# Spanning tree modulus for secure broadcast games

## TL;DR

This paper explores the application of $p$-modulus theory to spanning trees, providing a probabilistic and game-theoretic framework for secure broadcast communication on graphs.

## Contribution

It introduces a novel game-theoretic interpretation of $p$-modulus for spanning trees, linking graph theory, probability, and security in broadcast games.

## Key findings

- $2$-modulus corresponds to an even distribution over spanning trees.
- A new game-theoretic model for secure broadcast using modulus.
- Framework connects graph theory with probabilistic security strategies.

## Abstract

The theory of $p$-modulus provides a general framework for quantifying the richness of a family of objects on a graph. When applied to the family of spanning trees, $p$-modulus has an interesting probabilistic interpretation. In particular, the $2$-modulus problem in this case has been shown to be equivalent to the problem of finding a probability distribution on spanning trees that utilizes the edges of the graph as evenly as possible. In the present work, we use this fact to produce a game-theoretic interpretation of modulus by employing modulus to solve a secure broadcast game.