# Graph Anomaly Detection with Graph Neural Networks: Current Status and
Challenges

Hwan Kim, Byung Suk Lee, Won-Yong Shin, , and Sungsu Lim H. Kim and S. Lim are
with the Department of Computer Science and Engineering, Chungnam National
University, Daejeon 34134, Republic of Korea (e-mail<EMAIL_ADDRESS>sungsu@cnu.ac.kr). B. S. Lee is with the Department of Computer Science,
University of Vermont, Burlington, Vermont 05405, USA (e-mail: bslee@uvm.edu).
W.-Y. Shin is with the School of Mathematics and Computing (Computational
Science and Engineering), Yonsei University, Seoul 03722, Republic of Korea,
and also with Pohang University of Science and Technology (POSTECH)
(Artificial Intelligence), Pohang 37673, Republic of Korea (e-mail:
wy.shin@yonsei.ac.kr).(Corresponding author: Sungsu Lim.)

###### Abstract

Graphs are used widely to model complex systems, and detecting anomalies in a
graph is an important task in the analysis of complex systems. Graph anomalies
are patterns in a graph that do not conform to normal patterns expected of the
attributes and/or structures of the graph. In recent years, graph neural
networks (GNNs) have been studied extensively and have successfully performed
difficult machine learning tasks in node classification, link prediction, and
graph classification thanks to the highly expressive capability via message
passing in effectively learning graph representations. To solve the graph
anomaly detection problem, GNN-based methods leverage information about the
graph attributes (or features) and/or structures to learn to score anomalies
appropriately. In this survey, we review the recent advances made in detecting
graph anomalies using GNN models. Specifically, we summarize GNN-based methods
according to the graph type (i.e., static and dynamic), the anomaly type
(i.e., node, edge, subgraph, and whole graph), and the network architecture
(e.g., graph autoencoder, graph convolutional network). To the best of our
knowledge, this survey is the first comprehensive review of graph anomaly
detection methods based on GNNs.

###### Index Terms:

Dynamic graph, graph anomaly detection, graph neural network, node anomaly,
static graph.

##  I Introduction

Graphs are an effective data structure for efficiently representing and
extracting complex patterns of data and are used widely in numerous areas like
social media, e-commerce, biology, academia, communication, and so forth. Data
objects represented in a graph are interrelated, and the objects are typically
represented as nodes and their relationships as edges between nodes. The
structure of a graph refers to how the nodes are related via individual edges,
and can effectively represent even far-reaching relationships between nodes.
Moreover, graphs can be enriched semantically by augmenting their structural
representations with attributes of nodes and/or edges.

Anomaly detection is the process to identify abnormal patterns that
significantly deviate from patterns that are typically observed. This is an
important task with increasing needs and applications in various domains.
There have been significant research efforts on anomaly detection since Grubbs
et al. [1] first introduced the notion of anomaly (or outlier). Since then,
with the advancement of graph mining over the past years, graph anomaly
detection has been drawing much attention [2, 3].

Early work on graph anomaly detection has been largely dependent on domain
knowledge and statistical methods, where features for detecting anomalies have
been mostly handcrafted. This handcrafted detection task is naturally very
time-consuming and labor-intensive. Furthermore, real-world graphs often
contain a very large number of nodes and edges labeled with a large number of
attributes, and are thus large-scale and high-dimensional. To overcome the
limitations of the early work, considerable attention has been paid to deep
learning approaches recently when detecting anomalies from graphs [4]. Deep
learning’s multi-layer structure with non-linearity can examine large-scale
high-dimensional data and extract patterns from the data, thereby achieving
satisfactory performance without the burden of handcrafting features [5, 6].

More recently, graph neural networks (GNNs) have been adopted to efficiently
and intuitively detect anomalies from graphs due to the highly expressive
capability via the message passing mechanism in learning graph representations
(e.g., [7, 8]). With GNNs, learning and extracting anomalous patterns from
graphs, even those with highly complex structures or attributes, are
relatively straightforward as GNN itself handles a graph with attributes as
the input data [9]. The state-of-the-art graph anomaly detection approaches
[7, 10] combine GNN with existing deep learning approaches, in which GNN
captures the characteristics of a graph and deep learning captures other types
of information (e.g., time). Fig. 1 illustrates an example of graph anomaly
detection with GNN. Suppose that nodes (A) and (C) are detected anomalous in
terms of the node attributes, and nodes (A) and (B) are detected anomalous in
terms of the graph topology. Then, only node (A) should be detected anomalous
if both node attributes and graph topology are taken into account together as
anomalous factors. GNN models enable us to detect such anomalies by examining
both graph topology and node attributes simultaneously.

