A FLOW EQUATION FOR DYNAMIC GRAPH CONTROL: APPLICATIONS TO SOCIAL NETWORK ANALYSIS

Abstract

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 and 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, and 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.