35, 36, 34, 27, 67]. This
paper brings the approach to bylyny – the heroic epics of Eastern Slavs.

Table 1 captures some network properties of the societies in this and other
epic and mythological narratives. All full and friendly networks are small
world in that average path lengths are similar to random average path length
and they have high clustering coefficient. Additionally, their maximum degrees
are much greater than the average, indicating the degree distributions all
have right skew. These are unifying characteristics - placing bylyny firmly in
the category of other European and world narratives.

It is the assortativity that shows the key differences between these networks
- but even these differences unite. As discussed in Ref. [34], the social
networks properties often reflect the type of story. For example, Iceland’s
Njáls saga and Laxdæla Saga are stories mostly of a people and set in a single
location. Beowulf and the Odyssey, for example, are focused on a protagonist
who travels between locations. Narratives like the Iliad and Egils saga lie
between these two in that they have protagonists with relatively large degrees
(decreasing the value of $r_{k}$) and their friendly networks are assortative.
Bylyny are mostly focused on a single node making it more similar to these
heroic epics than the other two types of story. It also shares many network
properties with Ireland’s Táin Bó Cúailnge and the Ulster cycle of Irish
mythology.

Vasyl Avenarius in the introduction to his book [4] notes that Prince
Volodymyr is called ‘‘the sun’’ because all the characters orbit around him
like the planets orbit around the sun. Our results support this opinion.
Prince Volodymyr is the most important node by degree, closeness and
betweenness centralities. Bylyny social networks are disassortative by nodes
degree, a property that is shared with most of the epics in Table 2. As with
the character Beowulf in the eponymous tale, by removing him we see the rest
of the social network is assortative [35], Prince Volodymyr therefore drives
the disassortativity and the previous suggestion that he is an amalgamation (a
suggestion similar to one made previously for the Irish Táin Bó Cuailnge
[35]), reduces his degree and therefore the assortativity, making the network
more like that of the Iliad and Egils saga. Indeed, the friendly network with
Prince Volodymyr node removed, becomes slightly assortative.

Thus the Kyiv bylyny cycle of east Slavic epic narratives falls nicely within
the European tradition in network terms — it is in many ways like Ireland’s
heroic tradition and Iceland’s social ones.

Author Contributions: Data were collected and translations from chronicles
were performed by Petro Sarkanych. Most of the humanities contextual
information was provided by Nazar Fedorak. The remaining authors contributed
to the technical side, interpretation and writing of the paper. Although a
number of years in germination, this paper was completed in haste as half its
authors were in a warzone. Thus we were limited in the extent to which we
could discuss the final version. The last author takes full responsibility for
any errors and omissions. All suggestions for improvements and corrections
should be addressed to him.

Acknowledgements: We would like to thank Bertrand Berche, Reinhard Folk,
Julian Honchar, Maddy Janickyj, Taras Yavorskyi for academic discussions. The
project is part supported by Coventry University’s allocation of UKRI
Participatory Research funding. Yu.H. acknowledges support of the JESH
mobility program of the Austrian Academy of Sciences and hospitality of the
Complexity Science Hub Vienna when finalizing this paper. We thank people of
Ukraine for inspirational bylyny and for inspirational heroism and defence of
freedom, including academic freedom. We thank many academics from other
countries — including some Slavic ones — who have sent public and private
messages of support, despite some being neither free nor academically free to
speak out. We look forward to collaborating with them in future enlightening
all of our populations so that mistakes of the past are left there.

Special Note: National epics like the ones discussed in this paper are
important elements of national identity. Many countries use representations of
iconic characters from the mythological or historical past in identity
documents, iconography and coinage. In his recent essay, ‘‘On the Historical
Unity of Russians and Ukrainians’’, Vladimir Putin invoked the distant past
when he said [51] ‘‘The spiritual choice made by St. Vladimir, who was both
Prince of Novgorod and Grand Prince of Kiev, still largely determines our
affinity today.’’444The Kyivan Rus’ name “Volodymyr” transform to “Vladimir”
in the Russian language. Likewise “Kiev” is the Russian spelling for “Kyiv”.
This is a basis for his view that ‘‘the idea of Ukrainian people as a nation
separate from the Russians [has] no historical basis – and could not have been
any.’’ Putin’s erroneous view of culture and history has been roundly refuted
in multiple authoritative quarters. In his subsequent interview, author and
historian Timothy Snyder says of Putin [57]: ‘‘He considers himself the second
Volodymyr the Great, and sees his task as completing his work, which began
more than a thousand years ago.’’

