# Knowledge Dispersion Index for Measuring Intellectual Capital

Vikram Dhillon Electronic address<EMAIL_ADDRESS>
###### Abstract

In this paper we propose a novel index to quantify and measure the flow of
information on macro and micro scales. We discuss the implications of this
index for knowledge management fields and also as intellectual capital that
can thus be utilized by entrepreneurs. We explore different function and human
oriented metrics that can be used at micro-scales to process the flow of
information. We present a table of about 23 metrics, such as change in IT
inventory and percentage of employees with advanced degrees, that can be used
at micro scales to wholly quantify knowledge dispersion as intellectual
capital. At macro scales we split the economy in an industrial and consumer
sector where the flow of information in each determines how fast an economy is
going to grow and how overall an economy will perform given the aggregate
demand. Lastly, we propose a model for knowledge dispersion based on graph
theory and show how corrections in the flow become self-evident. Through the
principals of flow conservation and capacity constrains we also speculate how
this flow might seeks some equilibrium and exhibit self-correction codes. This
proposed model allows us to account for perturbations in form of local noise,
evolution of networks, provide robustness against local damage from lower
nodes, and help determine the underlying classification into network super-
families.

###### Index Terms:

network flow, perturbations, intellectual capital, metrics.

##  I Introduction

Lord Kelvin is often quoted for saying that if one can’t measure something
they can’t improve it. This is critical in the field of knowledge management
as metric provide convincing data for entrepreneurs to make decisions and help
capitalize it for economic and social progress. The aspiration behind
developing this index arose in response to lack of a quantifying measure for
the following:

  * •

The exchange of tactical knowledge concerning one particular field between
employees.

  * •

Capture of that information in a knowledge-base for use by other employees.

  * •

The reuse rate of frequently accessed knowledge.

This index will be divided into two levels, each further consisting of its own
metrics, the outputs from each level can be used as independent indicators and
the gross measure will complete the Knowledge Dispersion Index (KDI) for a
given location. It must be noted that this analysis involves human input
therefore some aspects can not be captured effectively, although we do include
an assumption called the Theory Y of management which asserts that management
assumes employees may be ambitious, self-motivated, exercise self-control and
if allocated adequate resources, they will perform at their very best. Given
that assumption, we establish the two levels of our index:

  * •

Organizational knowledge metric: This metric will account for aggregate
dispersion at micro scales and indicate the growth of the industrial sector.

  * •

General dispersion metric: This metric will account for dispersion at macro
scales and indicate how the consumer side is performing.

##  II Micro Scale (Organizational Knowledge Metric)

At the micro scale industries play a prominent role, the reason for including
industries at the micro scale pertains to their role in the economy. The
distributer’s side is generally smaller in comparison to the consumer side. In
addition to that, there are some particular mechanisms that each of the firms
employ to enhance their success and if they are not fine-tuned, the results
can be disastrous. For that very reason we present a comprehensible list (see
Appendix A for the list) to account for the flow of information, the gross
result obtained from the table in the Appendix will present a reliable measure
of the information infrastructure of a company111In this paper we don’t
provide definite benchmarks which can then be used to compare, a case study
however, regarding those benchmarks is underway. . There is however another
very important role that the organizational knowledge metric plays, that of
identifying the most efficient method of dispersion and the faults that may
occur in the dispersion through the use of a theoricial construction called a
flow networks.

###  II-A Flow Networks

Flow networks are the key structure in network analysis and here we show how
the traditional flow network model can be employed by a company to analyze the
flow of information in their infrastructure. First we review the traditional
flow network model [2], a flow network is a directed graph where each edge has
a capacity and each edge receives a flow. The amount of flow on an edge cannot
exceed the capacity of the edge. A flow must satisfy the restriction that the
amount of flow into a node equals the amount of flow out of it, except when it
is a source, which has more outgoing flow, or sink, which has more incoming
flow.

Formally, $G(V,\,E)$ is a directed graph where each edge
$(u$$\,v)\>\epsilon\,E$ has a non-negative, real valued capacity given by a
function $c(u\,v)$. There are however two special vertices where the capacity
constrains don’t hold: a source $s$ and a sink $t$. The rest of the nodes
$u,\,v$ follow the following rules:

  * •

Capacity Limit: $f\,(u,\,v)\>\leq c\,(u,\,v).$ This relation implies that the
flow to one node can not exceed the capacity limit given to that node.

  * •

Skew Symmetry: $f\,(u,\,v)\;=-f\,(u,\,v).$ This relation implies that the net
flow from one node to another or from $u$$\rightarrow v$ must be the same from
$v\rightarrow u$.

  * •

Flow conservation: $\sum\,f\,(u,\,w)=k.$ This relation can be seen from the
two above, the net flow to a node is some constant $k$ which holds the same
value for each node at the same hierarchy but changes value at different
levels of management, except for the two cases of source and sink.