Figure 1: Example of graph anomaly detection. Nodes A and C are detected
anomalous attribute-wise. Nodes A and B are detected anomalous structure-wise
(as they do not belong to any community). Using GNN detects node A to be
anomalous both attribute-wise and structure-wise.

In this survey, we provide an overview of GNN-based approaches for graph
anomaly detection and review them primarily by the types of graphs, namely
static graphs and dynamic graphs. Compared with other surveys on related
topics — on graph anomaly detection (in general) [2, 3], graph anomaly
detection specifically using deep learning [11, 12], and general anomaly
detection using deep learning [13, 14] — this survey aims to touch on the
unique angle of graph anomaly detection _using GNN models_. Given the
significance of GNN and the active ongoing research efforts for its use in
graph anomaly detection, it is our conviction that a comprehensive survey on
this particular topic is timely and beneficial to the research community.

Fig. 2 shows the timeline of the surveyed methods. The survey in Section III
is organized according to the classification framework used by other surveys
on graph anomaly detection [3, 2, 11, 12]. This area is still new, and yet the
published methods cover a broad range of graphs (static versus dynamic, plain
versus attributed) and anomaly types (structure, node, edge, subgraph)
although the distribution of the study topics seems skewed toward node
anomalies in static graphs. Additionally, in Section IV, we share our opinions
on several promising opportunities and challenges pertaining to graph anomaly
detection using GNN.

Figure 2: Timeline of graph anomaly detection methods using GNN models. The
methods above the timeline are for static graphs, and those below are for
dynamic graphs.

##  II GNN Frameworks

GNNs have been widely used as an effective method to extract useful features,
especially from attributed networks, while performing graph representation
learning (also known as network embedding) through the message passing
mechanism. Model architectures of GNNs have been actively developed, and
include, but not limited to, graph convolutional network (GCN) [15], GraphSAGE
[16], and graph attention network (GAT) [17]. The main idea of such GNN models
is message passing, which aggregates individual features from $h$-hop
neighbors. The message passing mechanism of GNNs can be expressed as follows
[18]:

$\displaystyle\mathbf{m}_{u}^{(k-1)}$
$\displaystyle\leftarrow\textrm{AGGREGATE}^{(k-1)}(\\{\mathbf{h}_{v}^{(k-1)},\forall
v\in\mathcal{N}(u)\cup\\{u\\}\\}),$ $\displaystyle\mathbf{h}_{u}^{(k)}$
$\displaystyle\leftarrow\textrm{UPDATE}^{(k-1)}\left(\mathbf{h}_{u}^{(k-1)},\mathbf{m}_{u}^{(k-1)}\right),$

where AGGREGATE and UPDATE are arbitrary differentiable functions and
$\mathbf{m}_{u}$ is the message that is aggregated from the neighborhood
$\mathcal{N}(u)$ of node $u$ as well as the node itself. At the $k$-th layer
of a GNN, the previous embedding $\mathbf{h}_{u}^{(k-1)}$ of $u$ is updated to
$\mathbf{h}_{u}^{(k)}$ by aggregating neighborhood information via message
passing. The initial embeddings are set to the features of nodes, and the
output at the final layer corresponds to the embeddings of the underlying GNN
model.

GCN originally presented an effective network representation model that
naturally combines the network structure and node attributes in the learning
process. Subsequently, Hamilton et al. [16] introduced GraphSAGE, which
samples nodes for message aggregation in a neighbor to handle large graphs.
GAT learns the weights of each node in a neighbor during message passing.

There have been follow-up studies that use alternative model architectures.
For example, Wang et al. [19] introduced a graph stochastic neural network
(GSNN) to alleviate the inefficiency of a deterministic way used in existing
GNN models. Most existing GNN approaches embed networks into either the
Euclidean or hyperbolic space. These approaches have the issue of
inflexibility in modeling a complex graph topology. To address this issue, Zhu
et al. [20] proposed a graph geometry interaction learning (GIL) algorithm,
which employs _both_ Euclidean and hyperbolic spaces.

##  III GNN-Based Graph Anomaly Detection

The surveyed methods are categorized by the graph types (static versus
dynamic), anomaly types (nodes, edges, subgraphs, and whole graphs), and
network architectures. Table I outlines the organization of our survey.

###  III-A GNN-based static graph anomaly detection

A majority of research efforts on static graph anomaly detection addressed
node anomalies, and only a few addressed edge anomalies and subgraph
anomalies.

####  III-A1 Anomalous Node Detection

Detecting anomalous _nodes_ using GNNs was carried out mostly in attributed
graphs. That is, each of GNN-based methods extracts node attribute information
as well as structural information from a static attributed graph and evaluates
the anomaly score of nodes using a certain scoring algorithm. Various GNN-
based approaches have been proposed to effectively extract the necessary
features from attributed graphs. We categorize these methods according to
their network architectures and then briefly describe the key ideas behind
each method.

