A Closeness- and Priority-Based Logical Study of Social Network Creation

Abstract

This paper is part of an ongoing programme on the study of the logical aspects of social network formation. It recalls the so-called social network model, discussing the properties of a notion of closeness between agents (in terms of the number of traits they have in common); then introduces an extended social network model in which different agents might assign different values to different traits, discussing the properties of the notion of weighted closeness that arises. These notions are used to define social network creation operations by means of a threshold strategy. The paper studies the properties of the social networks the updates create, providing sound and complete axiom systems for formal languages describing these updates' effects.

Comparing Social Network Dynamic Operators

“…In probabilistic models, it is usual to assume that agents who are more similar are more likely to connect than those who are less similar [23,4]. In deterministic models, this has been translated by a similarity threshold: two agents get connected as soon as they are similar enough [18,20,19,21].…”

“…Both types of changes have been addressed in logic. Indeed, a number of logical frameworks has flourished to reason about threshold-based social influence [2,6,5,16,14], and about threshold-based link formation [18,20,19,21]. Yet, to the exception of [11,15,1], either the two aspects have been treated separately [22,18,20,19,21,10], or the two types of changes have been taken to happen one after the other [19].…”

“…Indeed, a number of logical frameworks has flourished to reason about threshold-based social influence [2,6,5,16,14], and about threshold-based link formation [18,20,19,21]. Yet, to the exception of [11,15,1], either the two aspects have been treated separately [22,18,20,19,21,10], or the two types of changes have been taken to happen one after the other [19]. To our knowledge, only [1] provides a logic capturing specifically simultaneous changes of the network structure and the state of the agents.…”