Topological properties of a time-integrated activity driven network

TL;DR

This paper analytically investigates the topological properties of integrated networks from the activity driven model, revealing how they depend on integration time and activity distribution, and confirming results with simulations.

Contribution

It provides exact and asymptotic analytical expressions for the topological features of the integrated network, extending understanding of the activity driven model.

Findings

Analytical expressions for degree distribution and clustering coefficients.

Confirmation of theoretical results through numerical simulations.

Insights into differences between model predictions and real social networks.

Abstract

Here we consider the topological properties of the integrated networks emerging from the activity driven model [Perra at al. Sci. Rep. 2, 469 (2012)], a temporal network model recently proposed to explain the power-law degree distribution empirically observed in many real social networks. By means of a mapping to a hidden variables network model, we provide analytical expressions for the main topological properties of the integrated network, depending on the integration time and the distribution of activity potential characterizing the model. The expressions obtained, exacts in some cases, the results of controlled asymptotic expansions in others, are confirmed by means of extensive numerical simulations. Our analytical approach, which highlights the differences of the model with respect to the empirical observations made in real social networks, can be easily extended to deal with improved, more realistic modifications of the activity driven network paradigm.