Robustness of Dynamic Social Networks

The cyclic entropy of a real virtual friendship network provides an insight on the degree of its robustness. Cyclic entropy depends on counting the number of cycles of different sizes in the network, in which a probability distribution function is resulted. Counting the number of cycles in the network is an NP problem. In this work we used a polynomial time approximation algorithm to count the number of cycles in an undirected graph that is based on regression and on a statistical mechanics approach. We used this approximation algorithm to analysis the dynamicity of a virtual social network, E-mail Messages Exchange Network (EMEN) where nodes and edges appear and disappear through time. We analyze the exact and approximated cyclic entropy variation with time as a function of the number of nodes and edges in the network. We further compare the cyclic entropy variation of the network to the traditional degree entropy variation. The purpose is to establish the robustness of the network. In addition, we study the effect of weighed links (number of interactions between users) on the analysis of such graphs. An actual friendship network is found to have cyclic entropy bounded between random and small-world networks models.