Synthetic Graphs Research Articles

Reliable and Faithful Generative Explainers for Graph Neural Networks

Graph neural networks (GNNs) have been effectively implemented in a variety of real-world applications, although their underlying work mechanisms remain a mystery. To unveil this mystery and advocate for trustworthy decision-making, many GNN explainers have been proposed. However, existing explainers often face significant challenges, such as the following: (1) explanations being tied to specific instances; (2) limited generalisability to unseen graphs; (3) potential generation of invalid graph structures; and (4) restrictions to particular tasks (e.g., node classification, graph classification). To address these challenges, we propose a novel explainer, GAN-GNNExplainer, which employs a generator to produce explanations and a discriminator to oversee the generation process, enhancing the reliability of the outputs. Despite its advantages, GAN-GNNExplainer still struggles with generating faithful explanations and underperforms on real-world datasets. To overcome these shortcomings, we introduce ACGAN-GNNExplainer, an approach that improves upon GAN-GNNExplainer by using a more robust discriminator that consistently monitors the generation process, thereby producing explanations that are both reliable and faithful. Extensive experiments on both synthetic and real-world graph datasets demonstrate the superiority of our proposed methods over existing GNN explainers.

Synthetic graphs for link prediction benchmarking

Abstract Predicting missing links in complex networks requires algorithms that are able to explore statistical regularities in the existing data. Here we investigate the interplay between algorithm efficiency and network structures through the introduction of suitably-designed synthetic graphs. We propose a family of random graphs that incorporates both micro-scale motifs and meso-scale communities, two ubiquitous
structures in complex networks. A key contribution is the derivation of theoretical upper bounds for link prediction performance in our synthetic graphs, allowing us to estimate the predictability of the task and obtain an improved assessment of the performance of any method. Our results on the performance of classical methods (e.g., Stochastic Block Models, Node2Vec, GraphSage) show that the performance of all methods correlate with the theoretical predictability, that no single method is universally superior, and that each of the methods exploit different characteristics known to exist in large classes of networks. Our findings underline the need for careful consideration of graph structure when selecting a link prediction method and emphasize the value of comparing performance against synthetic benchmarks. We provide open-source code for generating these synthetic graphs, enabling further research on link
prediction methods.

Bias reduction via cooperative bargaining in synthetic graph dataset generation

Bias reduction via cooperative bargaining in synthetic graph dataset generation

Enhancing the Performance of Automated Scoring Model for Kinematic Graph Answers Using Synthetic Graph Images

Enhancing the Performance of Automated Scoring Model for Kinematic Graph Answers Using Synthetic Graph Images

Making It Tractable to Detect and Correct Errors in Graphs

This paper develops \(\mathsf {Hercules} \) , a system for entity resolution (ER), conflict resolution (CR), timeliness deduction (TD) and missing value/link imputation (MI) in graphs. It proposes \(\mathsf {GCR^{+}\!s} \) , a class of graph cleaning rules that support not only predicates for ER and CR, but also temporal orders to deduce timeliness and data extraction to impute missing data. As opposed to previous graph rules, \(\mathsf {GCR^{+}\!s} \) are defined with a dual graph pattern to accommodate irregular structures of schemaless graphs, and adopt patterns of a star form to reduce the complexity. We show that while the implication and satisfiability problems are intractable for \(\mathsf {GCR^{+}\!s} \) , it is in PTIME to detect and correct errors with \(\mathsf {GCR^{+}\!s} \) . Underlying \(\mathsf {Hercules} \) , we train a ranking model to predict the temporal orders on attributes, and embed it as a predicate of \(\mathsf {GCR^{+}\!s} \) . We provide an algorithm for discovering \(\mathsf {GCR^{+}\!s} \) by combining the generations of patterns and predicates. We also develop a method for conducting ER, CR, TD and MI in the same process to improve the overall quality of graphs, by leveraging their interactions and chasing with \(\mathsf {GCR^{+}\!s} \) ; we show that the method has the Church-Rosser property under certain conditions. Using real-life and synthetic graphs, we empirically verify that \(\mathsf {Hercules} \) is 53% more accurate than the state-of-the-art graph cleaning systems, and performs comparably in efficiency and scalability.

