The Hierarchy Structure in Directed and Undirected Signed Networks

Jamal Maktoubian,Mahta Amini,Mohebollah Noori,Mehran Ghasempour-Mouziraji

doi:10.4236/ijcns.2017.1010012

Abstract

The concept of social stratification and hierarchy among human dates is back to the origin of human race. Presently, the growing reputation of social networks has given us with an opportunity to analyze these well-studied phenomena over different networks at different scales. Generally, a social network could be defined as a collection of actors and their interactions. In this work, we concern ourselves with a particular type of social networks, known as trust networks. In this type of networks, there is an explicit show of trust (positive interaction) or distrust (negative interaction) among the actors. In a social network, actors tend to connect with each other on the basis of their perceived social hierarchy. The emergence of such a hierarchy within a social community shows the manner in which authority manifests in the community. In the case of signed networks, the concept of social hierarchy can be interpreted as the emergence of a tree-like structure comprising of actors in a top-down fashion in the order of their ranks, describing a specific parent-child relationship, viz. child trusts parent. However, owing to the presence of positive as well as negative interactions in signed networks, deriving such “trust hierarchies” is a non-trivial challenge. We argue that traditional notions (of unsigned networks) are insufficient to derive hierarchies that are latent within signed networks.

Highlights

Structural analysis of complex networks has been a dynamic and challenging area of interest among researchers for the past few decades [1]
In this type of networks, there is an explicit show of trust or distrust among the actors
We argue that traditional notions are insufficient to derive hierarchies that are latent within signed networks

Summary

Introduction

Structural analysis of complex networks has been a dynamic and challenging area of interest among researchers for the past few decades [1]. Facebook is an example for undirected networks with edges depicting only mutual friendships. Another type of classification termed as the trust networks deals with nature of interactions (positive or negative) involved in social networks. In the real world, the relationships need not always be positive in nature Signed networks, capture this aspect of society allowing explicit show of trust or distrust among actors. Capture this aspect of society allowing explicit show of trust or distrust among actors They can designate others as friends or foes [8]. E-opinions, Slashdot Zoo network are some of the examples of signed networks that indicate trust/friends or distrust/foes explicitly among themselves using an edge-weight of +1 and −1 respectively. If A is connected to B as a foe, there should be an edge directed from A to B with a score of −1

Background and Prior Work

Classification of Networks

Hierarchy in Signed Networks

Interpretations of Hierarchies in Signed Network

Findings

Conclusions and Future Work