However, as we see in this paper, Prince Volodymyr is a character strongly
connected with people of different opinions — people such as Illya, ‘‘who does
not always blindly perform the orders of prince Volodymyr and sometimes
transforms them or even resists them.’’ In the future, the narrative of the
current political situation will be written by historians and other academics,
and not by autocrats or sycophants. As for the heroic Kyiv cycle of Ukrainian
bylyny, we expect that that story will be of heroes again embracing freedom of
thought and dissenting opinions; and will centered on a free and peaceful
Kyiv.

## References

  * [1] Abello, J., Broadwell, P., and Tangherlini, T. R., Computational folkloristics, _Communications of the ACM_ 55 (2012) 60–70.
  * [2] Abramovych, D., _The Lives of SS. Borys and Hlib (in Russian)._ (Department of Russian Language and Literature of the Imperial Academy of Sciences Publishing House, Saint Petersburg, 1916).
  * [3] Amaral, L. A. N., Scala, A., Barthelemy, M., and Stanley, H. E., Classes of small-world networks, _Proceedings of the national academy of sciences_ 97 (2000) 11149–11152.
  * [4] Avenarius, V., _Book of bylyny. Collection of selected examples of Russian folk epic poems (in Russian)_ (Kushnerev and Co. printing house, Moscow, 1902).
  * [5] Barabási, A.-L. and Albert, R., Emergence of scaling in random networks, _Science_ 286 (1999) 509–512.
  * [6] Berezkin, Y. E., Peopling of the new world from data on distributions of folklore motifs, in _Maths meets myths: quantitative approaches to ancient narratives_ (Springer, 2017), pp. 71–89.
  * [7] Bod, R., _A new history of the humanities: The search for principles and patterns from antiquity to the present_ (Oxford University Press, Oxford, 2013).
  * [8] Bollobás, B., The diameter of random graphs, _Transactions of the American Mathematical Society_ 267 (1981) 41–52.
  * [9] Brandes, U., A faster algorithm for betweenness centrality, _Journal of mathematical sociology_ 25 (2001) 163–177.
  * [10] Aarne-Thompson-Uther classification of folk tales, http://www.mftd.org/index.php?action=atu, accessed: 14.03.2022.
  * [11] Čiževsky, D., Yaroslav the wise in east-slavic epic poetry, _The Journal of American Folklore_ 69 (1956) 201–215.
  * [12] Cross, S. H., Sherbowitz-Wetzor, O. P., Sherbowitz-Wetzor, O. P., _et al._ , _The Russian Primary Chronicle: Laurentian Text_ , Vol. 60 (Mediaeval academy of America, 1953).
  * [13] Danilov, K., _Old Russian poems collected by Kirsha Danilov (in Russian)_ (Ripol Classic, Moscow, 1977).
  * [14] D’Huy, J., Polyphemus: a palaeolithic tale?, _The Retrospective Methods Network Newsletter_ 9 (2015) 43–64.
  * [15] Elson, D., Dames, N., and McKeown, K., Extracting social networks from literary fiction, in _Proceedings of the 48th Annual Meeting of the Association for Computational Linguistics_ (Association for Computational Linguistics, Uppsala, Sweden, 2010), pp. 138–147, https://aclanthology.org/P10-1015.
  * [16] Erdös, P. and Rényi, A., On the evolution of random graphs, _Publ. Math. Inst. Hung. Acad. Sci_ 5 (1960) 17–60.
  * [17] Foley, J., _Traditional Oral Epic The Odyssey, Beowulf, and the Serbo-Croation Return Song_ (University of California Press, 1993).
  * [18] Gessey-Jones, T., Connaughton, C., Dunbar, R., Kenna, R., MacCarron, P., O’Conchobhaire, C., and Yose, J., Narrative structure of A Song of Ice and Fire creates a fictional world with realistic measures of social complexity, _PNAS_ 117 (2020) 28582–28588.
