New classes of clustering coefficient locally maximizing graphs
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...
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| Veröffentlicht in: | Discrete Applied Mathematics 2014-01, Vol.162, p.202-213 |
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| container_title | Discrete Applied Mathematics |
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| creator | Fukami, Tatsuya Takahashi, Norikazu |
| description | 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. |
| doi_str_mv | 10.1016/j.dam.2013.09.013 |
| format | Article |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Clustering Clustering coefficient Coefficients Complex network Connected caveman graph Graphs Mathematical analysis Rewiring Trees |
| title | New classes of clustering coefficient locally maximizing graphs |
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