Graph partitioning and a componentwise PageRank algorithm

Engström, Christopher; Silvestrov, Sergei

doi:10.48550/arxiv.1609.09068

Cited by 1 publication

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“…Theorem 3. If λ 1 > λ 2 and the relation in (11) holds, then as k → ∞, the rank vector for the lower component can be expressed as :…”

Section: An Overview Of the Methodsmentioning

confidence: 99%

“…Component finding: Find the strongly connected components of the graph as well as their levels in the graph. Done using a modified version of Tarjan's algorithm as described in [11,14]. The algorithm is mainly written in Matlab, but with a few selected parts which are written in C or C++ in order to improve the performance of some operations which are comparatively slow in Matlab.…”

Section: Methodsmentioning

confidence: 99%

“…In ranking problems, partitioning network structures as strongly connected components plays a crucial role in improving computational drawbacks [11]. In such a case, the corresponding components yield adjacency matrix A with a block triangular form, that is,…”

Section: Graph Partitioningmentioning

confidence: 99%

“…For details on the component finding step we refer to [11]. The main difference from Tarjan's algorithm for finding strongly connected components is a little extra bookkeeping (to store levels), as well as updating them at the appropriate steps.…”

Section: Component Findingmentioning

confidence: 99%

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Eigenvector Centrality and Uniform Dominant Eigenvalue of Graph Components

Anguzu¹,

Engström²,

Mango³

et al. 2021

Preprint

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Eigenvector centrality is one of the outstanding measures of central tendency in graph theory. In this paper we consider the problem of calculating eigenvector centrality of graph partitioned into components and how this partitioning can be used. Two cases are considered; first where the a single component in the graph has the dominant eigenvalue, secondly when there are at least two components that share the dominant eigenvalue for the graph. In the first case we implement and compare the method to the usual approach (power method) for calculating eigenvector centrality while in the second case with shared dominant eigenvalues we show some theoretical and numerical results.

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“…Theorem 3. If λ 1 > λ 2 and the relation in (11) holds, then as k → ∞, the rank vector for the lower component can be expressed as :…”

Section: An Overview Of the Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Graph Partitioningmentioning

confidence: 99%

Section: Component Findingmentioning

confidence: 99%

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