On the basis of the structural information, anomalous nodes can be further
divided into the following three types: global anomalies, structural
anomalies, and community anomalies [12]. Global anomalies are referred to as
deviated node attributes in the graph; structural anomalies are referred to as
deviated structural information in the graph; and community anomalies are
referred to as both deviated node attributes and structural information in the
same community.

Note that a fair number of GNN-based approaches are built upon the graph
autoencoder (GAE) framework instantiated with either GCN or GAT. For anomalous
node detection in static graphs, we review GNN-based GAE methods as well as
standalone GNN methods.

TABLE I: Taxonomy and summary of graph anomaly detection methods using GNN
models.

Graph type | Anomaly type | Network architecture | Method | Summary (key issue addressed $\to$ solution)
---|---|---|---|---
Static graph | Node anomaly | GCN-based GAE | DOMINANT [7] (2019) | Complex interactions, sparsity, non-linearity $\to$ GCN-based encoder
Dual-SVDAE [21] (2021) | Overfitting for normal & abnormal $\to$ hypersphere embedding space
GUIDE [22] (2021) | Complex interactions $\to$ higher-order structure decoder
SpecAE [8] (2019) | Over-smoothing issue $\to$ tailored embedding space
ComGA [23] (2022) | Over-smoothing issue $\to$ community-specific representation
ALARM [24] (2020) | Heterogeneous attributes $\to$ multiple GCN-based encoders
AnomMAN [25] (2022) | Heterogeneous attributes $\to$ multiple GCN-based encoders
SL-GAD [26] (2021) | Contextual information $\to$ subgraph sampling & contrastive learning
GCN alone | Semi-GCN [27] (2021) | Label information $\to$ semi-supervised learning by GCN
HCM [28] (2021) | Label & contextual information $\to$ hop-count prediction model
ResGCN [29] (2021) | Over-smoothing issue $\to$ GCN with residual-based attention
CoLA [30] (2021) | Targeting issue of GAE $\to$ contrastive self-supervised learning
ANEMONE [31] (2021) | Contextual information $\to$ multi-scale contrastive learning
PAMFUL [32] (2021) | Contextual information $\to$ pattern mining algorithm with GCN
GAT-based GAE | AnomalyDAE [33] (2020) | Complex interactions $\to$ GAT-based encoder
GATAE [34] (2020) | Over-smoothing issue $\to$ GAT-based encoder
AEGIS [35] (2020) | Handling unseen nodes $\to$ generative adversarial learning with GAE
Other GNN-based model | OCGNN [36] (2021) | Targeting issue of GAE $\to$ GNN with hypersphere embedding space
AAGNN [37] (2021) | Targeting issue of GAE $\to$ GNN with hypersphere embedding space
Meta-GDN [38] (2021) | Hard work to label anomalies $\to$ meta-learning with auxiliary graphs
Edge anomaly | GCN-based GAE | AANE [39] (2020) | Noise or adversarial links $\to$ GAE with a loss for anomalous links
eFraudCom [40] (2022) | Fraud detection $\to$ heterogeneous graph and representative data sampling
GCN alone | SubGNN [41] (2021) | Fraud detection $\to$ GIN and extracting and relabeling subgraphs
Subgraph anomaly | GAT-based GAE | HO-GAT [42] (2021) | Abnormal subgraphs $\to$ hybrid-order attention with motif instances
Graph-level anomaly | GCN alone | OCGIN [43] (2021) | Graph-level anomaly detection $\to$ graph classification with GIN
OCGTL [44] (2022) | Hypersphere collapse $\to$ set of GNNs for embedding
GLocalKD [45] (2022) | Graph-level anomalies $\to$ joint learning global & local normality
Dynamic graph | Edge anomaly | GCN and GRU | AddGraph [10] (2019) | Long-term patterns $\to$ temporal GCN with attention-based GRU
DynAD [46] (2020) | Long-term patterns $\to$ temporal GCN with attention-based GRU
Hierarchical-GCN [47] (2020) | Dynamic data evaluation $\to$ temporal & hierarchical GCN
StrGNN [48] (2021) | Structural change $\to$ mining unusual temporal subgraph structures
Node anomaly | GCN & DRNN-based GAE | H-VGRAE [49] (2020) | Anomalous nodes $\to$ modeling stochasticity and multi-scale ST dependency
GCN and GRU | DEGCN [50] (2022) | To capture node- and global-level patterns $\to$ DGCN and GGRU
GCN alone | TDG with GCN [51] (2022) | Malicious connections on traffic $\to$ extracting TDGs

##### GCN-Based GAE Framework

GAE has been most widely used for detecting graph anomalies. For anomalous
node detection in static graphs, while existing GAEs mostly use GCN in the
encoder, they adopt their own decoders depending on the perspective on which
each method focuses. Additionally, an anomaly scoring function, following the
decoder, identifies the abnormality by scoring each node on the basis of
reconstruction errors from the decoder.

