Arun Kadavankandy

Konstantin Avrachenkov, Arun Kadavankandy, Nelly Litvak

We analyse a mean-field model of Personalized PageRank on the Erdos-Renyi random graph containing a denser planted Erdos-Renyi subgraph. We investigate the regimes where the values of Personalized PageRank concentrate around the mean-field value. We also study the optimization of the damping factor, the only parameter in Personalized PageRank. Our theoretical results help to understand the applicability of Personalized PageRank and its limitations for local graph clustering.

Arun Kadavankandy, Konstantin Avrachenkov, Laura Cottatellucci et al.

In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erdős-Rényi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of two kinds of side-information. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when an effective signal-to-noise ratio (SNR) parameter falls below a threshold. In contrast, in the presence of non-trivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of the SNR parameter. We validate our results through simulations on synthetic datasets as well as on a few real world networks.