The Role of Second Trials in Cascades of Information over Networks

TL;DR

This paper investigates how initial and subsequent exposures influence information spread in social networks, revealing that second trials enhance propagation in dense areas while first trials explore new regions.

Contribution

It introduces a cascade model distinguishing first and subsequent contact probabilities, highlighting their different roles in network diffusion dynamics.

Findings

Second trials amplify spread in dense network regions.

First trials are crucial for exploring new network areas.

Cascade size depends non-trivially on probabilities and network structure.

Abstract

We study the propagation of information in social networks. To do so, we focus on a cascade model where nodes are infected with {probability $p_1$ after their first contact with the information and with probability $p_2$ at all subsequent contacts.} The diffusion starts from one random node and leads to a cascade of infection. It is shown that first and {subsequent} trials play different roles in the propagation and that the size of the cascade depends in a non-trivial way on $p_1$, $p_2$ and on the network structure. Second trials are shown to amplify the propagation in dense parts of the network while first trials are {dominant for the exploration of} new parts of the network and launching new seeds of infection.