It is likely that graphs are sparse in real-world situations. Moreover,
complex interactions between individual nodes are difficult to capture due to
the non-linear characteristics. To address these issues, _deep anomaly
detection on attributed networks (DOMINANT)_ [7] detected the global and
structural anomalies using GCN as the encoder while discovering node
representations from a given attributed graph. Decoders in DOMINANT were
designed in the sense of reconstructing the original graph structure and nodal
attributes.

To capture complex interactions of GAE-based approaches in high-dimensional
graphs, Zhang et al. [21] proposed a one-class classification-based framework,
called _dual support vector data description based autoencoder (Dual-SVDAE)_ ,
which aims to learn the hypersphere boundary on the normal nodes’ latent space
based on the graph structure and attributes in order to detect global and
structural anomalies. Specifically, its AE has a dual encoder–decoder
architecture — 1) a GCN-based encoder and an inner product-based decoder for
structural features and 2) a multilayer perceptron (MLP)-based encoder–decoder
for attributes. The nodes outside of the hypersphere space are regarded as
anomalous nodes.

Subsequently, Yuan et al. [22] presented a dual GAE framework, _higher-order
structure based anomaly detection (GUIDE)_ , which leverages the higher-order
structures in modeling the complex interaction to detect global and structural
anomalies. Specifically, it consists of the attribute AE for attribute
embeddings and the structure AE for structural embeddings based on the
attention mechanism.

Since GCNs learn node representations via message passing from the neighbors,
they could over-smooth the representations, making anomalous nodes less
distinguishable from the normal nodes. To alleviate the over-smoothing issue,
_spectral AE (SpecAE)_ [8] was presented an approach for detecting global and
community anomalies by employing the Laplacian to calculate the inter-node
distances and to simultaneously embed attributes and relations in the
underlying graph. It used the GCN encoder and the deconvolutional decoder.
Similarly, Luo et al. [23] proposed _community-aware attributed graph anomaly
detection framework (ComGA)_ to detect global and community anomalies by
propagating community-specific representations of each node with a gateway. In
a community detection module, communities were encoded and decoded for
community representations. In a tailored deep GCN (tGCN) module, the
representations, structural information, and nodal attributes were used as
input of GCN layers. The gateway concatenates the community feature,
structure, and attribute. Finally, in an anomaly detection module, the well-
designed structure decoder and attribute decoder reconstruct the output from
the tGCN module.

Most existing studies do not carefully take multi-view properties into
consideration. The complementary information from multi-view attributes can
help detect anomalies more efficiently. In a multi-view attributed network,
each node is affiliated with a set of multi-dimensional features (attributes),
which can be represented by $k$ distinct feature spaces along with $k$ views.
By making use of the multi-view attributes, Peng et al. [24] proposed a _deep
multi-view framework for anomaly detection (ALARM)_ for detecting global and
structural anomalies. Specifically, it employs multiple GCNs to embed a multi-
view attributed graph as an encoder and uses two decoders, each of which
reconstructs the graph structure and attributes.

Chen et al. [25] proposed a framework, called _anomaly on multi-view
attributed networks on attributed networks (AnomMAN)_ , which aims to detect
community anomalies. It first decomposes multi-view attributed graphs into
$k$-subgraphs and encodes the subgraphs with GCNs. Then, the representations
from different subgraphs are concatenated using the attention mechanism and
reconstructed by a decoder with respect to both structures and attributes of
the multi-view graphs.

The existing GAE-based approaches do not effectively extract the contextual
information (e.g., neighboring nodes and subgraphs). In addition, they focused
primarily on node-level representation learning. To address these issues,
Zheng et al. [26] proposed _self-supervised learning for graph anomaly
detection (SL-GAD)_ , where the GCN-based encoder and decoder are used to
capture node- and subgraph-level features along with a self-supervised
learning strategy for community anomalies. Specifically, a target node and
subgraphs centered on each target node (i.e., contextual information) were
sampled and fed into the encoder. Afterward, generative attribute
reconstruction and contrastive learning modules were leveraged to extract the
useful features in a self-supervised fashion. The GCN-based decoder
reconstructs the node attributes, and then the anomaly score is calculated on
the basis of both modules.