  * [19] Gleiser, P. M., How to become a superhero, _Journal of Statistical Mechanics: Theory and Experiment_ 2007 (2007) P09020.
  * [20] Gurevitch, M., _The social structure of acquaintanceship networks_ , Ph.D. thesis, Massachusetts Institute of Technology (1961).
  * [21] Harary, F. _et al._ , On the notion of balance of a signed graph., _The Michigan Mathematical Journal_ 2 (1953) 143–146.
  * [22] Heider, F., Attitudes and cognitive organization, _The Journal of psychology_ 21 (1946) 107–112.
  * [23] Heinrich, L. L., _The Kievan chronicle: a translation and commentary._ (Vanderbilt University, 1977).
  * [24] Holovatch, Y., Kenna, R., MacCarron, P., Sarkanych, P., Fedorak, N., and Yose, J., Universality and network analysis of bylyny. (in ukrainian), _Ukraina Moderna_ 27 (2019) 108–138.
  * [25] Hrushevsky, M., _The history of Ukrainian literature. Volume 4. Book 1. (in Ukrainian)_ (Lybid’, Kyiv, 1994).
  * [26] Karsdorp, F., Kranenburg, P. v., Meder, T., and van den Bosch, A., Casting a spell: Identification and ranking of actors in folktales, _n: Proceedings of the Second Workshop on Annotation of Corpora for Research in the Humanities (ACRH-2). Edicoes Cilibri, 2012_ (2012) 39–50.
  * [27] Kenna, R. and Mac Carron, P., Maths meets myths: network investigations of ancient narratives, in _Journal of Physics: Conference Series_ , Vol. 681 (IOP Publishing, 2016), p. 012002.
  * [28] Kenna, R. and MacCarron, P., A networks approach to mythological epics, in _Maths Meets Myths: Quantitative Approaches to Ancient Narratives_ (Springer, 2017), pp. 21–43.
  * [29] Kotliarevsky, A., Were the Little Russians the original inhabitants of the Polyana land or came from the Carpathians in the XIV century? (in Russian), _Osnova_ 10 (1862) 14.
  * [30] Krohn, K., _Die folkloristische arbeitsmethode_ , Vol. 5 (H. Aschehoug & Company, 1926).
  * [31] Labatut, V. and Bost, X., Extraction and analysis of fictional character networks: A survey., _ACM Comput. Surv._ 52 (2019) 89.
  * [32] Labatut, V. and Bost, X., Extraction and analysis of fictional character networks: A survey, _ACM Computing Surveys (CSUR)_ 52 (2019) 1–40.
  * [33] Larin, B., _Russian-English dictionary-diary of Richard James (1618-1619) (in Russian)_ (Leningrad University Press, Leningrad, 1959).
  * [34] Mac Carron, P., _A network theoretic approach to comparative mythology_ , Ph.D. thesis, Coventry University, UK (2014).
  * [35] Mac Carron, P. and Kenna, R., Universal properties of mythological networks, _EPL (Europhysics Letters)_ 99 (2012) 28002.
  * [36] Mac Carron, P. and Kenna, R., Network analysis of the Íslendinga sögur–the Sagas of Icelanders, _The European Physical Journal B_ 86 (2013) 407.
  * [37] Makhnovets, L., _Rus’ chronicles (in Ukrainian)._ (Dnipro, Kyiv, 1989).
  * [38] Milgram, S., The small world problem, _Psychology today_ 2 (1967) 60–67.
  * [39] Newman, M., _Networks: an introduction_ (Oxford University Press, Oxford, 2010).
  * [40] Newman, M. E., The structure of scientific collaboration networks, _Proceedings of the national academy of sciences_ 98 (2001) 404–409.
  * [41] Newman, M. E., Assortative mixing in networks, _Physical Review Letters_ 89 (2002) 208701.
  * [42] Newman, M. E., The structure and function of complex networks, _SIAM review_ 45 (2003) 167–256.
  * [43] Newman, M. E. and Girvan, M., Finding and evaluating community structure in networks, _Physical review E_ 69 (2004) 026113.
