A paper I read a while ago, The Duality of Persons and Groups, demonstrates a method for building a connection graph between people based solely on their membership in groups. With this graph in place we can calculate the centrality of a person or group (some relative importance metric).
A common method for calculating graph centrality is via an iterative Eigenvector calculation, which I use in the linked repo. https://github.com/aekeus/simple-network-analysis
(More links at the end of the article)
Group Membership (Input)
Group Membership (GM) is a 6x5 matrix of 0 or 1. Rows are members, columns are groups.
Person To Person Connections
PP = GM * transpose(GM)
Group to Group Connections
GG = transpose(GM) * GM
Member Centrality A 0.214 XXXXXXXXX B 0.079 XXXX C 0.24 XXXXXXXXXX D 0.649 XXXXXXXXXXXXXXXXXXXXXXXXXX E 0.398 XXXXXXXXXXXXXXXX F 0.558 XXXXXXXXXXXXXXXXXXXXXXX Group Centrality 1 0.126 XXXXXX 2 0.455 XXXXXXXXXXXXXXXXXXX 3 0.545 XXXXXXXXXXXXXXXXXXXXXX 4 0.545 XXXXXXXXXXXXXXXXXXXXXX 5 0.427 XXXXXXXXXXXXXXXXXX
Person to person centrality
Group to group centrality