Roles of clustering properties for degree-mixing pattern networks

The clustering coefficients have been extensively investigated for analyzing the local structural properties of complex networks. In this paper, the clustering coefficients for triangle and square structures, namely C3 and C4, are introduced to measure the local structure properties for different degree-mixing pattern networks. Firstly, a network model with tunable assortative coefficients is introduced. Secondly, the comparison results between the local clustering coefficients C3(k) and C4(k) are reported, one can find that the square structures would increase as the degree k of nodes increasing in disassortative networks. At the same time, the Pearson coefficient p between the clustering coefficients C3(k) and C4(k) is calculated for networks with different assortative coefficients. The Pearson coefficient p changes from −0.5 to 0.98 as the assortative coefficient r increasing from −0.5 to 0.45, which suggests that the triangle and square structures have the same growth trend in assortative networks whereas the opposite one in disassortative networks. Finally, we analyze the clustering coefficients 〈C3〉 and 〈C4〉 for networks with tunable assortative coefficients and find that the clustering coefficient 〈C3〉 increases from 0.0038 to 0.5952 while the clustering coefficient 〈C4〉 increases from 0.00039 to 0.005, indicating that the number of cliquishness of the disassortative networks is larger than that of assortative networks.