  * [44] Newman, M. E. and Park, J., Why social networks are different from other types of networks, _Physical review E_ 68 (2003) 036122.
  * [45] Newman, M. E. _et al._ , Random graphs as models of networks, _Handbook of graphs and networks_ 1 (2003) 35–68.
  * [46] Oinas, F., _Studies in Finnic Folklore_ (Routledge, 1997).
  * [47] Oinas, F. J., Folklore activities in russia, _The Journal of American Folklore_ 74 (1961) 362–370.
  * [48] Oinas, F. J., The political uses and themes of folklore in the soviet union, _Journal of the Folklore Institute_ 12 (1975) 157–175.
  * [49] Potebnia, A., _Explanations of Little Russian and related folk songs (in Russian)._ (M. Zemkeevich and V. Noakovsky Printing House, Warsaw, 1883).
  * [50] Putilov, B., Byliny: Collection (in Russian), _Soviet writer, Leningrad_ (1986).
  * [51] Putin, V., On the Historical Unity of Russians and Ukrainians, http://en.kremlin.ru/events/president/news/66181 (2021), accessed: 17.03.2022.
  * [52] Ravasz, E. and Barabási, A.-L., Hierarchical organization in complex networks, _Physical review E_ 67 (2003) 026112.
  * [53] Rybnikov, P., _Songs collected by PN Rybnikov_ (Typography A. Semena, Moscow, 1861-1867).
  * [54] Sarkanych, P., _Universality of complex systems: partition function zeros analysis and complex networks_ , Ph.D. thesis, Coventry University, UK and Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine (2020).
  * [55] Sarkanych, P., Holovatch, Y., Kenna, R., and MacCarron, P., Mathematics and Myths: quantitative approach to comparative mythology. (in Ukrainian), _J. Phys. Stud._ 20 (2016) 4801.
  * [56] Shevchuk, V., _Ukrainian bylyny: Historical and literary edition of east Slavic epic (in Ukrainian)._ (Veselka, Kyiv, 2003).
  * [57] Sierakowski, S., The Empire is attacking again. What is Putin’s ultimate goal? (Interview with prof. Timothy Snyder,in Polish), https://www.polityka.pl/tygodnikpolityka/swiat/2157397,1,imperium-znow-atakuje-co-jest-ostatecznym-celem-putina.read (2022), Polityka 11.03.2022. (accessed 17.03.2022.).
  * [58] Szell, M. and Thurner, S., Measuring social dynamics in a massive multiplayer online game, _Social networks_ 32 (2010) 313–329.
  * [59] Tangherlini, T. R., _Facebook for Vikings: Social Network Analysis and Egil’s Saga_ (University of Toronto Press, 2015), pp. 149–172.
  * [60] Tehrani, J. J., The phylogeny of little red riding hood, _PloS one_ 8 (2013) e78871.
  * [61] Tuptalo, D., _Lives of the Saints (in Ukrainian)_ , Vol. 11 (Svichado, Lviv, 2013).
  * [62] Veselovsky, A., Bylyny of South Russia (in Russian)., _Collection of the Department of Russian Language and Literature of the Academy of Sciences_ 22 (1881).
  * [63] Vlasto, A., "The Hypatian Codex", II:" The Galician-Volynian Chronicle"(Book Review), _Slavonic and East European Review_ 53 (1975) 106.
  * [64] Watts, D. J. and Strogatz, S. H., Collective dynamics of ’small-world’ networks, _Nature_ 393 (1998) 440.
  * [65] Weingart, S. B. and Jorgensen, J., Computational analysis of gender and the body in european fairy tales., Vol. 28 (Oxford University Press, 2013), pp. 404–416.
  * [66] Yose, J., _A Network Scientific Approach To The Quantitative Analysis of Epic Texts_ , Ph.D. thesis, Coventry University, UK (2017).
  * [67] Yose, J., Kenna, R., MacCarron, P., Platini, T., and Tonra, J., A networks-science investigation into the epic poems of Ossian, _Advances in Complex Systems_ 19 (2016) 1650008.

