Clustering Coefficient Of A Class Of Evolving Network With Clustering Preferential Attachment

Many complex systems can be described by complex network. In recent years, the researchof complex network becomes popular. The close relation between the network topology andnetwork behavior makes the formation mechanism of complex network features become aresearch focus. Many empirical studies showed that scale-free behavior of the degree distributionand high clustering properties are important features of the complex network. However, themathematical characterization of the clustering coefficient is a difficulty of complex networkresearch, and there is no efficient mathematical expression to calculate the clustering coefficientyet.In order to describe the clustering coefficient of complex network, we investigate a class ofevolving network with clustering preferential connection and degree preferential attachment. Inthis model, at each operation step, a new node with two edges is added into the network, and itstwo edges are linked to the previous network by clustering preferential connection and degreepreferential attachment respectively. By mathematical derivation, the degree, the sum ofneighbors’ degree and the number of edges between neighbors of an arbitrary node at time t and itsclustering coefficient are obtained. Based on these, the degree distribution and the accurateexpression of clustering coefficient of evolving network are given as well. Then, we illustrate thatthe clustering coefficient expression is consistent with the simulation result.