Rumor centrality
Rumor centrality
quantifies the likelihood that a node is the source of information spread under the susceptible-infected (SI) model [2, 3].
For a tree-structured infected subgraph \(G_N\) of \(N\) nodes, the rumor centrality of a candidate source node \(v\) is defined as
\[
R(v, G_N) = \frac{N!}{\prod_{u \in G_N} T^v_u},
\]
where \(T^v_u\) is the number of nodes in the subtree rooted at \(u\) when the tree is rooted at \(v\). The rumor centrality
\(R(v, G_N)\) counts the number of infection sequences consistent with the SI model if \(v\) were the source.
In regular trees, maximizing \(R(v, G_N)\) yields the exact maximum-likelihood rumor source (the
rumor center
).
For irregular trees, a randomized estimator weighted by \(R(v, G_N)\) is used, and for general graphs, \(R(v, G_N)\) is approximated on the breadth-first search (BFS) tree rooted at \(v\).
Nodes with higher rumor centrality are more plausible spread origins and tend to be more influential in diffusion processes.