Planted clique recovery in random geometric graphs
This addresses anomaly detection in network analysis, though it appears incremental as it compares two existing algorithmic approaches.
The paper tackles the problem of identifying planted cliques in random geometric graphs, showing that exact recovery is achieved with high probability as graph size increases, with the common neighbors algorithm significantly outperforming the vertex degrees algorithm.
We investigate the problem of identifying planted cliques in random geometric graphs, focusing on two distinct algorithmic approaches: the first based on vertex degrees (VD) and the other on common neighbors (CN). We analyze the performance of these methods under varying regimes of key parameters, namely the average degree of the graph and the size of the planted clique. We demonstrate that exact recovery is achieved with high probability as the graph size increases, in a specific set of parameters. Notably, our results reveal that the CN-algorithm significantly outperforms the VD-algorithm. In particular, in the connectivity regime, tiny planted cliques (even edges) are correctly identified by the CN-algorithm, yielding a significant impact on anomaly detection. Finally, our results are confirmed by a series of numerical experiments, showing that the devised algorithms are effective in practice.