Neighborhood Subgraphs Research Articles

Inductive Subgraph Embedding for Link Prediction

AbstractLink prediction, which aims to infer missing edges or predict future edges based on currently observed graph connections, has emerged as a powerful technique for diverse applications such as recommendation, relation completion, etc. While there is rich literature on link prediction based on node representation learning, direct link embedding is relatively less studied and less understood. One common practice in previous work characterizes a link by manipulate the embeddings of its incident node pairs, which is not capable of capturing effective link features. Moreover, common link prediction methods such as random walks and graph auto-encoder usually rely on full-graph training, suffering from poor scalability and high resource consumption on large-scale graphs. In this paper, we propose Inductive Subgraph Embedding for Link Prediciton (SE4LP) — an end-to-end scalable representation learning framework for link prediction, which utilizes the strong correlation between central links and their neighborhood subgraphs to characterize links. We sample the “link-centric induced subgraphs” as input, with a subgraph-level contrastive discrimination as pretext task, to learn the intrinsic and structural link features via subgraph classification. Extensive experiments on five datasets demonstrate that SE4LP has significant superiority in link prediction in terms of performance and scalability, when compared with state-of-the-art methods. Moreover, further analysis demonstrate that introducing self-supervision in link prediction can significantly reduce the dependence on training data and improve the generalization and scalability of model.

DiG-In-GNN: Discriminative Feature Guided GNN-Based Fraud Detector against Inconsistencies in Multi-Relation Fraud Graph

Fraud detection on multi-relation graphs aims to identify fraudsters in graphs. Graph Neural Network (GNN) models leverage graph structures to pass messages from neighbors to the target nodes, thereby enriching the representations of those target nodes. However, feature and structural inconsistency in the graph, owing to fraudsters' camouflage behaviors, diminish the suspiciousness of fraud nodes which hinders the effectiveness of GNN-based models. In this work, we propose DiG-In-GNN, Discriminative Feature Guided GNN against Inconsistency, to dig into graphs for fraudsters. Specifically, we use multi-scale contrastive learning from the perspective of the neighborhood subgraph where the target node is located to generate guidance nodes to cope with the feature inconsistency. Then, guided by the guidance nodes, we conduct fine-grained neighbor selection through reinforcement learning for each neighbor node to precisely filter nodes that can enhance the message passing and therefore alleviate structural inconsistency. Finally, the two modules are integrated together to obtain discriminable representations of the nodes. Experiments on three fraud detection datasets demonstrate the superiority of the proposed method DiG-In-GNN, which obtains up to 20.73% improvement over previous state-of-the-art methods. Our code can be found at https://github.com/GraphBerry/DiG-In-GNN.

Social network node pricing based on graph autoencoder in data marketplaces

Data have become a valuable digital resource. It has in turn precipitated the emergence of big data marketplaces. For social network date in the marketplaces, each node should be priced according to its influence. The key challenge is that deep learning based pricing models require initial cascade graphs as inputs to predict influence, which cannot be obtained while pricing nodes. Furthermore, node pricing must enhance purchase intentions while being consistent with their influence. To address these challenges, a node-pricing framework is proposed, in which market price is determined based on the predicted influence. In this framework, corrections are performed by using a graph autoencoder (GAE). The corrections are used to augment the neighborhood subgraph and facilitate the extraction of valid sequence features, which are then used to predict influence. An approximate Shapley value for node influence is used to evaluate the price of the nodes. A multi-perspective pricing approach is further investigated, where consumer utility and the approximate Shapley value for influence are the objectives. An inflection point is chosen on the Pareto frontier to select a price that enhances consumer utility. Extensive experiments were conducted on two real-world social network datasets. The results indicate that our performance is higher than DeepCas by 10.38% in Twitter and 9.64% in Weibo . The price output by our framework is consistent with the nodes’ social marketing value while maximizing consumer utility.

An approach to extracting graph kernel features from functional brain networks and its applications to the analysis of the noisy EEG signals

Since electroencephalographic data (EEG) usually carries a certain amount of noise, it is important to study a method that can propose an effective noise-adaptive feature from EEG signals and can be effectively used for problem-solving. Firstly, to address the problem that the application of noisy EEG in problem-solving based on functional brain networks is significantly worse, we study the extraction of global topological features, called graph kernel features, from functional brain networks with better noise immunity, and propose a method for extracting graph kernel features from networks based on neighborhood subgraph pairwise distances. Secondly, to address the problem of huge data of graph kernel features proposed from functional brain networks, dimensionality reduction of graph kernel features based on kernel principal component analysis is proposed. Finally, to verify that the graph kernel features can not only be effectively used for problem-solving, but also have good noise immunity, the research on fatigue driving and emotion recognition based on the graph kernel feature extraction side of the functional brain network is carried out, and the corresponding fatigue driving state recognition model and emotion state recognition model is constructed. By testing the simulated EEG noisy data on the real fatigue driving dataset and the publicly available emotion recognition dataset Seed with different methods, it is verified that the graph kernel features are effective in classifying the noisy EEG data and have a good generalization ability for different noises.

