Fast Katz and Commuters: Efficient Estimation of Social Relatedness in Large Networks

Esfandiar, Pooya; Bonchi, Francesco; Gleich, David F.; Greif, Chen; Lakshmanan, Laks V. S.; On, Byung-Won

doi:10.1007/978-3-642-18009-5_13

Cited by 10 publications

(4 citation statements)

References 22 publications

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“…(A) Co-authorship graphs: The vertices denote scientists, and the edges represent collaborations between co-authors of a scientific publication. The datasets include co-authorship graphs constructed from arXiv submissions in three different scientific disciplines ( H P , A P and C M ), as well as larger graphs comprising the largest connected component of the arXiv and DBLP coauthorship graphs ( X [13]…”

Section: Datasetsmentioning

confidence: 99%

Mining Large Quasi-cliques with Quality Guarantees from Vertex Neighborhoods

Konar

Sidiropoulos

2020

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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Mining dense subgraphs is an important primitive across a spectrum of graph-mining tasks. In this work, we formally establish that two recurring characteristics of real-world graphs, namely heavy-tailed degree distributions and large clustering coefficients, imply the existence of substantially large vertex neighborhoods with high edge-density. This observation suggests a very simple approach for extracting large quasi-cliques: simply scan the vertex neighborhoods, compute the clustering coefficient of each vertex, and output the best such subgraph. The implementation of such a method requires counting the triangles in a graph, which is a well-studied problem in graph mining. When empirically tested across a number of real-world graphs, this approach reveals a surprise: vertex neighborhoods include maximal cliques of non-trivial sizes, and the density of the best neighborhood often compares favorably to subgraphs produced by dedicated algorithms for maximizing subgraph density. For graphs with small clustering coefficients, we demonstrate that small vertex neighborhoods can be refined using a local-search method to "grow" larger cliques and near-cliques. Our results indicate that contrary to worst-case theoretical results, mining cliques and quasi-cliques of non-trivial sizes from real-world graphs is often not a difficult problem, and provides motivation for further work geared towards a better explanation of these empirical successes.

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Section: Datasetsmentioning

confidence: 99%

Mining Large Quasi-cliques with Quality Guarantees from Vertex Neighborhoods

Konar

Sidiropoulos

2020

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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“…Starting from the query node, the push style method propagates the proximity value to the nodes in the neighborhood of the query node, and obtains approximate proximity values for them. This basic idea has been adapted to compute the top- k nodes for effective importance [9], RoundTripRank [10], and Katz score [23]. Most of the existing local search methods cannot guarantee the exactness.…”

Section: Related Workmentioning

confidence: 99%

Efficient and Exact Local Search for Random Walk Based Top-K Proximity Query in Large Graphs

Jin

Zhang

2016

IEEE Trans. Knowl. Data Eng.

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Top-k proximity query in large graphs is a fundamental problem with a wide range of applications. Various random walk based measures have been proposed to measure the proximity between different nodes. Although these measures are effective, efficiently computing them on large graphs is a challenging task. In this paper, we develop an efficient and exact local search method, FLoS (Fast Local Search), for top-k proximity query in large graphs. FLoS guarantees the exactness of the solution. Moreover, it can be applied to a variety of commonly used proximity measures. FLoS is based on the no local optimum property of proximity measures. We show that many measures have no local optimum. Utilizing this property, we introduce several operations to manipulate transition probabilities and develop tight lower and upper bounds on the proximity values. The lower and upper bounds monotonically converge to the exact proximity value when more nodes are visited. We further extend FLoS to measures having local optimum by utilizing relationship among different measures. We perform comprehensive experiments on real and synthetic large graphs to evaluate the efficiency and effectiveness of the proposed method.

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“…Other methods are runtime-bound, sometimes using computations which are ( 3 ) or worse (matrix inversions being the most frequent offender). It should be noted that there are published methods to approximate or optimize many of the significant link prediction algorithms (Katz [13], [14], SimRank [15], [16], [17], PageRank [18], [19], etc.). While these advanced approaches may or may not make the entire Flickr graph tractable, they often come with the added costs of specialized data structures, additional preprocessing steps, or rely on assumptions that only hold for undirected graphs.…”

Section: A Extracting the Subgraphmentioning

confidence: 99%

Graph-based features for supervised link prediction

Cukierski

Hamner

Yang³

2011

The 2011 International Joint Conference on Neural Networks

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The growing ubiquity of social networks has spurred research in link prediction, which aims to predict new connections based on existing ones in the network. The 2011 IJCNN Social Network challenge asked participants to separate real edges from fake in a set of 8960 edges sampled from an anonymized, directed graph depicting a subset of relationships on Flickr. Our method incorporates 94 distinct graph features, used as input for classification with Random Forests. We present a three-pronged approach to the link prediction task, along with several novel variations on established similarity metrics. We discuss the challenges of processing a graph with more than a million nodes. We found that the best classification results were achieved through the combination of a large number of features that model different aspects of the graph structure. Our method achieved an area under the receiver-operator characteristic (ROC) curve of 0.9695, the 2nd best overall score in the competition and the best score which did not de-anonymize the dataset.

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Fast Katz and Commuters: Efficient Estimation of Social Relatedness in Large Networks

Cited by 10 publications

References 22 publications

Mining Large Quasi-cliques with Quality Guarantees from Vertex Neighborhoods

Mining Large Quasi-cliques with Quality Guarantees from Vertex Neighborhoods

Efficient and Exact Local Search for Random Walk Based Top-K Proximity Query in Large Graphs

Graph-based features for supervised link prediction

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