Now we will explore how a model following these rules can help us explore the
efficiency of the information infrastructure. First we see that the capacity
limit holds to how much information should be made avialable to employees at
each stage, this limit helps us understand better where in the graph is too
much information is present as that in itself is a loss or waste since one
employee can only utilize so much of what is given to them. Knowing the
capacity limit for the nodes can also help us by reducing the flow to one
stressed node by spreading it amongst other available nodes at the same level
of hierarchy. The skew symmetry serves as a test that can be employeed by the
management to asses whether each employee at their current level is utilizing
their resources to their maximum or not, the full employement of the resources
at each level would result in for instance completion of more patents being
filed or more solutions being completed by a company as the demand for that
particular solution increases. It must be noted here that this relation holds
dual values, the flow of information decreases as it reaches the top as can be
seen in the case of a software development company, the CEO of the company is
generally well-versed in business techniques and not in lower-level coding
therefore the higher-level overview being presented to them in the form of a
flowchart would be represented by a decrease in the flow of information
reaching them. This should not be considered a short-coming of the model
because each level of hierarchy will have a constant flow, so as information
moves up that hierarchy and reached the management positions of a company, the
flow will decrease and stabalize. The third rule indicates the communication
infrastructure present in a company occuring among various nodes (employees)
at each level. A company generally has several different departments or
smaller level committes to perform various tasks, this rule applies to how
well each of those departments interact with the other ones to finish a given
task. The other two rules provided before can also be applied here to each of
the departments to obtain more specifics. We argue that modelling a company as
a flow model and following a combination of these three rules will provide a
very good estimate of the information flow in a company. The data requried to
asses these rules will be provided by the gross result from the list in
Appendix A.

####  II-A1 Self Correction Codes

Using the flow model for information dispersion also gives us the ability to
use the inherent correction features present in the flow model. We assert that
a company modeled as a traditional flow model will have the tendency to
correct itself as needed, this is also a basic assumption in game theory, that
if each employee is seen a player in a game, each player will make the best
possible move. We generalize that assertion in the following:

###### Conjecture 1

If leadership is emplyoed in a multi-player show definitegame, the leader will
make the best possible choice for the players.

This will help in the evolution of the network, as the company prospers the
network will expand and stabalize for definite capacity limits at every level,
this is true of a successful company. For a newly developing company, the
governing dynamics will be different, each new employee is in a learning stage
but are required to follow skew symmetry and flow conservation. As a result of
that, there will be a discrepancy in the rules as the new employee will be a
pseudo-node and this discrepancy can be analyzed in terms of a pertubation to
the model. The flow model approach provides a solution for the model to be
robust against such changes, to address local pertubations, we propose the
following:

###### Conjecture 2

Given a recently established company, and a measure of reliability determined
from our Appendix, some nodes with a high measure of reliability should be
overloaded.

It should be noted here that overloading those nodes doesn’t necessarily imply
a decrease in efficiency of those employees, the idea is to vary the flow
amongst those reliable nodes and split flow conservation into two levels, one
for the newer employees and the other for the reliable ones. This allows the
learning stage of the new employees which acts as a pertubation to be absorbed
in by the overloading of those nodes. The output provided by the newer pseudo-
nodes 222The new employees only act as pseudo-nodes while they are under some
initial training, as soon as they are ready, we decrease the flow to the nodes
at which the new employees are to work, that allows a smooth introduction of
new nodes in the flow. will also go through a similar process but the
difference is that the output gets absorbed by the these overloaded nodes.

Now we will address how network super-families arise in this evolved flow,
from Conjecture 2.2 we determined a reliability measure that can help use
overload some nodes, those nodes at each hierarchical level will constitute
our network super-family. Formally, the members of the yet to be formed
superfamiliy will appear as outliers if a statistical analysis such as ANOVA
is performed because of their reliability profile established from the
Appendix metrics. Once super-families are identified in a flow, our network
becomes very strong and is robust to local and internal damage.

###### Conjecture 3

Given a flow network with identified network super-families, local damage can
be diverted to specified nodes, decreasing its impact.

Local or internal damage lacks a formal operational definition so we have to
rely on a situational definition. Any intentional efforts to disrupt a well
established flow of information constitutes local damage, if the causes of
which are identified, for instance an attack targeting some confidential
information can be diverted to the pseudo-nodes, rendering it useless since
the pseudo-nodes have lower level clearance.

##  III Macro Scale (General Dispersion Metric)

We now analyze how information disperses amongst the general public or the
consumer side. It must be noted here that KDI would only be compelte as an
index once we can get results from both the metrics, implying that we need to
quantify how information flows amongst industries which form the micro scale
and the consumer side or the general public which form the macro scale. The
methods of analysis being employed before simply become inefficient here
because of the graphes modelling a large amount people would easily break down
and is quite inefficient computationally. There are however some metrics that
can help us here such as:

  * •

Transport infrastructure

  * •

Availability of communications facilities such as television and internet

  * •

Public spending on broadcasting

  * •

Access to internet

  * •

Frequency of local awareness campaigns such as seminars and so on.

We will here employ another theoretical construction to analyze how
information is spread to the general population or the consumers sector. Some
charateristics of this study are that it must be general enough to account for
a vast variety of sources and at the same time be able to provide a definite
analysis for the comparison of the output from each source.

