1. Applying Graph Theory to Communication and Exchange Flows
Stakeholder Network Analysis (SNA) applies mathematical graph theory to chart the informal social networks, exchange lines, and hidden communication flows between disparate stakeholder groups. By identifying “central brokers” (nodes with high betweenness centrality) and “isolated nodes,” SNA allows risk teams to figure out exactly which community influencers can pass messages efficiently across an entire ecosystem, or where information blocks exist that isolate marginalized populations. 
 
2. The Betweenness Centrality Formula
The capacity of a specific stakeholder node (v) to act as an information broker, communication gatekeeper, or structural bottleneck between other pairs of stakeholders is calculated using the Betweenness Centrality (C_B) formula.
 
Formula:

C_B(v) = Sum_for_nodes( [Sigma_st(v)] / [Sigma_st] )
 
Where:
  • Sigma_st = Total number of shortest path communication links connecting node ‘s’ to node ‘t’
  • Sigma_st(v) = The absolute number of those shortest paths that pass directly through target node ‘v’
  • The sum is evaluated for all pairs of nodes (s, t) such that s, t, and v are distinct.
 
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