GDLL: A Scalable and Share Nothing Architecture Based Distributed Graph Neural Networks Framework

Deep learning has recently been shown to be effective in uncovering hidden patterns in non-Euclidean space, where data is represented as graphs with complex object relationships and interdependencies. Because of the implicit data dependence in the big graphs with millions of nodes and billions of edges, it is hard for industrial communities to exploit these methods to address real-world challenges at scale. The skewness property of big graphs, distributed file system performance penalty on small k-hop neighborhood subgraphs, and varying size of subgraph makes Graph Neural Networks (GNNs) training further challenging in a distributed environment using parameter servers. To address such issues, we propose a scalable, layered, fault-tolerance, and in-memory distributed computing-based graph neural network framework called Graph Distributed Learning Library (GDLL). The base layer utilizes an optimized distributed file system and a scalable graph data store to reduce the performance penalty. The second layer provides distributed graph processing using in-memory graph programming models while optimizing and hiding the underlying complexity of information complete subgraph computation. In the third layer, GNN modules are deployed on top of the first two layers for efficient distributed training using parameter servers. Finally, we evaluate and compare GDLL with the state-of-the-art solutions and outperform it significantly in terms of efficiency while maintaining similar GNN convergence.

Hierarchical Attention Link Prediction Neural Network

In this paper, a novel end-to-end neural link prediction model, named Hierarchical Attention Link Prediction Neural Network (HalpNet), is proposed. HalpNet comprehensively explores neighborhood information, which has proved important for link prediction, via the core component, i.e., hierarchical attention mechanism. The proposed hierarchical attention mechanism consists of two neural attention layers, modeling crucial structure information at node level and subgraph level, respectively. At node level, a structure-preserving attention is developed to preserve structure features of each node in the neighborhood subgraph. Based on the latent node features, at subgraph level, a structure-aggregating attention is designed to learn how important that each node in the subgraph is for the linkage of the target node pair and aggregate node features with learned attentions as a comprehensive subgraph representation. Given this expressive representation of neighborhood subgraph, HalpNet is able to predict link score of target node pair effectively. We evaluate HalpNet on 8 benchmark datasets against 14 popular and state-of-the-art approaches. The experimental results demonstrate its significant superiority and wide applicability on link prediction problem.

Lengthening of average path length in social networks due to the effect of community structure

Community structure is a common phenomenon observed in various social networks. In this work, a novel community detection algorithm is proposed by estimating the effect of community structure on the average path length of a network. The Erdos-Renyi graph model is used as a reference to compute the change in the average path length of a network due to community formation. By experimenting with artificial networks, it is found that community structure in a social network contributes towards the lengthening of the average shortest path length. A random graph is found to have a lesser average shortest path length than a social network with community structure. As the size of individual communities increases, there is a decrease in the difference of average shortest path lengths, compared with a random graph containing an equal number of nodes and edges. This relationship is used to predict the average community size and their numbers in a network. The findings mentioned above are applied to the proposed algorithm. The proposed community detection algorithm is an enhancement over Fire Spread community detection algorithm (Pattanayak, 2019), in which the value of R for the R-radius neighborhood subgraph is automatically calculated.

Learning Structural Node Representations using Graph Kernels

Many applications require identifying nodes that perform similar functions in a graph. For instance, identifying structurally equivalent nodes can provide insight into the structure of complex networks. Learning latent representations that capture such structural role information about nodes has recently gained a lot of attention. Existing techniques for learning such representations typically rely on manually engineered features or are very expensive in terms of time and memory requirements. In this paper, we propose SEGK, a powerful framework for computing structural node representations. SEGK learns node representations by generating (or approximating) and decomposing a kernel matrix that incorporates structural similarity between nodes. To compute the similarity between two nodes, the proposed framework builds on well-established concepts from graph mining. Specifically, it compares the neighborhood subgraphs of increasing size of two nodes using graph kernels. SEGK is very flexible, and besides unlabeled graphs, it can also handle node-labeled and node-attributed graphs. We evaluate the proposed framework on several synthetic and real-world datasets, and compare its performance to state-of-the-art techniques for learning structural node embeddings. In almost all cases, the instances of the proposed framework outperform the competing methods, while their time complexity remains very attractive.

