### Abstract

A simple connected undirected graph G is called a clustering coefficient locally maximizing graph if its clustering coefficient is not less than that of any simple connected graph obtained from G by rewiring an edge, that is, removing an edge and adding a new edge. In this paper, we present some new classes of clustering coefficient locally maximizing graphs. We first show that any graph composed of multiple cliques with orders greater than two sharing one vertex is a clustering coefficient locally maximizing graph. We next show that any graph obtained from a tree by replacing edges with cliques with the same order other than four is a clustering coefficient locally maximizing graph. We also extend the latter result to a more general class.

Original language | English |
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Pages (from-to) | 202-213 |

Number of pages | 12 |

Journal | Discrete Applied Mathematics |

Volume | 162 |

DOIs | |

Publication status | Published - Jan 10 2014 |

### Fingerprint

### Keywords

- Clustering coefficient
- Complex network
- Connected caveman graph

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

**New classes of clustering coefficient locally maximizing graphs.** / Fukami, Tatsuya; Takahashi, Norikazu.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 162, pp. 202-213. https://doi.org/10.1016/j.dam.2013.09.013

}

TY - JOUR

T1 - New classes of clustering coefficient locally maximizing graphs

AU - Fukami, Tatsuya

AU - Takahashi, Norikazu

PY - 2014/1/10

Y1 - 2014/1/10

N2 - A simple connected undirected graph G is called a clustering coefficient locally maximizing graph if its clustering coefficient is not less than that of any simple connected graph obtained from G by rewiring an edge, that is, removing an edge and adding a new edge. In this paper, we present some new classes of clustering coefficient locally maximizing graphs. We first show that any graph composed of multiple cliques with orders greater than two sharing one vertex is a clustering coefficient locally maximizing graph. We next show that any graph obtained from a tree by replacing edges with cliques with the same order other than four is a clustering coefficient locally maximizing graph. We also extend the latter result to a more general class.

AB - A simple connected undirected graph G is called a clustering coefficient locally maximizing graph if its clustering coefficient is not less than that of any simple connected graph obtained from G by rewiring an edge, that is, removing an edge and adding a new edge. In this paper, we present some new classes of clustering coefficient locally maximizing graphs. We first show that any graph composed of multiple cliques with orders greater than two sharing one vertex is a clustering coefficient locally maximizing graph. We next show that any graph obtained from a tree by replacing edges with cliques with the same order other than four is a clustering coefficient locally maximizing graph. We also extend the latter result to a more general class.

KW - Clustering coefficient

KW - Complex network

KW - Connected caveman graph

UR - http://www.scopus.com/inward/record.url?scp=84888001394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888001394&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2013.09.013

DO - 10.1016/j.dam.2013.09.013

M3 - Article

AN - SCOPUS:84888001394

VL - 162

SP - 202

EP - 213

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -