Achieving spectral localization of network using betweenness-based edge perturbation

• Published in: Social network analysis and mining 2020-12, Vol.10 (1), p.74, Article 74
• Main Authors: Mohapatra, Debasis, Pradhan, Soubhagya Ranjan
• Format: Article
• Language: English
• Subjects: Algorithms; Applications of Graph Theory and Complex Networks; Complex systems; Computer Science; Data Mining and Knowledge Discovery; Diffusion rate; Economics; Eigenvectors; Epidemics; Game Theory; Graphs; Humanities; Law; Localization; Methodology of the Social Sciences; Optimization; Original Article; Perturbation; Social and Behav. Sciences; Social networks; Statistics for Social Sciences
• ISSN: 1869-5450; 1869-5469
• DOI: 10.1007/s13278-020-00687-y

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.