Adaptive GraphRank: A Ground Graph-Enhanced Algorithm for Ranking Important Nodes in Social Networks
Introduction
Identifying important nodes in social networks is a critical task with significant implications for understanding network structure, information diffusion, and influence propagation. These nodes, though few in number, disproportionately impact network functionality, making their accurate identification essential for applications such as rumor control, viral marketing, and cybersecurity. Traditional ranking algorithms, including PageRank (PR) and its variants, have laid the foundation for node importance evaluation. Among them, LeaderRank (LR) introduced a ground node to enhance connectivity and improve ranking performance. However, LR and its successors still suffer from the voting bias problem, where nodes with small out-degrees disproportionately influence their neighbors by concentrating their voting power.
To address this limitation, this paper proposes Adaptive GraphRank (AGR), a novel algorithm that replaces the single ground node in LR with a multi-node ground graph. This modification provides additional pathways for small out-degree nodes to distribute their influence, mitigating voting bias. Furthermore, AGR incorporates the H-index to guide biased random walks, ensuring that resources are allocated more efficiently based on node connectivity and influence. The algorithm demonstrates superior performance in propagation, network dismantling, and robustness, making it a promising solution for real-world applications.
Background and Motivation
Social networks consist of nodes (users) and edges (relationships), where certain nodes hold more influence than others. Identifying these influential nodes is crucial for optimizing information dissemination, detecting key players in criminal networks, and managing online communities. Traditional ranking algorithms evaluate node importance based on network topology, but they often struggle with biases and inefficiencies.
PageRank (PR) was among the first algorithms to rank nodes by simulating random walks, but it suffers from dangling nodes—nodes with no outgoing edges. LeaderRank (LR) addressed this by introducing a ground node connected bidirectionally to all other nodes, ensuring network connectivity and improving convergence. Despite its advantages, LR still exhibits voting bias, where nodes with few outgoing links disproportionately influence their neighbors. For instance, a node with only one outgoing link transfers all its influence to that single neighbor, skewing the ranking.
Recent improvements, such as Weighted LeaderRank (WLR) and Adaptive LeaderRank (ALR), introduced weighted edges and H-index-based adjustments to refine the ranking process. However, these methods still rely on a single ground node, limiting their ability to fully mitigate voting bias. This paper introduces AGR, which replaces the single ground node with a multi-node ground graph, significantly reducing bias while maintaining the benefits of previous approaches.
The Adaptive GraphRank (AGR) Algorithm
AGR enhances traditional ranking methods by introducing two key innovations: a multi-node ground graph and an H-index-based biased random walk.
Ground Graph Construction
Instead of using a single ground node, AGR constructs a ground graph with multiple nodes, each bidirectionally connected to all nodes in the original network. The ground graph is generated using the Barabási-Albert (BA) model, ensuring a scale-free structure that mimics real-world networks. The internal connections of the ground graph are bidirectional, maintaining strong connectivity.
This multi-node approach provides small out-degree nodes with more pathways to distribute their influence, preventing them from concentrating their voting power on a few neighbors. For example, a node with only one outgoing link in LR would transfer all its influence to that neighbor, whereas in AGR, it can distribute influence across multiple ground graph nodes, reducing bias.
H-Index-Based Biased Random Walk
The H-index measures a node’s influence by considering both its degree and the quality of its connections. AGR uses the H-index to weight the transition probabilities in the random walk, ensuring that resources flow preferentially toward high-influence nodes. This adjustment reduces the impact of low out-degree nodes, further mitigating voting bias.
The algorithm initializes each node (except ground graph nodes) with a unit resource and iteratively updates scores based on transition probabilities derived from the H-index. The process continues until scores stabilize, producing a final ranking of node importance.
Convergence and Stability
AGR ensures convergence by constructing a strongly connected network where every node can reach every other node. The transition matrix, guided by the H-index, guarantees a unique steady-state solution, meaning the algorithm reliably produces consistent rankings.
Experimental Evaluation
To validate AGR’s performance, extensive experiments were conducted on eight real-world social networks, covering diverse domains such as criminal networks, email communications, and online communities. The evaluation focused on three key dimensions: propagation capability, network dismantling efficiency, and robustness to noise.
Propagation Simulation
Using the SIR (Susceptible-Infected-Recovered) model, the top-ranked nodes from each algorithm were used as infection sources to simulate information spread. AGR consistently outperformed LR, PR, and other baselines, demonstrating faster and broader propagation. The multi-node ground graph and H-index weighting allowed AGR to identify nodes with higher influence, leading to more effective dissemination.
Network Dismantling
The dismantling experiment measured how quickly network connectivity degraded when nodes were removed in order of their importance. AGR’s rankings led to faster disintegration of the giant connected component (GCC), indicating that its identified nodes were more critical to network stability. The algorithm’s performance was particularly strong in large-scale networks, where traditional methods struggled.
Robustness to Noise
Real-world networks often contain missing or spurious connections. To test robustness, random edges were added or removed, and the stability of rankings was assessed. AGR exhibited lower sensitivity to noise compared to ALR and other variants, thanks to the ground graph’s ability to absorb perturbations. The simplified version, GR (without H-index weighting), showed the highest robustness, confirming the ground graph’s effectiveness in noisy environments.
Parameter Analysis
Additional experiments explored the impact of ground graph size and structure. A graph with 11 nodes was found to balance propagation and dismantling performance optimally. Interestingly, the ground graph’s internal topology (e.g., random, scale-free, or small-world) had minimal impact on ranking results, suggesting that the BA model’s scale-free property is sufficient for most applications.
Real-World Case Study
AGR was applied to a university’s local area network (LAN) to identify high-risk devices based on their connectivity patterns. The algorithm’s rankings closely matched an expert-assessed risk evaluation, outperforming other methods. This case study demonstrated AGR’s practical utility in cybersecurity, where accurately identifying critical nodes can prevent cascading failures.
Conclusion
Adaptive GraphRank (AGR) addresses the voting bias problem in social network ranking algorithms by introducing a multi-node ground graph and an H-index-based biased random walk. The ground graph provides additional pathways for influence distribution, while the H-index ensures efficient resource allocation. Extensive experiments confirmed AGR’s superiority in propagation, network dismantling, and robustness, making it a versatile tool for real-world applications.
Future work could explore adaptive ground graph sizing for different network scales and investigate alternative connection schemes between the ground graph and the original network. Nevertheless, AGR represents a significant advancement in social network analysis, offering a more accurate and robust solution for identifying influential nodes.
doi.org/10.19734/j.issn.1001-3695.2024.07.0300
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