Core Discovery in Hidden Graphs

Abstract

Massive network exploration is an important research direction with many applications. In such a setting, the network is, usually, modeled as a graph $G$, whereas any structural information of interest is extracted by inspecting the way nodes are connected together. In the case where the adjacency matrix or the adjacency list of $G$ is available, one can directly apply graph mining algorithms to extract useful knowledge. However, there are cases where this is not possible because the graph is \textit{hidden} or \textit{implicit}, meaning that the edges are not recorded explicitly in the form of an adjacency representation. In such a case, the only alternative is to pose a sequence of \textit{edge probing queries} asking for the existence or not of a particular graph edge. However, checking all possible node pairs is costly (quadratic on the number of nodes). Thus, our objective is to pose as few edge probing queries as possible, since each such query is expected to be costly. In this work, we center our focus on the \textit{core decomposition} of a hidden graph. In particular, we provide an efficient algorithm to detect the maximal subgraph of $S_k$ of $G$ where the induced degree of every node $u \in S_k$ is at least $k$. Performance evaluation results demonstrate that significant performance improvements are achieved in comparison to baseline approaches.