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.

In this paper, for overlapping community detection, we propose a novel framework of the link-space transformation that transforms a given original graph into a link-space graph. Its unique idea is to consider topological structure and link similarity separately using two distinct types of graphs: the line graph and the original graph. For topological structure, each link of the original graph is mapped to a node of the link-space graph, which enables us to discover overlapping communities using non-overlapping community detection algorithms as in the line graph. For link similarity, it is calculated on the original graph and carried over into the link-space graph, which enables us to keep the original structure on the transformed graph. Thus, our transformation, by combining these two advantages, facilitates overlapping community detection as well as improves the resulting quality. Based on this framework, we develop the algorithm LinkSCAN that performs structural clustering on the link-space graph. Moreover, we propose the algorithm LinkSCAN* that enhances the efficiency of LinkSCAN by sampling. Extensive experiments were conducted using the LFR benchmark networks as well as some real-world networks. The results show that our algorithms achieve higher accuracy, quality, and coverage than the state-of-the-art algorithms.

In recent years, many recommender systems using network embedding (NE) such as graph neural networks (GNNs) have been extensively studied in the sense of improving recommendation accuracy. However, such attempts have focused mostly on utilizing only the information of positive user-item interactions with high ratings. Thus, there is a challenge on how to make use of low rating scores for representing users' preferences since low ratings can be still informative in designing NE-based recommender systems. In this study, we present SiReN, a new Sign-aware Recommender system based on GNN models. Specifically, SiReN has three key components: 1) constructing a signed bipartite graph for more precisely representing users' preferences, which is split into two edge-disjoint graphs with positive and negative edges each; 2) generating two embeddings for the partitioned graphs with positive and negative edges via a GNN model and a multilayer perceptron (MLP), respectively, and then using an attention model to obtain the final embeddings; and 3) establishing a sign-aware Bayesian personalized ranking (BPR) loss function in the process of optimization. Through comprehensive experiments, we empirically demonstrate that SiReN consistently outperforms state-of-the-art NE-aided recommendation methods.

Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss? Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large graphs can be fast and easy if they are compressed sufficiently to fit in main memory or even cache. Graph summarization, which yields a coarse-grained summary graph with merged nodes, stands out with several advantages among graph compression techniques. Thus, a number of algorithms have been developed for obtaining a concise summary graph with little information loss or equivalently small reconstruction error. However, the existing methods focus solely on reducing the number of nodes, and they often yield dense summary graphs, failing to achieve better compression rates. Moreover, due to their limited scalability, they can be applied only to moderate-size graphs. In this work, we propose SSumM, a scalable and effective graph-summarization algorithm that yields a sparse summary graph. SSumM not only merges nodes together but also sparsifies the summary graph, and the two strategies are carefully balanced based on the minimum description length principle. Compared with state-of-the-art competitors, SSumM is (a) Concise: yields up to 11.2X smaller summary graphs with similar reconstruction error, (b) Accurate: achieves up to 4.2X smaller reconstruction error with similarly concise outputs, and (c) Scalable: summarizes 26X larger graphs while exhibiting linear scalability. We validate these advantages through extensive experiments on 10 real-world graphs.

This paper proposes LinkBlackHole*, a novel algorithm for finding communities that are (i) overlapping in nodes and (ii) mixing (not separating clearly) in links. There has been a small body of work in each category, but this paper is the first one that addresses both. LinkBlackHole* is a merger of our earlier two algorithms, LinkSCAN* and BlackHole, inheriting their advantages in support of highly-mixed overlapping communities. The former is used to handle overlapping nodes, and the latter to handle mixing links in finding communities. Like LinkSCAN and its more efficient variant LinkSCAN*, this paper presents LinkBlackHole and its more efficient variant LinkBlackHole*, which reduces the number of links through random sampling. Thorough experiments show superior quality of the communities detected by LinkBlackHole* and LinkBlackHole to those detected by other state-of-the-art algorithms. In addition, LinkBlackHole* shows high resilience to the link sampling effect, and its running time scales up almost linearly with the number of links in a network.

Recent years have witnessed a growing interest in understanding the fundamental principles of how epidemic, ideas or behaviour spread over large networks (e.g. the Internet or online social networks). The conventional approach is to use the susceptible-infected-susceptible (SIS) model or its derivatives. We like to note that these models are often too restrictive and may not be applicable in many realistic situations. In this paper, we propose a ‘generalized SIS model’ by allowing the existence of intermediate states between susceptible and infected states. To analyse the diffusion process of the generalized SIS model on large graphs, we use the ‘mean-field analysis technique’ to determine which initial condition leads to or prevents the outbreak of information or virus. For any general connected graphs, we show that the condition which can prevent the spread of contagions depends on two de-coupled effects: the network topology and the parametric values of the generalized SIS model. Experimental results based on both synthetic and real-world datasets show that our methodology can accurately predict the behaviour of the phase-transition process for any general graphs. We also extend our generalized SIS model to analyse the dynamics and behaviour of two competing sources. This is useful if one wants to model competing products in a large network or competition between virus and antidote in a large communication network. We present the analytical derivation and show via experiment how different factors such as initial condition, transmission rates, recovery rates or the number of states can affect the phase transition process and the final equilibrium. Our models and methodology can serve as an essential tool in analysing and understanding the information diffusion process in large networks.