Fraction of Connections Among Friends of Friends as a New Metric for Network Analysis

Abstract

Network generation models try to mimic real world networks. Basic models of network generation like Random and Preferential Attachment result in networks without communities and having clustering coefficients less than that of real networks. We have proposed an alternative model to generate network having high clustering coefficient as well as community structure. We have included two new features in our model to achieve this. They are: $i$) to allow a person to make friends in iterations and ii) to make a particular fraction (say f) of links among friends of friends and rest among others. By preferring the connections among friends of friends, the clustering coefficient increases. By varying the fraction f, we can generate network with desired clustering coefficient. The proposed model has certain interesting properties. it generates community structure where number of communities and their interconnectedness can also be controlled by varying f. Finally, network size, and fraction $f$ are deciding the value of clustering coefficient of the network and responsible for having communities.