Mathematicians can now find the leader of a secret group just by watching how fast news hits a few random outsiders.
March 24, 2026
Original Paper
Vertex Centrality Reconstruction in an Inverse Problem for Information Diffusion
arXiv · 2603.20710
The Takeaway
Normally, finding the most influential person in a group requires a map of every connection. This algorithm proves you can pinpoint the 'mastermind' simply by measuring the exact time it takes for a rumor or signal to reach a handful of people on the network's periphery.
From the abstract
We consider an inverse problem in information diffusion modeled by random walks on combinatorial graphs. The problem concerns reconstruction of vertex centrality from the distribution of the first passage times observed on a subset of vertices. We adapt the boundary control method to obtain a direct algorithm that computes the unobserved vertex centrality. The algorithm is numerically implemented and validated on small graphs.