A flow equation for dynamic graph control: applications to social network analysis

Abstract

[EN] Consider a model of information propagation through a network based on time -dependent directed graphs. Let us consider a pulse that starts at any node , an index-a real function acting on the nodes of the network-that represents the state of a node with respect to the transit of this signal. We present a flow-type equation to be satisfied by these indices, which allows us to unify the method for writing the mathematical formulas describing their evolution , also to define new indices for global evaluation of the information circulation process. We focus our attention on the dissemination of information through Twitter, showing that PageRank is a basic example of index satisfying the flow equation, and also that we can use the flow equation to generate new meaningful indices in a constructive way.