##### GCN Framework

Since labeling anomalies is labor-intensive and costly, many efforts have
focused on unsupervised learning. Nonetheless, labeling information can help
enhance the model performance. For this reason, Kumagai et al. [27] proposed a
simple yet effective GCN-based method, called _semi-GCN_ , which is capable of
embedding nodes into a hypersphere space while taking advantage of the
structure and attribute features of a graph by stacking graph convolutional
layers in order to detect global anomalies.

To address the issue above in unsupervised learning and leverage global
context information, Huang et al. [28] proposed the _hop-count based model
(HCM)_ based on self-supervised learning with the _PairwiseDistance_ algorithm
[52] in which hop counts of node pairs are leveraged as labels [52].
Specifically, it consists of a preprocessing module for labeling, GCNs for
learning the representation of graphs, and the MLP module for calculating the
anomaly scores.

Pei et al. [29] proposed _residual GCN (ResGCN)_ to alleviate the sparsity and
over-smoothing issues in modeling attributed graphs. It uses the attention
mechanism with residual information, modeled by MLP layers, in a graph.

Basically, GAE can bring sub-optimal performance on the anomaly detection
task. To tackle this problem raised by GAE-based methods, Liu et al. [30]
proposed _contrastive self-supervised learning (CoLA)_ , which concentrates on
modeling the relations between nodes and their neighboring subgraphs to detect
the community anomalies. More precisely, the well-organized node and its
subgraph pairs were carefully sampled, and then the GCN-based contrastive
learning model embedded the pairs. Subsequently, a readout module computed
discriminative scores, while showing the abnormality of a target node of the
pairs.

Jin et al. [31] presented _graph anomaly detection framework with multi-scale
contrastive learning (ANEMONE)_ , which detects community anomalies, to
overcome the sub-optimality based on a multi-scale contrastive learning model.
In the model, two GCN-based contrastive networks are trained at a patch-level
(i.e., node–node) and a context-level (i.e., node–egonet) to catch the
information in multiple graph scales. Then, a statistical anomaly estimator
computes the anomaly scores of target nodes on the basis of the patch- and
context-level scores.

There were a few studies that jointly take into account pattern mining and
GNNs for graph anomaly detection. For example, Zhao et al. [32] introduced a
GCN-based framework, _pattern mining and feature learning (PAMFUL)_ , which
employs pattern mining to guide the GCN in aggregating local information in
order to catch global patterns in the sense of detecting the global and
structural anomalies.

##### GAT-Based GAE Framework

While the GCN-based framework exhibits good performance in anomalous node
detection, its simple aggregation operation, which can cause the over-
smoothing issue, limits the GCN’s ability to extract useful features. To
overcome this, GAT-based approaches have been developed as an alternative.

Earlier studies did not take into account the complex interactions between
nodes and attributes due to the shallow learning architecture. To solve this
issue, Fan et al. [33] proposed a _deep joint representation learning
framework for anomaly detection through a dual AE (AnomalyDAE)_ , which
captures the complex interactions between the structure and attributes to
detect global and structural anomalies. Specifically, it consists of a GAT-
based structure encoder and an attribute encoder, each employing an inner
product decoder.

Moreover, to alleviate the over-smoothing issue in GCNs, the _graph attention-
based AE (GATAE)_ [34] embedded the input attributed graph by using multiple
graph attention layers as an encoder in order to detect global and structural
anomalies. An inner product decoder was used for reconstruction of the graph
structure, and a decoder with the same architecture as its encoder was used to
reconstruct node attributes.

Since most efforts have not yet handled the unseen nodes, the underlying model
may be unnecessarily retrained for newly discovered nodes in graphs. To
address the issue, _adversarial graph differentiation network (AEGIS)_ [35]
detected the community anomalies using an attention-based graph
differentiation network (GDN). Specifically, an encoder based on GDNs first
embeds the graphs at node- and neighborhood-levels, and then a GDN-based
decoder reconstructs the input graphs along with the anomaly ranking list.

##### Other GNN Frameworks

Wang et al. [36] proposed _one-class graph neural network (OCGNN)_ , which
aims at detecting the global anomalies. OCGNN combines the representation
capability of GNNs with a hypersphere learning objective function, which
enables us to learn a hypersphere boundary and detect points that are outside
the boundary as anomalous nodes.

Despite significant efforts, it remains an open challenge to learn suitable
communities for effective anomaly detection. Additionally, defining anomalies
is nontrivial since the deviation patterns of anomalies are not easily
disclosed. To address these issues, Zhou et al. [37] introduced _abnormality-
aware GNN (AAGNN)_ , which employs a subtractive aggregation method to decide
the pattern deviation between a target node and its nearby nodes along with
hypersphere learning for community anomaly detection. Specifically, by
subtracting the feature of a target node from the aggregated feature in the
$k$-hop neighborhood, abnormality of the node is determined for further
embedding into the hypersphere space.

