Inter-arrival times of message propagation on directed networks

TL;DR

This paper models message propagation on directed networks as random walks, analyzing inter-arrival times to understand dynamics similar to spam arrival, revealing non-Poissonian behavior across different network topologies.

Contribution

It introduces a novel approach to study message propagation dynamics using inter-arrival times of random walkers on directed networks, applicable to unstructured peer-to-peer and botnet networks.

Findings

Propagation is not a pure Poisson process.

Universal features observed on Poissonian networks.

Complex behavior identified on scale-free networks.

Abstract

One of the challenges in fighting cybercrime is to understand the dynamics of message propagation on botnets, networks of infected computers used to send viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We map this problem to the propagation of multiple random walkers on directed networks and we evaluate the inter-arrival time distribution between successive walkers arriving at a target. We show that the temporal organization of this process, which models information propagation on unstructured peer to peer networks, has the same features as SPAM arriving to a single user. We study the behavior of the message inter-arrival time distribution on three different network topologies using two different rules for sending messages. In all networks the propagation is not a pure Poisson process. It shows universal features on Poissonian networks and a more complex behavior on scale free networks. Results open the possibility to indirectly learn about the process of sending messages on networks with unknown topologies, by studying inter-arrival times at any node of the network.