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Achieving spectral localization of network using betweenness-based edge perturbation

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Abstract

Graph is a simple but effective way to represent a complex system, where a node represents a component of the system and edge represents connection between the components. Several insights can be inferred by analyzing such graphs. In this field, optimization of spread and localization are relatively a new research domain. The objective of the spread problem is to maximize the influence, whereas localization controls the diffusion. In this paper, our focus is on the eigenvector localization of the network adjacency matrix using inverse participation ratio (IPR). In this context, we propose betweenness centrality-based perturbation (BP) to localize the network. The results show that the BP approach achieves a better localization than the existing random perturbation (RP) approach. It shows maximum IPR than RP. The performance of the approaches is evaluated using threshold rate of diffusion (τ), number of modifications and IPR. Susceptible–infected–susceptible model is used to investigate the τ value.

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Abbreviations

IPR:

Inverse participation ratio

SIS:

Susceptible–infected–susceptible

SIR:

Susceptible–infected–recovered

SI:

Susceptible–infected

RP:

Random perturbation

BP:

Betweenness centrality-based perturbation

τ :

Rate of diffusion (threshold)

NM:

Number of modifications

PEV:

Principal eigenvector

LEV:

Largest eigenvalue

IPR*:

Optimal IPR

BC:

Betweenness centrality

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Authors and Affiliations

  1. Parala Maharaja Engineering College, Berhampur, 761003, India

    Debasis Mohapatra & Soubhagya Ranjan Pradhan

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  1. Debasis Mohapatra
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  2. Soubhagya Ranjan Pradhan
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Correspondence to Debasis Mohapatra.

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Mohapatra, D., Pradhan, S.R. Achieving spectral localization of network using betweenness-based edge perturbation. Soc. Netw. Anal. Min. 10, 74 (2020). https://doi.org/10.1007/s13278-020-00687-y

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