Maintenance of Structural Hole Spanners in Dynamic Networks

TL;DR

The paper tackles maintaining Top-$k$ structural hole spanners in dynamic networks by formulating the Structural Hole Spanner Tracking (SST) problem. It introduces an efficient update mechanism that identifies affected nodes after each edge deletion and updates scores within the corresponding components, avoiding full recomputation. A fast, component-scoped computation of the pairwise connectivity score combined with a heap-based top-$k$ update drives incremental maintenance, with theoretical guidance from lemmas about bridge vs non-bridge deletions. Empirically, the method achieves speedups up to $11.89\times$ (average $3.24\times$ for $k=1$ and $6.56\times$ for $k=5$) across real networks, establishing the practicality and novelty of dynamic SH spanner tracking.

Abstract

Structural Hole (SH) spanners are the set of users who bridge different groups of users and are vital in numerous applications. Despite their importance, existing work for identifying SH spanners focuses only on static networks. However, real-world networks are highly dynamic where the underlying structure of the network evolves continuously. Consequently, we study SH spanner problem for dynamic networks. We propose an efficient solution for updating SH spanners in dynamic networks. Our solution reuses the information obtained during the initial runs of the static algorithm and avoids the recomputations for the nodes unaffected by the updates. Experimental results show that the proposed solution achieves a minimum speedup of 3.24 over recomputation. To the best of our knowledge, this is the first attempt to address the problem of maintaining SH spanners in dynamic networks.

Figures (2)

• Figure 1: Illustration of structural hole spanners.
• Figure 2: Illustration of affected and unaffected nodes due to updates in the network (a) Original network (b) Updated network.