Estimate Mass Density Value as A Priori Information for Gravity by using Bayesian Markov Chain Monte Carlo (MCMC)

<p class="Abstract">In the gravity method, information about mass density value is very important because it will influence the characteristic of the 1-D gravity acceleration graph. However, it is quite difficult to guess the mass density value so that is suitable to the 1-D acceleration graph. This is called “a priori” information. Trial and error way is one way to solve this problem. It is a very random value guess also. To make sure that the initial guess of mass density is a good parameter, Bayesian Markov Chain Monte Carlo (MCMC) can be used. It generates many possibilities from the guess value and then these possibilities will be selected to the best one by likelihood way. The validation is expressed by the random graph as a consequence of the iteration number step of the possibilities. This research is started by using certain values of mass density to create a synthetic model for the field data in Banggai Sula because the area has a complex geology. The synthetic model is used because the gravity forward modelling equation has the sinusoidal form. After Bayesian MCMC is applied to the initial mass density value, it will produce a new mass density value or the estimation value with its response to the 1-D gravity acceleration synthetic graph. Finally, this information will be very useful to create the 2D or 3D inverse modelling in Gravity.</p>

Cross-community affinity: A polarization measure for multi-community networks

This article introduces a heterophily-based metric for assessing polarization in social networks when different opposing ideological communities coexist. The proposed metric measures polarization at the node level and is based on a node’s affinity for other communities. Node-level values can then be aggregated at the community, network, or any intermediate level, resulting in a more comprehensive map of polarization. We looked at our metric on the Polblogs network, the White Helmets Twitter interaction network with two communities, and the VoterFraud2020 domain network with five communities. Additionally, we evaluated our metric on different sets of synthetic graphs to confirm that it yields low polarization scores, as expected. We employed three ways to build synthetic networks: synthetic labeling, dK-series, and network models, in order to assess how the proposed measure behaves to various topologies and network features. Then, we compared our metric to two commonly used polarization metrics, Guerra’s boundary polarization and the random walk controversy score. We also examined how our suggested metric correlates with two network metrics: assortativity and modularity.

Unsupervised Learning for Lateral-Movement-Based Threat Mitigation in Active Directory Attack Graphs

Cybersecurity threats, particularly those involving lateral movement within networks, pose significant risks to critical infrastructures such as Microsoft Active Directory. This study addresses the need for effective defense mechanisms that minimize network disruption while preventing attackers from reaching key assets. Modeling Active Directory networks as a graph in which the nodes represent the network components and the edges represent the logical interactions between them, we use centrality metrics to derive the impact of hardening nodes in terms of constraining the progression of attacks. We propose using Unsupervised Learning techniques, specifically density-based clustering algorithms, to identify those nodes given the information provided by their metrics. Our approach includes simulating attack paths using a snowball model, enabling us to analytically evaluate the impact of hardening on delaying Domain Administration compromise. We tested our methodology on both real and synthetic Active Directory graphs, demonstrating that it can significantly slow down the propagation of threats from reaching the Domain Administration across the studied scenarios. Additionally, we explore the potential of these techniques to enable flexible selection of the number of nodes to secure. Our findings suggest that the proposed methods significantly enhance the resilience of Active Directory environments against targeted cyber-attacks.