Due to the expensive labeling cost, there have been only a few methods
designed in a supervised manner. Ding et al. [38] introduced a supervised GNN-
based framework, _few-shot network anomaly detection via cross-network meta-
learning (Meta-GDN)_ , which aims to detect the global anomalies on the target
graph by using very limited knowledge of ground-truth anomalies from auxiliary
graphs with the GCN-based encoder. Meta-GDN was built upon graph deviation
networks (GDNs), which first score each node by using a GCN-based anomaly
score learner and then use the deviation loss to enforce the model to give
high anomaly scores to nodes whose features deviate from normal nodes
significantly.

####  III-A2 Anomalous Edge Detection

Anomalous edges generally represent different or atypical interactions between
nodes in a graph. Research on such anomalous edge detection in a static graph
has been relatively limited.

Duan et al. [39] proposed _anomaly aware network embedding (AANE)_ , which was
designed for plain graphs and implemented using the GCN-based GAE framework.
This method adjusts the fitting loss and the “anomaly-aware” loss, which
consists of both the deviation loss and the removal loss. The probability from
the loss functions is the score of an edge. An edge with a lower probability
is more likely to be an anomalous edge.

Song et al. [41] proposed _subgraph-based framework (SubGNN)_ for fraud
detection. Sub-graphs near target edges are extracted and relabeled for entity
independence. The proposed relational graph isomorphism network (R-GIN) learns
the features for precise fraud detection.

Zhang et al. [40] proposed a _competitive graph neural network (CGNN)_ -based
fraud detection system (eFraudCom) to detect fraudulent behaviors on an
e-commerce platform. The CGNN is a GCN-based GAE system. The eFraudCom system
consists of a data processor and a fraud detector. Specifically, in the data
processor, representative normal data were sampled, and a heterogeneous graph
with the sampled normal data and the rest was generated; and in the fraud
detector, neighbors in the graph were sampled and anomalous edges were
detected by the CGNN.

####  III-A3 Anomalous Subgraph Detection

Anomalous subgraph detection is far more challenging than anomalous node or
edge detection. For one noticeable thing, nodes and edges in an anomalous
subgraph may be considered normal in themselves. Moreover, a subgraph can be
very diverse in its structure and size. Presumably due to this challenge,
there exist only a limited number of studies in the literature. We have found
one GAT-based GAE method.

Huang et al. [42] proposed a GAT-based GAE framework, called _hybrid-order
graph attention network (HO-GAT)_ , to detect anomalous nodes and subgraphs
simultaneously by using the structure and attributes of abnormal nodes and
subgraphs. To define the most representative subgraph, the motif — the widely
studied higher-order structure characterized as a densely connected subgraph —
was leveraged. To model the relations between nodes and motifs, HO-GAT
effectively measured the significance of four relations: a node to another
node, a node to a motif, a motif to a node, and a motif to another motif.
Specifically, the graph attention layer was used in the encoder in order to
capture information of the four relations mentioned above. Additionally, two
individual decoders were employed to reconstruct the structure and attributes.

####  III-A4 Graph-level Anomaly Detection

Graph-level anomaly detection (GLAD) finds graphs that are notably different
from most of the graphs in a set of graphs. There have been limited studies on
addressing this task. As mentioned above, GNN-based methods have proven its
capabilities in graph-structured data, and several methods such as OCGNN [36]
and DOMINANT [7] have successfully applied GNN to graph anomaly detection
tasks. Recently, there have been attempts to adapt GNN-based graph
classification methods to GLAD tasks.

Zhao and Akoglu [43] proposed _one-class graph-level anomaly detector (OCGIN)_
based on Graph Isomorphism Network (GIN) [53], which has drawn attention to
barely studied GLAD tasks while improving the detection performance. GIN [53]
generalizes the Weisfeiler-Lehman (WL) test [54], which can efficiently
distinguish a broad class of graphs [55], and achieves powerful classification
capability among GNNs. Specifically, it optimizes the one-class Deep Support
Vector Data Description (deep SVDD) objective function [56] at the output
layer of a GIN model.

To further improve the performance and overcome the hypersphere collapse where
the deep one-class objective encourages all graph embeddings in the training
data to concentrate within a hypersphere, Qiu et al. [44] presented a new GNN-
based approach, _one-class graph transformation learning (OCGTL)_ , which
integrates advantages of deep one-class classification (deep OCC) [56, 43] and
self-supervised anomaly detection with learnable transformations [57].
Specifically, OCGTL consists of a set of GNNs to embed its input graphs into a
latent space. Afterward, the various embeddings were used for training to be
close to the reference embedding.