###### Definition 1

There are several sources that aid the process, such as television, newspaper,
etc. however, for simplicity of analysis, we will collectively refer to these
different sources as media.

###  III-A Deep Current Sets

The most common source for information available to the public333We simply
refer it to as a source, its arguable which source constitues as the most
widely available for different regions. outputs vast amounts of interpreted
information, this output can be viewed as a surface wave or a current in an
ocean. This analogy of ocean currents is being used because the currents
themselves are very dynamic and based on very delicate balance, we imply that
in the same degree as ocean currents on the surface can influence the weather
pattern of the atmosphere above, the general croud is influenced by the larger
waves or the media source that is most influencial, imposing similar constant
weather conditions over a large portion of the atmosphere. This construction
helps analyze the behaviour and choices of the people in the given region in
the past to make deductions about the future, from that we determine how the
information flow that once only occured amongst a small group of people has
evolved now to spread to much larger networks. We present a worked example of
deep current sets in the light of a hypothetical developing situation.

###### Conjecture 4

Given an area and a developing situation, the flow of information is given as
follows:

Before the development: Those involved with an event may share or record their
ideas, theories, or plans alone in a lab or personal journal, with friends or
colleagues. The sharing of this information forms the "invisible college."
Usually, the ideas generated by the "invisible college" are simply not
available to the public and is nonexistent as a form of information today,
especially for things in the distant past. This sets the stage for the
currents to arise in the ocean.

As the development occurs: Early news releases may appear on TV or radio, in
newspapers, over newswires, and on the Web. The initial information about
these events generally accompnies the "who", "what", "where" and "when" and
most often exclude the "why"

The next day or the days after: Articles appear in newspapers/newswires;
information is disseminated on TV, radio, and the Web. Depending on the event,
the information may be prolific or sparse.

In a week or the weeks after: Articles may appear in general or subject-
focused popular magazines.

In a month or time that follows: Articles appear in scholarly journals. This
is also when scholars and researchers may start holding conferences on the
topic and eventually, conference papers will be published.

We see how through the development of this situation the ocean currents are
forming, the before sets up the currents and the next phase is when the
currents are out in the ocean and their relative size determines how the
weather is changes. From the changes in weather which are easily observable,
we can reliably make deduction about the past history of the people. The
advantage of this analysis provides is that even though a given region may
have changed now, we can still see the effects of the currents in the
future444This in some sense is similar to a pebble skipping across water,
whereever it lands, even for a brief moment of time, it leaves behind ripples
that can be the analyzed to trace its path., this analysis of the past can
also assist in the development of better dynamics modelling the behaviour of
that region. In addition to that, we can also determine what forms of media
are most prevalent in that given region. This analysis can be conducted based
on a past event and hold its validity for a long time.

As we see, the quantization of information flow here can be further assisted
through the use of metrics such as % access to cable, people with advanced
degrees, average household income and so on. This can help determine the
interests of people and classify them into sets, however in our construction,
we can construct computer models based on using restricted boltzmann machines
through a technique called deep learning. If a technology firm sees an
opportunity to start developing in a given region, if they can identify the
type of issues being discussed amongst the community (where people can be
organized into different sets based on interests), they can identify the
region555Formally, where the largest set is interested in the same objective
as the company where it is best for them to work and since people in that
community are willing to work on those issues, establishing new businesses
there to give them an opportuinity is the best way to unleash intellectual
power.

##  IV Conclusion

In this paper, we presented how intellectual capital can be measured through
the use of a novel index, KDI. We also discussed how the metrics present in
the index can help increase the efficiency of an organization by modeling the
structure of a company using network flow models. The last section discussed
how the information flow among people in a given region can help organizations
unleash intellectual power and capitalize on it by providing the people the
necessary resources. We are currently unable to provide numerical analysis of
our index and therefore we are lacking milestones that can provide comparative
analysis however a case study to quantify those milestones is being
undertaken. Further research would include the aforementioned milestones and a
more sophisticated models of flow networks.

I would like to thank Christopher Norris for helpful discussions in the
writing of this paper.

##  Appendix A Appendix

Here is the list of metrics [1] that we will be using at micro scales (mostly
applicable to companies/firms), we do make two assumptions here:

  * •

These metrics can be easily obtained from available data and this will become
self-evident to some extent.

  * •

The use of IT and various related means yields to the best dispersion of
knowledge/information within an organization.

Patents pending
---
% Investment in IT
% R&D invested in basic research
Average years of service with the company
Number of employees
Number of managers
Average duration of employment
Number of new solutions/products suggested
New patents/software/etc. filed
IT development expense/IT expense
Average age of employees
IT literacy of a staff
Company managers with advanced degrees
Revenues resulting from new business operations
IT performance/employee
IT capacity (CPU and DASD)
Changes in IT inventory

## References

  * [1] Jay Liebowitz, Ching Y. Suen.  Developing knowledge management metrics for measuring intellectual capital.  _Journal of Intellectual Capital,_ Vol. 1 Iss: 1, pp.54 - 67, 2000.
  * [2] Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin.  Network Flows: Theory, Algorithms and Applications.  Prentice Hall, 1993.