Hardening Active Directory Graphs via Evolutionary Diversity Optimization based Policies

Active Directory (AD) is the default security management system for Windows domain networks. An AD environment can be described as a cyber-attack graph, with nodes representing computers, accounts, etc., and edges indicating existing accesses or known exploits that enable attackers to move from one node to another. This paper explores a Stackelberg game model between one attacker and one defender on an AD attack graph. The attacker’s goal is to maximize their chances of successfully reaching the destination before getting detected. The defender’s aim is to block a constant number of edges to minimize the attacker’s chance of success. The paper shows that the problem is #P-hard and, therefore, intractable to solve exactly. To defend the AD graph from cyber attackers, this paper proposes two defensive approaches. In the first approach, we convert the attacker’s problem to an exponential sized Dynamic Program that is approximated by a Neural Network (NN). Once trained, the NN serves as an efficient fitness function for defender’s Evolutionary Diversity Optimization based defensive policy. The diversity emphasis on the defender’s solution provides a diverse set of training samples, improving the training accuracy of our NN for modeling the attacker. In the second approach, we propose a RL based policy to solve the attacker’s problem and Critic network assisted Evolutionary Diversity Optimization based defensive policy to solve defender’s problem. Experimental results on synthetic AD graphs show that the proposed defensive policies are scalable, highly effective, approximate attacker’s problem accurately, and generate good defensive plans.

STEP: Sequence of time-aligned edge plots

We present sequence of time-aligned edge plots (STEP): a sequence- and edge-scalable visualization of dynamic networks and, more broadly, graph ensembles. We construct the graph sequence by ordering the individual graphs based on specific criteria, such as time for dynamic networks. To achieve scalability with respect to long sequences, we partition the sequence into equal-sized subsequences. Each subsequence is represented by a horizontal axis placed between two vertical axes. The horizontal axis depicts the order within the subsequence, while the two vertical axes depict the source and destination vertices. Edges within each subsequence are depicted as segmented lines extending from the source vertices on the left to the destination vertices on the right throughout the entire subsequence, and only the segments corresponding to the sequence members where the edges occur are drawn. By partitioning the sequence, STEP provides an overview of the graphs’ structural changes and avoids aspect ratio distortion. We showcase the utility of STEP for two realistic datasets. Additionally, we evaluate our approach by qualitatively comparing it against three state-of-the-art techniques using synthetic graphs with varying complexities. Furthermore, we evaluate the generalizability of STEP by applying it to a graph ensemble dataset from the architecture domain.

ADPSCAN: Structural Graph Clustering with Adaptive Density Peak Selection and Noise Re-Clustering

Structural graph clustering is a data analysis technique that groups nodes within a graph based on their connectivity and structural similarity. The Structural graph clustering SCAN algorithm, a density-based clustering method, effectively identifies core points and their neighbors within areas of high density to form well-defined clusters. However, the clustering quality of SCAN heavily depends on the input parameters, ϵ and μ, making the clustering results highly sensitive to parameter selection. Different parameter settings can lead to significant differences in clustering results, potentially compromising the accuracy of the clusters. To address this issue, a novel structural graph clustering algorithm based on the adaptive selection of density peaks is proposed in this paper. Unlike traditional methods, our algorithm does not rely on external parameters and eliminates the need for manual selection of density peaks or cluster centers by users. Density peaks are adaptively identified using the generalized extreme value distribution, with consideration of the structural similarities and interdependencies among nodes, and clusters are expanded by incorporating neighboring nodes, enhancing the robustness of the clustering process. Additionally, a distance-based structural similarity method is proposed to re-cluster noise nodes to the correct clusters. Extensive experiments on real and synthetic graph datasets validate the effectiveness of our algorithm. The experiment results show that the ADPSCAN has a superior performance compared with several state-of-the-art (SOTA) graph clustering methods.

Synthetic lethal connectivity and graph transformer improve synthetic lethality prediction.

