Network as a computer: ranking paths to find flows

TL;DR

This paper introduces a mathematical model using Markov chains to analyze network computation, focusing on ranking paths to identify communities and understand data flow biases in complex networks.

Contribution

It extends ranking methods from nodes to paths, enabling extraction of flow biases and semantic content from network data without uniform structure.

Findings

Path ranking reveals flow biases in networks

Community detection correlates with data semantics

Method applicable to diverse network types

Abstract

We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social networks, and so on. The main problem of interaction with such spontaneously evolving computational systems is that the data are not uniformly structured. An interesting approach is to try to extract the semantical content of the data from their distribution among the nodes. A concept is then identified by finding the community of nodes that share it. The task of data structuring is thus reduced to the task of finding the network communities, as groups of nodes that together perform some non-local data processing. Towards this goal, we extend the ranking methods from nodes to paths. This allows us to extract some information about the likely flow biases from the available static information about the network.