Naslov
A note on graphs whose largest eigenvalues of the modularity matrix equals zero

Autori
Majstorović, Snježana ; Stevanović, Dragan

Izvornik
The electronic journal of linear algebra (1081-3810) 27 (2014), 256; 611-618

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Modularity matrix ; Community structure ; Largest eigenvalue ; Complete multipartite graph

Sažetak
Informally, a community within a graph is a subgraph whose vertices are more connected to one another than to the vertices outside the community. One of the most popular community detection methods is the Newman’s spectral modularity maximization algorithm, which divides a graph into two communities based on the signs of the principal eigenvector of its modularity matrix in the case that the modularity matrix has positive largest eigenvalue. Newman defined a graph to be indivisible if its modularity matrix has no positive eigenvalues. It is shown here that a graph is indivisible if and only if it is a complete multipartite graph.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA