Complexity and heterogeneity in a dynamic network. (March 2018) - Lambert, David; Vanni, Fabio
Abstract: We present an approximate analytical solution for the connectivity of a network model with a "non-simultaneous" linking scheme. This model exhibits node-space correlations in the link distribution, anomalous fluctuations in the time series of the connectivity variable, and a finite-size effect: the maximum number of links occurs away from the critical value of the system parameter. We derive an exact Master Equation for this model in the form of an infinitesimal time-evolution operator. Fluctuations are much more important than the mean-field approximation predicts, which we attribute to the heterogeneity in the model. Finally, we give a sketch of possible real world applications where the value of a network is related to the number of links.