Synthetic lethality (SL) has shown great promise for the discovery of novel targets in cancer. CRISPR double-knockout (CDKO) technologies can only screen several hundred genes and their combinations, but not genome-wide. Therefore, good SL prediction models are highly needed for genes and gene pairs selection in CDKO experiments. However, lack of scalable SL properties prevents generalizability of SL interactions to out-of-sample data, thereby hindering modeling efforts. In this paper, we recognize that SL connectivity is a scalable and generalizable SL property. We develop a novel two-step multilayer encoder for individual sample-specific SL prediction model (MLEC-iSL), which predicts SL connectivity first and SL interactions subsequently. MLEC-iSL has three encoders, namely, gene, graph, and transformer encoders. MLEC-iSL achieves high SL prediction performance in K562 (AUPR, 0.73; AUC, 0.72) and Jurkat (AUPR, 0.73; AUC, 0.71) cells, while no existing methods exceed 0.62 AUPR and AUC. The prediction performance of MLEC-iSL is validated in a CDKO experiment in 22Rv1 cells, yielding a 46.8% SL rate among 987 selected gene pairs. The screen also reveals SL dependency between apoptosis and mitosis cell death pathways.

MST: Topology-Aware Message Aggregation for Exascale Graph Processing of Traversal-Centric Algorithms

This paper presents MST, a communication-efficient message library for fast graph traversal on exascale clusters. The key idea is to follow the multi-level network topology to perform topology-aware message aggregation, where small messages are gathered and scattered at each level of domain. To facilitate message aggregation, we equip MST with flexible buffer management including active buffer switching and dynamic buffer expansion. We implement MST on the newest-generation Tianhe supercomputer and evaluated its performance using various traversal-centric algorithms on both synthetic trillion-scale graphs and real-world big graphs. The results show that MST-based graph traversal is orders of magnitude faster than that based on Active Messages Library (AML). For the Graph500-BFS benchmark, MST-based Tianhe (with 77.2K nodes) outperforms the Fugaku supercomputer (with 148.5K nodes) by 18.53%, while Fugaku is ranked No. 1 in the latest Graph500-BFS ranking (June 2023). MST also greatly improves graph processing performance on other commercial large-scale computing systems at the National Supercomputing Center in Changsha (NSCC) and WuzhenLight.

On the effectiveness of hybrid pooling in mixup-based graph learning for language processing

Graph neural network (GNN)-based graph learning has been popular in natural language and programming language processing, particularly in text and source code classification. Typically, GNNs are constructed by incorporating alternating layers which learn transformations of graph node features, along with graph pooling layers that use graph pooling operators (e.g., Max-pooling) to effectively reduce the number of nodes while preserving the semantic information of the graph. Recently, to enhance GNNs in graph learning tasks, Manifold-Mixup, a data augmentation technique that produces synthetic graph data by linearly mixing a pair of graph data and their labels, has been widely adopted. However, the performance of Manifold-Mixup can be highly affected by graph pooling operators, and there have not been many studies that are dedicated to uncovering such affection. To bridge this gap, we take an early step to explore how graph pooling operators affect the performance of Mixup-based graph learning. To that end, we conduct a comprehensive empirical study by applying Manifold-Mixup to a formal characterization of graph pooling based on 11 graph pooling operations (9 hybrid pooling operators, 2 non-hybrid pooling operators). The experimental results on both natural language datasets (Gossipcop, Politifact) and programming language datasets (JAVA250, Python800) demonstrate that hybrid pooling operators are more effective for Manifold-Mixup than the standard Max-pooling and the state-of-the-art graph multiset transformer (GMT) pooling, in terms of producing more accurate and robust GNN models.Editor’s note: Open Science material was validated by the Journal of Systems and Software Open Science Board.

A simple and effective convolutional operator for node classification without features by graph convolutional networks.

