The Decay of Impact with Network Distance in Linear Diffusion Processes
Eigenvector centrality predicts influence decay in social networks...
A team of researchers (Murray-Watters, Wang, Hipp, Lakon, and Butts) has published a paper on arXiv (2604.23034) examining how influence decays across social networks. Their work focuses on linear diffusion models like the Friedkin-Johnsen model, Katz and Bonacich status scores, and network autocorrelation models. While it's long been assumed that impact through any single path falls exponentially with path length, total impact involves contributions from walks of all lengths—making the relationship nontrivial.
The authors provide an approximate solution showing that total impact between nodes is, to first order, a product of eigenvector centrality scores multiplied by an exponential decay term based on the graph's eigenvalues. Their numerical study on interpersonal networks from educational settings confirms an average exponential decline in impact strength under the linear diffusion model. This simple approximation can serve as a practical proxy for exact solutions, enabling easier modeling of social influence and status processes in various real-world networks.
- Total impact between nodes decays exponentially with network distance, driven by graph eigenvalues.
- First-order approximation uses eigenvector centrality scores multiplied by a spectral decay term.
- Numerical validation on educational interpersonal networks confirms the exponential decline pattern.
Why It Matters
Simplifies modeling influence spread in social networks, enabling scalable predictions for status and power dynamics.