Vertex Centrality Reconstruction in an Inverse Problem for Information Diffusion

TL;DR

This paper introduces a novel inverse problem approach to reconstruct vertex centrality in graphs based on observed first passage times, using a boundary control method for direct computation.

Contribution

It adapts the boundary control method to efficiently reconstruct unobserved vertex centrality from diffusion data in graphs.

Findings

Algorithm successfully reconstructs vertex centrality on small graphs.

Numerical validation confirms the method's effectiveness.

Provides a new approach for inverse problems in network analysis.

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.