Ma et al. [45] proposed a GCN method, _global and local knowledge distillation
(GLocalKD)_ , which extracts graph- and node-level representations from a set
of graphs by using two different stacked GCN modules to detect locally or
globally anomalous subgraphs. Specifically, it consists of two GCNs, namely, a
random target network and a predictor network, that have the same GCN
architecture and incur the same distillation losses. GLocalKD learns the graph
normality at a fine-grained level by using the predictor network to predict
the graph- and node-level representations produced by the random target
network.

###  III-B GNN-based Dynamic Graph Anomaly Detection

Unlike a static graph, _temporality_ is an important factor in a dynamic graph
whose structure or attributes change over time. Recently, various methods for
detecting anomalies in graphs changing or evolving over time have been
proposed based on graph communities, compression, decomposition, distance
metrics, and probabilistic modeling of graph features [2]. There are several
approaches proposed for dynamic graphs where GCN is combined with deep
learning methods that are suitable for temporal processing, such as recurrent
neural network (RNN), gated recurrent unit (GRU), and transformer. A few
studies addressed detecting anomalies in edges or in nodes of a dynamic graph.
There is no study that addresses detecting anomalous subgraphs yet.

####  III-B1 Anomalous Edge Detection

The basic concept of using GCN and GRU together is that GCN extracts features
from a graph and GRU captures historical information useful for anomaly
detection. Alongside the fact that GCNs do not consider the temporal factors
in dynamic graphs, _anomaly detection in dynamic graph (AddGraph)_ [10]
combined GCN and GRU, which enables us to integrate long-term and short-term
patterns in a window in order to describe the normal edges by using
structural, attribute, and temporal information. Specifically, it leveraged
GCN to process the previous node state with edges in the current graph by
harnessing the structural and attribute features of nodes. The nodes’ states
in a short window were used as the short-term information. The GCN output and
the shot-term information were then combined in a contextual attention-based
GRU to extract the hidden state of nodes in order to calculate the anomaly
probability of an edge.

Note that Zheng et al.’s work [10] requires the entire set of nodes as the
input and, thus, is not able to effectively manage newly added nodes. To
address this issue, Zhu et al. [46] proposed _anomaly detection in dynamic
network (DynAD)_ , which uses evolving GCNs, consisting of multiple layers at
each time, and attention-based GRU for adaptive parameter learning.

There are multi-level data structure (in addition to temporal factors)
inherent in graphs. Thus, a hierarchical convolutional network model may be
conducive to simultaneously capture global and local features from those
graphs. In this regard, Wang et al. [47] employed a _hierarchical GCN_ with a
Laplacian-based graph coarsening algorithm to leverage the multi-level
structure. In addition, they captured temporal features by using GRU as well.

To take structural changes around the target edge in a window into
consideration, Cai et al. [48] proposed _structural graph neural network
(StrGNN)_ , which produces $h$-hop subgraphs from each temporal graph and uses
GCN and GRU to extract features and temporal dependencies. Specifically,
$h$-hop subgraphs centered on the target edge at each timeline were extracted
firstly. Then, GCNs and pooling technique were used to exploit features from
the subgraphs. Subsequently, GRUs captured the temporal dependencies.

####  III-B2 Anomalous Node Detection

Dynamic graphs often show complex variation patterns, which can be interpreted
by the stochasticity and spatiotemporal relationships between nodes and edges.
However, previous deterministic methods could not handle such a problem. To
solve this, Yang et al. [49] proposed _hierarchical variational graph
recurrent autoencoder (H-VGRAE)_ by employing GCN-based GAE and
RNN—specifically, by stacking multiple GCN layers and combining the GCN layers
with dilated RNN (DRNN) layers in the encoder. The same methods in the encoder
were used in the decoder except the Bernoulli and Gaussian MLP for
reconstruction in order to detect anomalous nodes. H-VGRAE jointly learns the
anomaly features of the nodes and edges, and detects node anomalies using
automatic threshold selection.

Zhang et al. [50] proposed a novel _dynamic evolving graph convolutional
network (DEGCN)_ model to capture evolving patterns of both local node-level
and global graph-level software behaviors. It consists of three stages. First,
the multi-scale graphs are generated by sliding windows. Second, on a directed
GCN (DGCN) model, in-degree node features and out-degree node features are
summarized simultaneously, and on a graph encoding-based GRU (GGRU) model, the
evolving patterns of graphs are learned for its time steps. Third, the
features from DGCN and GGRU are combined, and MLP layer calculates the
anomality score.

