Truss Decomposition on Large Probabilistic Networks using H-Index

Esfahani, Fatemeh; Daneshmand, Mahsa; Srinivasan, Venkatesh; Thomo, Alex; Wu, Kui

doi:10.1145/3468791.3468817

Cited by 11 publications

(9 citation statements)

References 18 publications

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“…Wang and Cheng [40] propose a fast in-memory algorithm for truss decomposition. In addition, truss decomposition has also been studied in various computing settings (e.g., external-memory algorithms [40], MapReduce algorithms [8], [11], and shared-memory parallel systems [35]) and different types of graphs (e.g., uncertain graphs [15], [24], [45], directed graphs [36], and dynamic graphs [22], [42]). Recently, several community models are built on the k-truss [2], [22], [23], [44].…”

Section: K-truss Mining and Indexingmentioning

confidence: 99%

“…If two different supernodes S u and S w have the same trussnesses as τ G N (v) (e), it merge two supernodes into one by assigning all S w 's feature to S u . Specifically, it unions two vertex lists as V Su = V Su ∪ V Sw and assign S u the edges that are incident to supernode S w , and then remove S w from V v (lines 10-12); Otherwise, it adds a superedge between S u and S w and assigns the edge weight as w((S u , S w )) = τ G N (v) (e) (line [14][15]. After processing all edges in L, the algorithm finally returns the GCT-index as…”

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confidence: 99%

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Truss-Based Structural Diversity Search in Large Graphs

Huang

2022

IEEE Trans. Knowl. Data Eng.

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Social decisions made by individuals are easily influenced by information from their social neighborhoods. A key predictor of social contagion is the multiplicity of social contexts inside the individuals contact neighborhood, which is termed structural diversity. However, the existing models have limited decomposability for analyzing large-scale networks, and suffer from the inaccurate reflection of social context diversity. In this paper, we propose a new truss-based structural diversity model to overcome the weak decomposability. Based on this model, we study a novel problem of truss-based structural diversity search in a graph G, that is, to find the r vertices with the highest truss-based structural diversity and return their social contexts. o tackle this problem, we propose an online structural diversity search algorithm in O(ρ(m + T )) time, where ρ, m, and T are respectively the arboricity, the number of edges, and the number of triangles in G. To improve the efficiency, we design an elegant and compact index, called TSD-index, for further expediting the search process. We further optimize the structure of TSD-index into a highly compressed GCT-index. Our GCT-index-based structural diversity search utilizes the global triangle information for fast index construction and finds answers in O(m) time. Extensive experiments demonstrate the effectiveness and efficiency of our proposed model and algorithms, against state-of-the-art methods.

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Section: K-truss Mining and Indexingmentioning

confidence: 99%

mentioning

confidence: 99%

Truss-Based Structural Diversity Search in Large Graphs

Huang

2022

IEEE Trans. Knowl. Data Eng.

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“…Moreover, the notion of global (k, η)-truss is proposed in [20] which is based on the probability of each edge belonging to a connected k-truss in a possible world. An approximate algorithm for the local truss decomposition is proposed by Esfahani et al in [21] to efficiently compute the tail probability of edge supports in the peeling process described in [20].…”

Section: Related Workmentioning

confidence: 99%

Multi-Stage Graph Peeling Algorithm for Probabilistic Core Decomposition

Guo¹,

Zhang²,

Esfahani³

et al. 2021

Preprint

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Mining dense subgraphs where vertices connect closely with each other is a common task when analyzing graphs. A very popular notion in subgraph analysis is core decomposition. Recently, Esfahani et al. presented a probabilistic core decomposition algorithm based on graph peeling and Central Limit Theorem (CLT) that is capable of handling very large graphs. Their proposed peeling algorithm (PA) starts from the lowest degree vertices and recursively deletes these vertices, assigning core numbers, and updating the degree of neighbour vertices until it reached the maximum core. However, in many applications, particularly in biology, more valuable information can be obtained from dense sub-communities and we are not interested in small cores where vertices do not interact much with others. To make the previous PA focus more on dense subgraphs, we propose a multi-stage graph peeling algorithm (M-PA) that has a two-stage data screening procedure added before the previous PA. After removing vertices from the graph based on the user-defined thresholds, we can reduce the graph complexity largely and without affecting the vertices in subgraphs that we are interested in. We show that M-PA is more efficient than the previous PA and with the properly set filtering threshold, can produce very similar if not identical dense subgraphs to the previous PA (in terms of graph density and clustering coefficient).

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“…Then, the algorithm checks if the condition Pr(X H, △,g ≥ k) ≥ θ is satisfied for each triangle △ in H (lines [10][11][12]. At the end, the algorithm returns all g-(k, θ )-nuclei H (line [14][15][16]. sample…”

Section: Global Nucleus Decompositionmentioning

confidence: 99%

“…Also, [22] proposed the notion of global (k, η)-truss based on the probability of each edge belonging to a connected k-truss in a possible world. In [16], an approximate algorithm for the local truss decomposition is proposed to efficiently compute the tail probability of edge supports in the peeling process of [22].…”

Section: Related Workmentioning

confidence: 99%

Nucleus Decomposition in Probabilistic Graphs: Hardness and Algorithms

Esfahani¹,

Srinivasan²,

Thomo³

et al. 2020

Preprint

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Finding dense components in graphs is of great importance in analysing the structure of networks. Popular and computationally feasible frameworks for discovering dense subgraphs are core and truss decompositions. Recently, SarÄśyÃĳce et al. introduced nucleus decomposition, a generalization which uses higher-order structures and can reveal interesting subgraphs that can be missed by core and truss decompositions.In this paper, we present nucleus decomposition in probabilistic graphs. We study the most interesting case of nucleus decomposition, k-(3, 4)-nucleus, which asks for maximal subgraphs where each triangle is contained in k 4-cliques. The major questions we address are: How to define meaningfully nucleus decomposition in probabilistic graphs? How hard is computing nucleus decomposition in probabilistic graphs? Can we devise efficient algorithms for exact or approximate nucleus decomposition in large graphs?We present three natural definitions of nucleus decomposition in probabilistic graphs: local, global, and weakly-global. We show that the local version is in PTIME, whereas global and weakly-global are #P-hard and NP-hard, respectively. We present an efficient and exact dynamic programming approach for the local case and furthermore, present statistical approximations that can scale to large datasets without much loss of accuracy. For global and weaklyglobal decompositions, we complement our intractability results by proposing efficient algorithms that give approximate solutions based on search space pruning and Monte-Carlo sampling. Our extensive experimental results show the scalability and efficiency of our algorithms. Compared to probabilistic core and truss decompositions, nucleus decomposition significantly outperforms in terms of density and clustering metrics.1 Or (k − 2) triangles depending on the definition.

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Truss Decomposition on Large Probabilistic Networks using H-Index

Cited by 11 publications

References 18 publications

Truss-Based Structural Diversity Search in Large Graphs

Truss-Based Structural Diversity Search in Large Graphs

Multi-Stage Graph Peeling Algorithm for Probabilistic Core Decomposition

Nucleus Decomposition in Probabilistic Graphs: Hardness and Algorithms

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