Graphs that locally maximize clustering coefficient in the space of graphs with a fixed degree sequence

Tatsuya Fukami; Norikazu Takahashi

doi:10.1016/j.dam.2016.10.002

Graphs that locally maximize clustering coefficient in the space of graphs with a fixed degree sequence

Tatsuya Fukami, Norikazu Takahashi

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

This paper studies the problem of finding graphs that locally maximize the clustering coefficient in the space of graphs with a fixed degree sequence. Such a graph is characterized by the property that the clustering coefficient cannot be increased, no matter how a single 2-switch is applied. First, an explicit formula for the amount of change in the clustering coefficient of a graph caused by a single 2-switch is given. Next, some classes of graphs with the property stated above are presented. An example of such a graph is the one obtained from a tree by replacing its edges with cliques with the same order.

Original language	English
Pages (from-to)	525-535
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	217
DOIs	https://doi.org/10.1016/j.dam.2016.10.002
Publication status	Published - Jan 30 2017

Keywords

2-switch
Clustering coefficient
Complex network

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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Fukami, T., & Takahashi, N. (2017). Graphs that locally maximize clustering coefficient in the space of graphs with a fixed degree sequence. Discrete Applied Mathematics, 217, 525-535. https://doi.org/10.1016/j.dam.2016.10.002

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