Zola et al. [51] proposed a graph-based approach to detect malicious
connections on traffic networks. Specifically, in the first stage, a temporal
dissection operation was used to split the entire network information into
time intervals and to extract Traffic Dispersion Graphs (TDGs). In the second
stage, new synthetic samples for each TDG were created to balance the number
of attackers and normal nodes. Finally, the TDGs were trained by GCNs and
anomalous nodes were detected.

##  IV Opportunities and Challenges

GNN-based graph anomaly detection is a quite challenging problem with lots of
potentials to build sophisticated methods based upon the existing approaches
presented in this survey, particularly for detecting edge anomalies and
subgraph anomalies. Further, there are research opportunities and open
challenges that are important and not addressed yet. This section summarizes
some of them.

##### Explainable GNNs for Detecting Graph Anomalies

The output of anomaly detection methods is either an anomaly score or a
top-$k$ ranking list. To intuitively understand the meaning of the score and
list, additional explanations need to be provided. Since GNN-based methods are
inherently less interpretable than traditional machine learning approaches, it
is important to resolve the issue along with explainable models for anomaly
detection. Currently, there is relatively little work on designing explainable
GNN models for graph anomaly detection (e.g., Deng et al. [58]).

##### Identification of Graph Anomalies with GNNs

Anomalies are mostly recognized on the basis of a reconstruction loss and a
distance-based stochastic function. Although this loss function is capable of
capturing deviating patterns in training, the reconstruction loss is
vulnerable to noise and the distance-based function does not work properly
when anomalous and normal data are distant in the embedding space. These
challenges will be no less, or rather worse, for the problem of identifying
graph anomalies. While many GNN-based approaches embed graphs into either
Euclidean or hyperbolic spaces, they do not fully utilize the information
available in graphs or lack the flexibility to model intrinsic complex graph
geometry [20]. Therefore, it is a promising future research direction to
design a suitable embedding space and loss functions to detect graph
anomalies.

##### Class Imbalance in Graph Anomaly Detection with GNNs

Imbalance between normal and anomalous data is inevitable since the anomalies
tend to occur rarely. As the model performance is heavily dependent on
training data, the class imbalance is a challenge that must be overcome.
Rather than naïvely using negative sampling, a better strategy may be
augmenting the training data, which is also a challenging issue in graph
domains. There is little research carried out to resolve the issue of class
imbalance in graph anomaly detection with GNNs in the literature (e.g., Zhao
et al. [59]).

##### Anomaly Detection with GNNs from Heterogeneous Graphs

A heterogeneous graph is a graph that contains multiple types of nodes and
edges and often occurs in practice. Studies on heterogeneous graph anomaly
detection with GNNs have been largely under-explored in the literature.
Handling the heterogeneity in solving the anomaly detection problem along with
GNNs would be challenging, particularly if compounded by the temporal factors
in a dynamic graph, due to the modeling difficulty including extraction of
multiple relations of nodes/edges. Feasible strategies may include (1)
sampling target edges or subgraphs via meta-paths and (2) extracting useful
information via embedding the types of heterogeneous graphs.

##### Few-Shot Graph Anomaly Detection with GNNs

Although GNN approaches have rapidly advanced over the past a few years, few-
shot graph anomaly detection with GNNs has nor been studied much yet. While,
in real-world scenarios, it is easy to obtain a few labeled anomalies from
graphs similar to the target graph, there have been only a few recent attempts
to leverage such a potential to develop GNN models that can leverage a small
number of labeled anomalies (e.g., Ding et al. [38]). There are still open
challenges on designing diverse meta-learning algorithms to conduct few-shot
graph anomaly detection aided by GNNs.

##  V Conclusion

In this paper, we provided a comprehensive survey of state-of-the-art graph
anomaly detection methods that were built upon GNN models. Additionally, we
presented several opportunities and challenges for further research in this
area. A majority of research efforts have been concentrated on detecting node
anomalies from static graphs, while types of graphs and anomaly types are
rapidly expanding to include dynamic graphs and edge/subgraph/graph-level
anomalies. This trend is expected to continue in the coming years. Some
specific application domains, such as anomaly detection in IoT, in program
analysis (e.g., Android malware and OS verification), remain for future
research. We hope that this survey will trigger and stimulate more active
research on graph anomaly detection using GNNs and be a stepping stone for
subsequent surveys as the research progresses.

## Acknowledgment

This research was supported by NRF grant funded by the Korea Government (MSIT)
(No. 2021R1A2C3004345) and by IITP grant funded by the Korea Government (MSIT)
(No. RS-2022-00155857, Artificial Intelligence Convergence Innovation Human
Resources Development (Chungnam National University)) and BK21 FOUR Program by
Chungnam National University Research Grant, 2022.

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