## Section: New Results

### Network topology quality using random walks

Participant : Bruno Sericola.

This work is a collaboration with the Inria team-project Asap. We proposed in [42] a fully decentralized algorithm to provide each node with a value reflecting its connectivity quality. Comparing these values between nodes, enables to have a local approximation of a global characteristic of the graph. Our algorithm relies on an anonymous probe visiting the network in a unbiased random fashion. Each node records the time elapsed between visits of the probe which is called the return time of the random walk. Computing the standard deviation of such return times enables to approximate the conductance of the graph. Typically, this information may be used by nodes to assess their position, and therefore the fact that they are critical, in a graph exhibiting low conductance.