A social network matrix for implicit and explicit social network plates

A majority of social network research deals with explicitly formed social networks. Although only rarely acknowledged for its existence, we believe that implicit social networks play a significant role in the overall dynamics of social networks. We propose a framework to evaluate the dynamics and characteristics of a set of explicit and associated implicit social networks. Specifically, we propose a social network matrix to measure the implicit relationships among the entities in various social networks. We also derive several indicators to characterize the dynamics in online social networks. We proceed by incorporating implicit social networks in a traditional network flow context to evaluate key network performance indicators such as the lowest communication cost, maximum information flow, and the budgetary constraints.