Distributed rewiring model for complex networking: The effect of local rewiring rules on final structural properties

Abstract

The study of complex networks has become an important subject over the last decades. It has been shown that these structures have special features, such as their diameter, or their average path length, which in turn are the explanation of some functional properties in a system such as its fault tolerance, its fragility before attacks, or the ability to support routing procedures. In the present work, we study some of the forces that help a network to evolve to the point where structural properties are settled. Although our work is mainly focused on the possibility of applying our ideas to Information and Communication Technologies systems, we consider that our results may contribute to understanding different scenarios where complex networks have become an important modeling tool. Using a discrete event simulator, we get each node to discover the shortcuts that may connect it with regions away from its local environment. Based on this partial knowledge, each node can rewire some of its links, which allows modifying the topology of the entire underlying graph to achieve new structural properties. We proposed a distributed rewiring model that creates networks with features similar to those found in complex networks. Although each node acts in a distributed way and seeking to reduce only the trajectories of its packets, we observed a decrease of diameter and an increase in clustering coefficient in the global structure compared to the initial graph. Furthermore, we can find different final structures depending on slight changes in the local rewiring rules.

Econophysics and sociophysics: Their milestones & challenges

“…It was then possible to obtain real-world features, like power-law degree distribution or high values of clustering coefficient. Besides, it was shown that a key to the proper scaling of the number of languages is triadic closure -type of rewiring proved to be very important in social networks [181].…”

A distributed geometric rewiring model

“…In this paper, we continue with a previous work on distributed rewiring for complex networking 10 and, we now propose a distributed geometric rewiring model that works as follows. It starts with a planar graph as initial topology, which is embedded in the Euclidean space, and then behaves as a distributed system, where nodes are agents able to exchange information through a geometric routing algorithm, called Compass Routing 11 .…”

Network generation and evolution based on spatial and opinion dynamics components

“…But while those models describe one statistics well, they fail to do the same for other measures of network properties [34]. Extensions of those models, including rewiring rules, aimed at a better description of relevant variables, have been studied [35,36,37,38,39,40]. Based on the initial ideas on how to generate Markov graphs [41], exponential random graph models [42,43,44] have been proposed as a way to generate network models that depend on known or assumed structural features.…”