Information Flow Simulations in Multi-dimensional and Dynamic Systems

Abstract

AbstractThe relevance of nodes with respect to the position they have in a network is often investigated with centrality measures. In particular, in cases where it is specifically meaningful to consider nodes’ ability to cumulate and convey information, like in economic systems, betweenness centrality is one of the most pertinent options because of its underlying concept. However, this statistic presents two limitations. First, as it relies on the computation of shortest paths, it is grounded on a binary topological evaluation: every time a node is not located in the shortest path between two other nodes, it gains no score at all in its centrality (even if it is located on a path just one step longer). Second, betweenness centrality does not allow the direct analysis of multi-dimensional and dynamic networks: it has to be computed one dimension and one instant at a time, and this causes problems of comparability in case of weighted connections. The scope and the originality of this work is to design a network model that makes it possible to solve these issues. The proposed Dynamic Multi-Layer Network (DMLN) allows the structural representation of the multi-dimensional and dynamic properties of nodes’ interactions. Then, this allows the computation of a metric that, based on Infomap random walks, assesses the level of information cumulated and conveyed by nodes in any moment and in any dimension of interaction. Importantly, this is performed without relying on a binary evaluation, and by jointly taking into account what occurred in all the dimensions and during the entire period, in which the system is observed. We present and discuss an implementation based on ICT worldwide trade of goods and services in the period 2004–2014.