## Appendix A: Dobrynya in epics and in chronicles

In humanities literature, the correspondence between the epic Dobrynya and the
chronicle Dobrynya (from the Tale of Bygone Years) is frequently studied, in
attempts to determine the extent to which the former is drawn from the latter.
In the chronicles, Dobrynya is a brother of Malusha (the wife of Prince
Svyatoslav, who himself is the father of Volodymyr the Great). He was a member
of the old aristocracy (a “boyar”), a warlord (“vojevoda”) of Kyiv and a
representative (“posadnyk”) of Volodymyr the Great in Novgorod. ‘‘In the year
6478 [970] Svyatoslav sent Yaropolk to Kyiv, and Oleh to Derevlyans as his
princes. At the same time, people of Novgorod came, asking the prince for
themselves: ‘If you do not go to us, then we will find the prince by
ourselves.’ Svyatoslav replied that he will find them a prince. Yaropolk and
Oleh refused, so Dobrynya suggested: ‘You should ask Volodymyr’ - because
Volodymyr was son of Malusha, sister of Dobrynya. Therefore Dobrynya was an
uncle of Volodymyr. The people of Novgorod were happy with Svyatoslav sending
Volodymyr to them. In the end, Volodymyr was sent to Novgorod together with
his uncle Dobrynya, and Svyatoslav was sent to Pereyaslavets’ ’’ [37].

Ten years later, in the year 980 according to the chronicles, Volodymyr
started a campaign in Novgorod, where, at that time, Prince Yaropolk already
was ruling. Here is the beginning of this story [the translation is ours]:

> ‘‘Volodymyr came with the Varangians [Vikings] to Novgorod and said to
> Yaropolk’s prince: ‘Go and tell my brother: ‘‘Volodymyr is going against
> you, prepare to fight.’’’ He then sat in Novgorod, and sent a [young]
> messenger to Rogvolod the prince of Polotsk, saying: ‘I want to take your
> daughter Rognida as a wife.’ Rogvolod then asked his daughter: ‘Do you want
> to merry Volodymyr?’ She replied: ‘I do not want to take off Volodymyrs
> shoes, but Yaropolk’s.’ Rogvold came from across the sea and had his volost’
> in Polotsk.555A Volost’ was a traditional administrative subdivision in the
> Kyivan Rus’, usually ruled by a local prince. …
>
> The messenger came back to Volodymyr, and told him the full answer of
> Rognida, the daughter of Rogvolod the Prince of Polotsk. Volodymyr gathered
> a huge army including Varangians, Slavs, Chood’ and Kryvychi - and went
> agains Rogvolod. At the same time Rognida was preparing to be sent to meet
> Yaropolk. But Volodymyr came to Polotsk, and killed Rogvolod and his two
> sons. He also took Rognida for the wife and continued his campaign against
> Yaropolk’’.[37]

In the same year, according to the Tale of Bygone Years, Volodymyr, having
defeated Yaropolk and finally becoming established in Novgorod, sat on the
princely throne in Kyiv.

> ‘‘Volodymyr began to reign in Kyiv alone. He set his idols on a hill outside
> the palace courtyard: the Perun666Here and below follow names of principal
> pagan deities of the Slavs: Perun, Khors, Dazhboh, Striboh, Simargal, and
> Mokosh. of the wood, and the head was silver, and the moustache of gold;
> Hors, and Dazhbog, and Strybog, and Simargal, and Mokosh. People were
> bringing human sacrifices to these idols, calling them gods, but sacrificing
> to demons. The land of the Rus’ and the hill were defiled by their
> sacrifices. But the precious god does not want death of sinners; on this
> hill there is now the Church of St. Vasyl the Great777Named after Prince
> Volodymyr second name Vasyl he got after baptisation. … ’’ [37].

Meanwhile,

> ‘‘Volodymyr has sent Dobrynya, his uncle, to Novgorod. Dobrynya, having come
> to Novgorod, placed the idol of Perun on the Volkhov River, and brought
> sacrifices of the Novgorod people as to this idol as God ’’ [37].

Here we see ‘‘uncle Dobrynya’’ as the most trusted person of Grand Prince
Volodymyr; he is trusted both politically and religiously - even in a pagan
sphere.

