Spectral counting of triangles via element-wise sparsification and triangle-based link recommendation

Tsourakakis, Charalampos E.; Drineas, Petros; Michelakis, Eirinaios; Koutis, Ioannis; Faloutsos, Christos

doi:10.1007/s13278-010-0001-9

Cited by 74 publications

(25 citation statements)

References 29 publications

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“…In the same direction, Davis et al [9] introduced a novel probabilistically weighted extension of the Adamic/Adar measure for heterogenous information networks. Recently, Tsourakakis et al [36] proposed a simple algorithm that for making link recommendations in online social networks by recommending those links that create as many triangles as possible.…”

Section: Related Workmentioning

confidence: 99%

Spectral clustering for link prediction in social networks with positive and negative links

Symeonidis

Mantas

2013

Soc. Netw. Anal. Min.

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Online social networks (OSNs) recommend new friends to registered users based on local features of the graph (i.e. based on the number of common friends that two users share). Real OSNs (e.g. Facebook) do not exploit all network structure. Instead, they consider only pathways of maximum length 2 between a user and his candidate friends. This can limit the accuracy of prediction. On the other hand, there are global approaches, which detect the overall path structure in a network, being computationally prohibitive for huge-size social networks. In this paper, we provide friend recommendations, by performing multi-way spectral clustering, which uses information obtained from the top few eigenvectors and eigenvalues of the normalized Laplacian matrix and computes a multi-way partition of the data. As a result, it produces a less noisy matrix, which is smaller and more compact than the original one, focusing on main linking trends of the social network. Thus, we are able to provide fast and more accurate friend recommendations. Moreover, spectral clustering compared to traditional clustering algorithms, such as k-means and DBSCAN, which assume globular (convex) regions in Euclidean space, is more flexible, in capturing the non-connected components of a social graph and a wider range of cluster geometries. We perform an extensive experimental comparison of the proposed method against existing link prediction algorithms, the k-means and two-way nCut clustering algorithms, using synthetic and three real data sets (Hi5, Facebook and Epinions). Our experimental results show that our SpectralLink algorithm outperforms the local approaches, the kmeans and two-way nCut clustering algorithms in terms of effectiveness, whereas it is more efficient than the global approaches. We show that a significant accuracy improvement can be gained by using information about both positive and negative edges.

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Section: Related Workmentioning

confidence: 99%

Spectral clustering for link prediction in social networks with positive and negative links

Symeonidis

Mantas

2013

Soc. Netw. Anal. Min.

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“…Triangle counting has emerged as an important building block in the study of social networks [23,14], identifying thematic structures of networks [7], spam and fraud detection [4], link classification and recommendation [21], and more. The triangle is an important subgraph, and the number of triangles reveals important structural information about the network.…”

Section: Introductionmentioning

confidence: 99%

Counting and sampling triangles from a graph stream

2013

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This paper presents a new space-efficient algorithm for counting and sampling triangles-and more generally, constant-sized cliques-in a massive graph whose edges arrive as a stream. Compared to prior work, our algorithm yields significant improvements in the space and time complexity for these fundamental problems. Our algorithm is simple to implement and has very good practical performance on large graphs.

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“…and is one of the main reasons which gave rise to the definitions of the transitivity ratio and the clustering coefficients of a graph in complex network analysis [27]. Triangles are used in several applications such as uncovering the hidden thematic structure of the web [13], as a feature to assist the classification of web activity [5] and for link recommendation in online social networks [36]. Furthermore, triangles are used as a network statistic in the exponential random graph model [14].…”

Section: Introductionmentioning

confidence: 99%

Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning

Kolountzakis

Peng

Tsourakakis

2010

Algorithms and Models for the Web-Graph

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Abstract. The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important real world applications such as spam detection, uncovering of the hidden thematic structure of the Web and link recommendation. Counting triangles in graphs with millions and billions of edges requires algorithms which run fast, use small amount of space, provide accurate estimates of the number of triangles and preferably are parallelizable. In this paper we present an efficient triangle counting algorithm which can be adapted to the semistreaming model [15]. The key idea of our algorithm is to combine the sampling algorithm of [34,35] and the partitioning of the set of vertices into a high degree and a low degree subset respectively as in [2], treating each set appropriately. We obtain a running time O m + m 3/2 ∆ log n tǫ 2 and an ǫ approximation (multiplicative error), where n is the number of vertices, m the number of edges and ∆ the maximum number of triangles an edge is contained. Furthermore, we show how this algorithm can be adapted to the semistreaming model with space usage O m 1/2 log n + m 3/2 ∆ log n tǫ 2 and a constant number of passes (three) over the graph stream. We apply our methods in various networks with several millions of edges and we obtain excellent results. Finally, we propose a random projection based method for triangle counting and provide a sufficient condition to obtain an estimate with low variance.

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Spectral counting of triangles via element-wise sparsification and triangle-based link recommendation

Cited by 74 publications

References 29 publications

Spectral clustering for link prediction in social networks with positive and negative links

Spectral clustering for link prediction in social networks with positive and negative links

Counting and sampling triangles from a graph stream

Efficient Triangle Counting in Large Graphs via Degree-Based Vertex Partitioning

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