Approximate Matching of Neighborhood Subgraphs — An Ordered String Graph Levenshtein Method

Given that exact pair-wise graph matching has a high computational cost, different representational schemes and matching methods have been devised in order to make matching more efficient. Such methods include representing the graphs as tree structures, transforming the structures into strings and then calculating the edit distance between those strings. However many coding schemes are complex and are computationally expensive. In this paper, we present a novel coding scheme for unlabeled graphs and perform some empirical experiments to evaluate its precision and cost for the matching of neighborhood subgraphs in online social networks. We call our method OSG-L (Ordered String Graph-Levenshtein). Some key advantages of the pre-processing phase are its simplicity, compactness and lower execution time. Furthermore, our method is able to match both non-isomorphisms (near matches) and isomorphisms (exact matches), also taking into account the degrees of the neighbors, which is adequate for social network graphs.

Coloring large complex networks

Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical importance of graph coloring, existing works have not systematically investigated or designed methods for large complex networks. In this work, we develop a unified framework for coloring large complex networks that consists of two main coloring variants that effectively balances the tradeoff between accuracy and efficiency. Using this framework as a fundamental basis, we propose coloring methods designed for the scale and structure of complex networks. In particular, the methods leverage triangles, triangle-cores, and other egonet properties and their combinations. We systematically compare the proposed methods across a wide range of networks (e.g., social, web, biological networks) and find a significant improvement over previous approaches in nearly all cases. Additionally, the solutions obtained are nearly optimal and sometimes provably optimal for certain classes of graphs (e.g., collaboration networks). We also propose a parallel algorithm for the problem of coloring neighborhood subgraphs and make several key observations. Overall, the coloring methods are shown to be (1) accurate with solutions close to optimal, (2) fast and scalable for large networks, and (3) flexible for use in a variety of applications.

MDS-Based Wormhole Detection Using Local Topology in Wireless Sensor Networks

Wormhole attack is a severe threat to wireless sensor networks (WSNs), which has received considerable attentions in the literature. However, most of the previous approaches either require special hardware devices or depend on rigorous assumptions on the network settings, which greatly limit their applicability. In this work, we attempt to relax the limitations in prior work, and propose a novel approach to detect wormhole attacks by only local topology information in WSNs. The basic idea is as follows. Each node locally collects its neighborhood information and reconstructs the neighborhood subgraph by multidimensional scaling (MDS). Potential wormhole nodes are detected by validating the legality of the reconstruction. Then, a refinement process is introduced to filter the suspect nodes and to remove false positives. Our approach solely relies on the local connectivity information and is extremely simple and lightweight, which makes it applicable in practical systems. Extensive simulations are conducted, and the results demonstrate the effectiveness and superior performance of our approach.

Neighborhood perfect graphs

The notion of neighborhood perfect graphs is introduced here as follows. Let G be a graph, α N ( G) denote the maximum number of edges such that no two of them belong to the same subgraph of G induced by the (closed) neighborhood of some vertex; let ϱ N ( G) be the minimum number of vertices whose neighborhood subgraph cover the edge set of G. Then G is called neighborhood perfect if ϱ N ( G′) = α N ( G′) holds for every induced subgraph G′ of G. It is expected that neighborhood perfect graphs are perfect also in the sense of Berge. We characterized here those chordal graphs which are neighborhood perfect. In addition, an algorithm to computer ϱ N ( G) = α N ( G) is given for interval graphs.

On graphs with a constant link, II

We study the following problem: For which finite graphs L do there exist graphs G such that the link (i.e., the neighborhood subgraph) of each vertex of G is isomorphic to L? We give a complete solution for the cases (i) L is a disjoint union of arcs, (ii) L is a tree with only one vertex of degree greater than two, (iii) L is a circle of prescribed length. Some other cases are also discussed. An interesting case is whether the situation is changed if we require G also to be finite. It transpires (see for example, Corollaries VII.3 and VII.4) that this is indeed the case. Part I of this paper will appear in [3]. It provides the basic definitions used in both part I and part II. Section III provides the basic tool, an identification procedure, that is used throughout the rest of the paper. Section IV sets up the basic building technique for the construction of more complicated graphs. It is shown how to build graphs such that the link of each vertex is an arc (of non-constant length), and how to control the proportional number of vertices with links of various lengths.

Matroid basis graphs. II

Several graph-theoretic notions applied to matroid basis graphs in the preceding paper are now tied more specifically to aspects of matroids themselves. Factorizations of basis graphs and disconnections of neighborhood subgraphs are related to matroid separations. Matroids are characterized whose basis graphs have only one or two of the three types of common neighbor subgraphs. The notion of leveling is generalized and related to matroid sums, minors, and duals. Also, the problem of characterizing regular and graphic matroids through their basis graphs is discussed. Throughout, many results are obtained quite easily with the aid of certain pseudo-combivalence systems of 0–1 matrices.