Community Detection in Complex Networks via Clique Conductance

Lu, Zhenqi; Wahlström, Johan; Nehorai, Arye

doi:10.1038/s41598-018-23932-z

Cited by 55 publications

(39 citation statements)

References 62 publications

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“…The per-vertex and per-edge counts are sometimes called local counts. In clustering applications, the local counts are used as vertex or edge weights, and are therefore even more useful than global counts [4,18,24,30,31,36]. Fig.…”

Section: Problem Statementmentioning

confidence: 99%

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The Power of Pivoting for Exact Clique Counting

Jain

Seshadhri

2020

Proceedings of the 13th International Conference on Web Search and Data Mining

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Clique counting is a fundamental task in network analysis, and even the simplest setting of 3-cliques (triangles) has been the center of much recent research. Getting the count of k-cliques for larger k is algorithmically challenging, due to the exponential blowup in the search space of large cliques. But a number of recent applications (especially for community detection or clustering) use larger clique counts. Moreover, one often desires local counts, the number of k-cliques per vertex/edge.Our main result is Pivoter, an algorithm that exactly counts the number of k-cliques, for all values of k. It is surprisingly effective in practice, and is able to get clique counts of graphs that were beyond the reach of previous work. For example, Pivoter gets all clique counts in a social network with a 100M edges within two hours on a commodity machine. Previous parallel algorithms do not terminate in days. Pivoter can also feasibly get local per-vertex and per-edge k-clique counts (for all k) for many public data sets with tens of millions of edges. To the best of our knowledge, this is the first algorithm that achieves such results.The main insight is the construction of a Succinct Clique Tree (SCT) that stores a compressed unique representation of all cliques in an input graph. It is built using a technique called pivoting, a classic approach by Bron-Kerbosch to reduce the recursion tree of backtracking algorithms for maximal cliques. Remarkably, the SCT can be built without actually enumerating all cliques, and provides a succinct data structure from which exact clique statistics (k-clique counts, local counts) can be read off efficiently.

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Section: Problem Statementmentioning

confidence: 99%

“…General clique counting has received much attention in recent times [1,10,13,16,17,19,21]. There is a line of recent work on exploiting clique counts for community detection and dense subgraph discovery [4,18,24,30,31,36].…”

Section: Introductionmentioning

confidence: 99%

The Power of Pivoting for Exact Clique Counting

Jain

Seshadhri

2020

Proceedings of the 13th International Conference on Web Search and Data Mining

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“…In the semantic network analysis, indicators that identify the characteristics of the network subject to analysis include "density," "degree" and "centrality" (Lu et al, 2018). Density is an indicator of how many relationships are between the nodes in the entire se- to which one node (keyword) is associated; and centrality is an indicator of how much each node constituting the semantic network is located in the center of the entire network.…”

Section: Sematic Network Between Abstractmentioning

confidence: 99%

An exploration of the knowledge structure in studies on old people physical activities in Journal of Exercise Rehabilitation: by semantic network analysis

Jeon¹,

Kim²

2020

J Exerc Rehabil

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Physical activity, a key component of maintaining health, is becoming an essential alternative in reducing medical expenses for the old people. This research was intended to analyze 51 research papers published in the Journal of Exercise Rehabilitation (JER) through semantic network analysis. The subjects of the study were the keywords that the authors of each paper used in journal search sites from 2013 to 2019. The present researcher analyzed the frequency, density, and centrality of the keywords of the indicators through semantic network analysis and then visualized them on the basis of findings using UCINET6 and the NetDraw program. Also, the researcher classified the hidden clusters by CONCOR (Convergence of iterated Correlations) analysis, which is a kind of cluster analysis. As a result, it was found that the keyword with the highest frequency was "exercise," followed by "cognition, "physical-activity," "old-women," "Korean," "fall," and "training." It was also found that most of the high-frequency keywords, such as "exercise," "cognition," "old-women," "program" and "depression" had high centrality. These keywords were classified into four clusters: (a) mental health research, (b) physical health research, (c) social behavior research, and (d) leisure efficacy research. This suggests that the old people-related research papers published in the JER have derived effective methods of maintaining physical and mental health using scientific exercise programs, and especially address the effects of exercise intervention for old women.

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“…In order to test our algorithm, we benchmark it against synthetic graphs with communities as well as some real-world graphs with known community structures. This is a natural and often used approach (see, for example, [16]). In all examples, we colour the vertices with respect to the known, ground-truth communities, but in the algorithm, we use the partition obtained via a graph clustering algorithm, as the algorithm is unsupervised.…”

Section: Datasetsmentioning

confidence: 99%

An unsupervised framework for comparing graph embeddings

Kamiński

Prałat

Théberge³

2019

Journal of Complex Networks

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Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these objectives are achieved, they are meaningful, understandable, and compressed representations of networks. They also provide more options and tools for data scientists as machine learning on graphs is still quite limited. Finally, vector operations are simpler and faster than comparable operations on graphs.The main challenge is that one needs to make sure that embeddings well describe the properties of the graphs. In particular, the decision has to be made on the embedding dimensionality which highly impacts the quality of an embedding. As a result, selecting the best embedding is a challenging task and very often requires domain experts.In this paper, we propose a "divergence score" that can be assign to various embeddings to distinguish good ones from bad ones. This general framework provides a tool for an unsupervised graph embedding comparison. In order to achieve it, we needed to generalize the well-known Chung-Lu model to incorporate geometry which is interesting on its own rights. In order to test our framework, we did a number of experiments with synthetic networks as well as real-world networks, and various embedding algorithms. each vertex such that nearby vertices are more likely to share an edge than those far from each other. In a good embedding most of the network's edges can be predicted from the coordinates of the vertices. For example, in [9] protein interaction networks are embedded in low-dimension Euclidean space. Unfortunately, in the absence of a general-purpose representation for graphs, very often graph embedding requires domain experts to craft features or to use specialized feature selection algorithms. Having said that, there are some graph embedding algorithms that work without any prior or additional information other than graph structure. However, these are randomized algorithms that are usually not so stable; that is, the outcome is often drastically different despite the fact that all the algorithm parameters remain the same.Consider a graph G = (V, E) on n vertices, and several embeddings of its vertices to some multidimensional spaces (possibly in different dimensions). The main question we try to answer in this paper is: how do we evaluate these embeddings? Which one is the best and should be used? In order to answer these questions, we propose a general framework that assigns the divergence score to each embedding which, in an unsupervised learning fashion, distinguishes good from bad embeddings. In order to benchmark embeddings, we generalize well-known Chung-Lu random graph model to incorporate geometry. The model is interesting on its own and should be useful for many other problems and tools. In order to test our algorithm, we experiment with synthetic networks as well as real-world networks, and various embedding algorithms.The paper is...

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Community Detection in Complex Networks via Clique Conductance

Cited by 55 publications

References 62 publications

The Power of Pivoting for Exact Clique Counting

The Power of Pivoting for Exact Clique Counting

An exploration of the knowledge structure in studies on old people physical activities in Journal of Exercise Rehabilitation: by semantic network analysis

An unsupervised framework for comparing graph embeddings

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