The next mention of Dobrynya comes five years later:

> "In the year 6493 [985] Volodymyr started a campaign to Bulgaria with
> Dobrynya, his uncle, in boats, while Torks travelled by horses. After
> defeating the Bulgarians, Dobrynya said to Volodymyr: ‘I looked at the
> prisoners, and they all were in boots. We will not take these as a tribute,
> we both go to look for those in the carbatinas.’ ’’[37]

This mentioning is interesting to us because Dobrynya is not only a close
proxy, but also Volodymyr’s counsellor, endowed with observation and ability
to make non-obvious conclusions.

The chronicle does not cover the death of Dobrynya. Together with the death of
Grand Prince Volodymyr-Vasyl the Great in the year 1015, his uncle also
disappears from the pages of the Tale of Bygone Years. But already in 1018 we
read about Dobrynya’s son named Constantin. Here is this episode where the
sons of Prince Volodymyr (Yaroslav, later named ‘‘the Wise’’) and Dobrynya met
each other:

> ‘‘When Yaroslav came to Novgorod, he wanted to flee the sea. Local prince
> Constantin, son of Dobrynya, with the Novgorodians destroyed the boats and
> said to Yaroslav: ‘We can still fight for you with Boleslav and Svyatopolk.’
> Novgorodians began to collect money: from a man - four coins; from an elder
> - ten hryvnias; and from a boyar - eighty hryvnias. This allowed Yaroslav to
> hire Varganians and to gather big army."[37]

Dobrynya son’s Christian name draws attention here — it indicates that
Dobrynya himself was baptized with Volodymyr in 988. Afterwards he gave his
son not a pagan Slavic name but a Christian one.

For completeness of the picture, we should mention another character with the
name Dobrynya from the ‘‘Tale of Bygone Years’’. This is Dobrynya Raguilovych
another prince of Novgorod, but in the year of 1096.

> ‘‘Oleh sent his brother Yaroslav [Svyatoslavych] to the vanguard. He stood
> on the field near Rostov. Mstyslav in the meantime consulted with
> Novgorodians. They sent in front of him Dobrynya Raguilovych, and Dobrynya
> first of all captured the collectors of the tribute. When Yaroslav heard
> that collectors were captured, because Yaroslav stood at the guard on the
> river, he ran away that night and ran to Oleh and told him that Mstyslav was
> coming, There was also a message to Oleh that his watchmen were captured, so
> he moved to Rostov.’’ [37].

Not going deep into the historical details of this message, it is worth noting
that Dobrynya Raguilovych mentioned here is also obviously a brave and smart
man (judging by the description of his deeds) and that he was a contemporary
of another well-known Prince Volodymyr – Volodymyr Monomakh. So different
Dobrynyas might have followed the same path as different Volodymyrs and became
a single character. We will endeavour to investigate these possibilities in a
further study.

## Appendix B: Bylyny giant component

In Figure 3 we present the largest connected component of the bylyny network
(including both friendly and hostile links) with vertices sized proportionate
to node degree $k$. Prince Volodymyr (#52) and Illya Muromets’ (#46) have the
highest degrees and corresponding nodes are largest. They also have highest
closeness and betweenness centralities ($C_{C}$ and $C_{B}$, respectively) and
similar plots for these measures can be constructed. Their clustering
coefficients are small, however and ac ounterpart plot for this measure is
given in Figure 4. Likewise Ivan Hostynyj Syn (#43) has a relatively high
centrality values but low node degree and clustering coefficient.

Figure 3: The largest connected component of the bylyny network with vertices
sized proportionate to node degree $k$.

Figure 4: The giant component with nodes weighted by clustering coefficient
$C$.

Finally, in Figure 5, we give a plot of the cumulative degree distribution
plotted against node degree. The fit is a power-law, suggestive of a scale-
free properties of the bylyny character network. We refer the reader to the
literature for similar plots for other epic tales [28].

Figure 5: Cumulative degree distribution $P(k)$ as a function of a node degree
in a double logarithmic scale. Straight black line shows a fit to a power-law
suggesting a scale-free property of the network.