Graph neural networks (GNNs), with their ability to incorporate node features into graph learning, have achieved impressive performance in many graph analysis tasks. However, current GNNs including the popular graph convolutional network (GCN) cannot obtain competitive results on the graphs without node features. In this work, we first introduce path-driven neighborhoods, and then define an extensional adjacency matrix as a convolutional operator. Second, we propose an approach named exopGCN which integrates the simple and effective convolutional operator into GCN to classify the nodes in the graphs without features. Experiments on six real-world graphs without node features indicate that exopGCN achieves better performance than other GNNs on node classification. Furthermore, by adding the simple convolutional operator into 13 GNNs, the accuracy of these methods are improved remarkably, which means that our research can offer a general skill to improve accuracy of GNNs. More importantly, we study the relationship between node classification by GCN without node features and community detection. Extensive experiments including six real-world graphs and nine synthetic graphs demonstrate that the positive relationship between them can provide a new direction on exploring the theories of GCNs.

On Breaking Truss-based and Core-based Communities

We introduce the general problem of identifying a smallest edge subset of a given graph whose deletion makes the graph community-free. We consider this problem under two community notions that have attracted significant attention: k -truss and k -core. We also introduce a problem variant where the identified subset contains edges incident to a given set of nodes and ensures that these nodes are not contained in any community: k -truss or k -core, in our case. These problems are directly applicable in social networks: The identified edges can be hidden by users or sanitized from the output graph; or in communication networks: the identified edges correspond to vital network connections. We present a series of theoretical and practical results. On the theoretical side, we show through non-trivial reductions that the problems we introduce are NP-hard and, in fact, hard to approximate. For the k -truss-based problems, we also show exact exponential-time algorithms, as well as a non-trivial lower bound on the size of an optimal solution. On the practical side, we develop a series of heuristics that are sped up by efficient data structures that we propose for updating the truss or core decomposition under edge deletions. In addition, we develop an algorithm to compute the lower bound. Extensive experiments on 11 real-world and synthetic graphs show that our heuristics are effective, outperforming natural baselines, and also efficient (up to two orders of magnitude faster than a natural baseline), thanks to our data structures. Furthermore, we present a case study on a co-authorship network and experiments showing that the removal of edges identified by our heuristics does not substantially affect the clustering structure of the input graph. This work extends a KDD 2021 paper, providing new theoretical results as well as introducing core-based problems and algorithms.

Community detection in the human connectome: Method types, differences and their impact on inference.

Community structure is a fundamental topological characteristic of optimally organized brain networks. Currently, there is no clear standard or systematic approach for selecting the most appropriate community detection method. Furthermore, the impact of method choice on the accuracy and robustness of estimated communities (and network modularity), as well as method-dependent relationships between network communities and cognitive and other individual measures, are not well understood. This study analyzed large datasets of real brain networks (estimated from resting-state fMRI from = 5251 pre/early adolescents in the adolescent brain cognitive development [ABCD] study), and = 5338 synthetic networks with heterogeneous, data-inspired topologies, with the goal to investigate and compare three classes of community detection methods: (i) modularity maximization-based (Newman and Louvain), (ii) probabilistic (Bayesian inference within the framework of stochastic block modeling (SBM)), and (iii) geometric (based on graph Ricci flow). Extensive comparisons between methods and their individual accuracy (relative to the ground truth in synthetic networks), and reliability (when applied to multiple fMRI runs from the same brains) suggest that the underlying brain network topology plays a critical role in the accuracy, reliability and agreement of community detection methods. Consistent method (dis)similarities, and their correlations with topological properties, were estimated across fMRI runs. Based on synthetic graphs, most methods performed similarly and had comparable high accuracy only in some topological regimes, specifically those corresponding to developed connectomes with at least quasi-optimal community organization. In contrast, in densely and/or weakly connected networks with difficult to detect communities, the methods yielded highly dissimilar results, with Bayesian inference within SBM having significantly higher accuracy compared to all others. Associations between method-specific modularity and demographic, anthropometric, physiological and cognitive parameters showed mostly method invariance but some method dependence as well. Although method sensitivity to different levels of community structure may in part explain method-dependent associations between modularity estimates and parameters of interest, method dependence also highlights potential issues of reliability and reproducibility. These findings suggest that a probabilistic approach, such as Bayesian inference in the framework of SBM, may provide consistently reliable estimates of community structure across network topologies. In addition, to maximize robustness of biological inferences, identified network communities and their cognitive, behavioral and other correlates should be confirmed with multiple reliable detection methods.

