Uncovering the role of elementary processes in network evolution

Abstract

The growth and evolution of networks has elicited considerable interest from the scientific community and a number of mechanistic models have been proposed to explain their observed degree distributions. Various microscopic processes have been incorporated in these models, among them, node and edge addition, vertex fitness and the deletion of nodes and edges. The existing models, however, focus on specific combinations of these processes and parameterize them in a way that makes it difficult to elucidate the role of the individual elementary mechanisms. We therefore formulated and solved a model that incorporates the minimal processes governing network evolution. Some contribute to growth such as the formation of connections between existing pair of vertices, while others capture deletion; the removal of a node with its corresponding edges, or the removal of an edge between a pair of vertices. We distinguish between these elementary mechanisms, identifying their specific role on network evolution.

A comparative analysis of the statistical properties of large mobile phone calling networks

“…The differences are of crucial interest as they might point to different mechanisms at play in mobile communication networks (and more generally in social networks) located at different parts of the world. For instance, we observed a different broadness of degree distributions, which might originate from different dynamics in social ties formation and disappearance37. The different behaviors that might explain formation and deletion of social ties indicate the presence of different elementary mechanisms governing social dynamics under different cultures and social norms.…”

Measuring microscopic evolution processes of complex networks based on empirical data

“…If Ω ≤ 1, the degree distribution is a power-law distribution with an exponential cutoff. The exponent γ is given by [12] …”

“…[12], the model of four elementary processes in network evolution was analyzed theoretically to understand the individual roles of adding and deleting nodes or links, as well as the random and preferential attachment in link creation. In this paper we will employ the model to investigate two empirical data sets: the Autonomous Systems Internet data and Scientific Collaboration data.…”

“…Section II briefly introduces the network evolution model in Ref. [12] and the empirical data sets we analyze. In Section III we present the methodology and corresponding results, especially the comparison of degree distribution between empirical data and theory.…”

“…[12], to understand the individual roles of adding and deleting processes in forming network topology, four elementary processes are included at each time step:…”