### 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 |

### Keywords

- Clustering coefficient
- Complex network
- Connected caveman graph

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics