Generic network sparsification via hybrid edge sampling

Network (or graph) sparsification benefits downstream graph mining tasks. Finding a sparsified subgraph $\hat{G}$ similar to the original graph $G$ is, however, challenging due to the requirement of preserving various (or at least representative) network properties. In this paper, we propose a general hybrid edge sampling scheme named LOGA, as the combination of the Local-filtering-based Random Edge sampling (LRE) (Hamann et al., 2016) and the Game-theoretic Sparsification with Tolerance (GST) (Su et al., 2022). LOGA fully utilizes the advantages of GST — in preserving complex structural properties by preserving local node properties in expectation – and LRE – in preserving the connectivity of a given network. Specifically, we first prove the existence of multiple equilibria in GST. This insight leads us to propose LOGA and its variant LOGA${}^{sc}$ by refining GST. LOGA is obtained by regarding LRE as an empirically good initializer for GST, while LOGA${}^{sc}$ is obtained by further including a constrained update for GST. In this way, LOGA/LOGA${}^{sc}$ generalize the work on GST to graphs with weights and different densities, without increasing the asymptotic time complexity. Extensive experiments on 26 weighted and unweighted networks with different densities demonstrate that LOGA${}^{sc}$ performs best for all 26 instances, i.e., they preserve representative network properties better than state-of-the-art sampling methods alone.