Fast Matrix Computations for Pairwise and Columnwise Commute Times and Katz Scores

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

doi:10.1080/15427951.2012.625256

Cited by 45 publications

(58 citation statements)

References 37 publications

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“…Typically, it is the ranking of the centrality values that matters-we only care whether one node is more or less important than another, so the vector x ∈ R N is equivalent to βx + γ1 for any β, γ > 0. We summarize here the concepts of Katz, eigenvector and degree centrality, refering to [1,6,12,25,29] for historical details and discussions of implementation issues. We also consider the PageRank algorithm [14,20,28] which has a different feel; summarizing incoming, rather than outgoing, information, but also assigns a positive real value to each node.…”

Section: Network Centrality Measuresmentioning

confidence: 99%

Centrality Analysis for Modified Lattices

Paton¹,

Akartunalı²,

Higham³

2017

SIAM J. Matrix Anal. & Appl.

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Abstract. We derive new, exact expressions for network centrality vectors associated with classical Watts-Strogatz style "ring plus shortcut" networks. We also derive easy-to-interpret approximations that are highly accurate in the large network limit. The analysis helps us to understand the role of the Katz parameter and the PageRank parameter, to compare linear system and eigenvalue based centrality measures, and to predict the behavior of centrality measures on more complicated networks.

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Section: Network Centrality Measuresmentioning

confidence: 99%

Centrality Analysis for Modified Lattices

Paton¹,

Akartunalı²,

Higham³

2017

SIAM J. Matrix Anal. & Appl.

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“…These metrics are insufficient to detect anomalous links in dynamic and complex networks. Moreover, the complexity of computational time and memory are crucial factors to implement real applications, but the Katz index has a limitation when applied to real-world networks because its cubic time complexity O(|V | 3 ), where |V | is the number of vertices in V [3,9], which makes it infeasible for analyzing a large network. In order to solve the fundamental cubic complexity problem of the Katz measure and make the calculation more efficient for large networks, we apply a heuristic method of partial simple paths by using the maximum length as a limiting factor.…”

Section: Link Appearance Metricmentioning

confidence: 99%

“…where 0 < β < 1 is an attenuation parameter [3] ensuring that shorter paths contribute more to the score [16].…”

Section: Path-dependent Metricmentioning

confidence: 99%

Data Stream Mining Based Dynamic Link Anomaly Analysis Using Paired Sliding Time Window Data

Han

Zhang

Liao

2014

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“…In this process to approximate the commute time a conjugate gradient algorithm is used or for Katz scores a technique based on exploiting an empirical localization property of the Katz matrix is used. This method also used algorithms for personalized PageRank to compute Katz scores [6].…”

Section: Introductionmentioning

confidence: 99%

Detecting Overlapping Nodes in MLM Chain Network

2017

IJSR

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When a particular node of a network concurrently belongs to more than a few communities, overlapping communities is form which is an open challenge related to community detection. This article evaluates the state-of-the-art in overlapping community detection algorithm in MLM Chain networks. Community discovery in MLM Chain networks is an interesting problem or task in complex networks, with the number of applications, particularly in the social and information networks knowledge extraction tasks. A community which is also referred or considered as a cluster or module is usually consisting of a group of nodes with more connections between its members than between its members and the remainder of the network. Clustering of social networks is an important task for analysis. A variety of clustering algorithms have recently been given to handle data that is not linearly separable. Customary graph partitioning algorithms are be unsuccessful to get the concealed knowledge present in modular structure appear, because they impose a top-down global view of a network. Due to the difficulties in detected communities and the limitations of scalable algorithms, the problem of overlapping community detection in large networks is remains an open problem. To avoid this problem or to get rid it; we proposed a method called Detecting Overlapping Node Structure a connection based algorithm proposed for discovering high quality overlapping structures in MLM Chain networks. The main idea of this paper is to find the seed by applying algorithm and then expanding these seeds. In our method, communities are allowed to overlap because communities are formed by adding peripheral nodes to cores. Here we focus on commonly used method commonly known as the tree edit distance. a polynomial-time algorithm is used for ordered trees compute it. Proposed method is fast, very limited parameter dependent and only requires local knowledge about the network chain. Furthermore, the community structures discovered is deterministic.

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Fast Matrix Computations for Pairwise and Columnwise Commute Times and Katz Scores

Cited by 45 publications

References 37 publications

Centrality Analysis for Modified Lattices

Centrality Analysis for Modified Lattices

Data Stream Mining Based Dynamic Link Anomaly Analysis Using Paired Sliding Time Window Data

Detecting Overlapping Nodes in MLM Chain Network

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