A Notion of Trustworthiness Based on Centrality in a Social Network

Abstract

We develop a measure of trustworthiness for members of a social network that supports collaborative effort in a domain. Edges represent explicitly declared friendships. The measure for a person is the geometric mean of their betweenness and eigenvector centralities in their network. The focus is on ranking people according to these values, which are normalized. We show the rankings of the people in an Erdős-Renyi (ER) network according to our measures. In experiments on Barabasi-Albert (BA) and Watts-Strogatz (WS) as well as ER networks, the average differences between the maximum and the minimum trustworthiness of the people are plotted against the independent variable of each model that results in an increasing number of edges. For the ER and WS networks, this difference decreased significantly and nearly linearly vs. the independent variable, but the trustworthiness values increase: it is harder to distinguish the trustworthy from the not trustworthy when all are pretty trustworthy. For the BA networks in contrast, this spread decreased to a minimum then increased. It is conjectured that, with an increasing number of edges, how embedded hubs are in the network becomes a dominant factor while non- hubs remain not very embedded. This measure has been used in defining a protocol for a group using a distributed authentication protocol to decide whether to admit a candidate, an example of how our work provides a secure way for people to collaborate that exploits human characteristics.