Comparing Social Network Dynamic Operators

TL;DR

This paper introduces a logic with dynamic operators to model asynchronous and synchronous changes in social networks, demonstrating their differences and conditions under which they can be reduced to each other.

Contribution

It presents a novel logic framework for reasoning about both asynchronous and synchronous social network dynamics, and characterizes when these operators can be interchanged.

Findings

Synchronous operators cannot generally be replaced by asynchronous ones.

The logic captures both opinion and network structure changes.

Conditions are identified under which synchronous changes can be simulated asynchronously.

Abstract

Numerous logics have been developed to reason either about threshold-induced opinion diffusion in a network, or about similarity-driven network structure evolution, or about both. In this paper, we first introduce a logic containing different dynamic operators to capture changes that are 'asynchronous' (opinion change only, network-link change only) and changes that are 'synchronous' (both at the same time). Second, we show that synchronous operators cannot, in general, be replaced by asynchronous operators and vice versa. Third, we characterise the class of models on which the synchronous operator can be reduced to sequences of asynchronous operators.