The Weighted Key Player Problem for Social Network Analysis

In social network analysis, information beyond the structure of relationships between actors or players is often not used. However, such information can be vital to understanding how the network behaves. This article extends the Key Player Problem Positive (KPP-Pos) to include player and relationship weights; this extension is referred to as the Weighted Key Player Problem Positive (WKPP-Pos). This article also presents an algorithm for finding the optimal solution to the KPP-Pos and WKPP-Pos. The WKPP-Pos is developed by reformulating the KPP-Pos as ap-median problem. This formulation allows for player and relationship weights and also for players to be ineligible for inclusion in the key player set solution. Once reformulated, the optimal solution to the problem is found using an integer program. A heuristic approach for solving the problem is also presented. The WKPP-Pos is demonstrated on a selection of real-world networks, to include the Krebs' 9/11 Hijackers Trusted Prior Contacts Dataset. The WKPP-Pos presented in this article introduces a new technique extending social network analysis by including player and relationship information beyond relationship structure.