Network-formation and its stability based on peripherality of nodes in social networks

Abstract

Centrality is a core concept in the field of network analysis and, therefore, much discussion is concerned with the centrality of each position (node) and less with peripherality. However, we can see that peripheral nodes are faced with a heavier burden than central nodes when expanding telecommunications, transportation, or other networks. Therefore, it is important to discuss the notion of peripherality. Peripherality measures would provide a solution for cost burdenproblems in such situations. In this paper, we propose a new peripherality measure axiomatically. Moreover, pairwise stability of networksis also discussed.