Discovering Top-k Structural Hole Spanners in Dynamic Networks

TL;DR

The paper tackles SHS discovery in dynamic networks, formalizing the Structural Hole Spanner Tracking (SST) problem and proving exact Top-$k$ SHS discovery is NP-hard. It proposes Tracking-SHS, an efficient greedy algorithm that updates Top-$k$ SHSs by focusing on affected nodes and reusing prior computations, along with GNN-SHS, a Graph Neural Network model trained to predict SHSs across snapshots for rapid inference. Theoretical analysis shows speedups (e.g., up to $1.6\times$ in certain graph families), and extensive experiments on real and synthetic data demonstrate substantial runtime improvements over naive recomputation, with GNN-SHS achieving extremely large speedups (up to $2996.9\times$) while maintaining high accuracy. The work provides a scalable, practical framework for monitoring SHS roles in evolving networks, with potential applications in information diffusion, central governance, and strategic network interventions.

Abstract

Structural Hole (SH) theory states that the node which acts as a connecting link among otherwise disconnected communities gets positional advantages in the network. These nodes are called Structural Hole Spanners (SHS). Numerous solutions are proposed to discover SHSs; however, most of the solutions are only applicable to static networks. Since real-world networks are dynamic networks; consequently, in this study, we aim to discover SHSs in dynamic networks. Discovering SHSs is an NP-hard problem, due to which, instead of discovering exact k SHSs, we adopt a greedy approach to discover Top-k SHSs. We first propose an efficient Tracking-SHS algorithm for updating SHSs in dynamic networks. Our algorithm reuses the information obtained during the initial runs of the static algorithm and avoids the recomputations for the nodes unaffected by the updates. Besides, motivated from the success of Graph Neural Networks (GNNs) on various graph mining problems, we also design a Graph Neural Network-based model, GNN-SHS, to discover SHSs in dynamic networks, aiming to reduce the computational cost while achieving high accuracy. We provide a theoretical analysis of the Tracking-SHS algorithm, and our theoretical results prove that for a particular type of graphs, such as Preferential Attachment graphs [1], Tracking-SHS algorithm achieves 1.6 times of speedup compared with the static algorithm. We perform extensive experiments, and our results demonstrate that the Tracking-SHS algorithm attains a minimum of 3.24 times speedup over the static algorithm. Also, the proposed second model GNN-SHS is on an average 671.6 times faster than the Tracking-SHS algorithm.

Figures (8)

• Figure 1: Structural Hole Spanners in the network.
• Figure 2: Comparison of various centrality measures.
• Figure 3: Embedding of node $i$.
• Figure 4: Illustration of snapshots of graph.
• Figure 5: Illustration of affected and unaffected nodes due to updates in the network (a) Original network (b) Updated network.

Theorems & Definitions (15)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Theorem 1: Dinh et al. dinh2011new
• Definition 5
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4