FulBM: Fast fully batch maintenance for landmark-based 3-hop cover labeling

Landmark-based 3-hop cover labeling is a category of approaches for shortest distance/path queries on large-scale complex networks. It pre-computes an index offline to accelerate the online distance/path query. Most real-world graphs undergo rapid changes in topology, which makes index maintenance on dynamic graphs necessary. So far, the majority of index maintenance methods can handle only one edge update (either an addition or deletion) each time. To keep up with frequently changing graphs, we research the ful ly b atch m aintenance problem for the 3-hop cover labeling, and proposed the method called FulBM . FulBM is composed of two algorithms: InsBM and DelBM, which are designed to handle batch edge insertions and deletions respectively. This separation is motivated by the insight that batch maintenance for edge insertions are much more time-efficient, and the fact that most edge updates in the real world are incremental. Both InsBM and DelBM are equipped with well-designed pruning strategies to minimize the number of vertex accesses. We have conducted comprehensive experiments on both synthetic and real-world graphs to verify the efficiency of FulBM and its variants for weighted graphs. The results show that our methods achieve 5.5 × to 228 × speedup compared with the state-of-the-art method.

Tensor Network Message Passing.

When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the exponential growth of the state space as the system size increases. Many standard methods have significant weaknesses. For instance, message-passing algorithms can be inaccurate and even fail to converge due to short loops, while tensor network methods can have exponential computational complexity in large graphs due to long loops. In this Letter, we propose a new method called "tensor network message passing." This approach allows us to compute local observables like marginal probabilities and correlations by combining the strengths of tensor networks in contracting small subgraphs with many short loops and the strengths of message-passing methods in globally sparse graphs, thus addressing the crucial weaknesses of both approaches. Our algorithm is exact for systems that are globally treelike and locally dense-connected when the dense local graphs have a limited tree width. We have conducted numerical experiments on synthetic and real-world graphs to compute magnetizations of Ising models and spin glasses, and have demonstrated the superiority of our approach over standard belief propagation and the recently proposed loopy message-passing algorithm. In addition, we discuss the potential applications of our method in inference problems in networks, combinatorial optimization problems, and decoding problems in quantum error correction.

IWO-IGA—A Hybrid Whale Optimization Algorithm Featuring Improved Genetic Characteristics for Mapping Real-Time Applications onto 2D Network on Chip

Network on Chip (NoC) has emerged as a potential substitute for the communication model in modern computer systems with extensive integration. Among the numerous design challenges, application mapping on the NoC system poses one of the most complex and demanding optimization problems. In this research, we propose a hybrid improved whale optimization algorithm with enhanced genetic properties (IWOA-IGA) to optimally map real-time applications onto the 2D NoC Platform. The IWOA-IGA is a novel approach combining an improved whale optimization algorithm with the ability of a refined genetic algorithm to optimally map application tasks. A comprehensive comparison is performed between the proposed method and other state-of-the-art algorithms through rigorous analysis. The evaluation consists of real-time applications, benchmarks, and a collection of arbitrarily scaled and procedurally generated large-task graphs. The proposed IWOA-IGA indicates an average improvement in power reduction, improved energy consumption, and latency over state-of-the-art algorithms. Performance based on the Convergence Factor, which assesses the algorithm’s efficiency in achieving better convergence after running for a specific number of iterations over other efficiently developed techniques, is introduced in this research work. These results demonstrate the algorithm’s superior convergence performance when applied to real-world and synthetic task graphs. Our research findings spotlight the superior performance of hybrid improved whale optimization integrated with enhanced GA features, emphasizing its potential for application mapping in NoC-based systems.