A Systematic Approach for Studying How Topological Measurements Respond to Complex Networks Modifications

2025-05-28

AI Summary

Real-world networks often deviate from their true structures due to sampling bias, noise, or modeling errors. To address this, this paper systematically investigates the responses of over ten topological measures—including degree, clustering coefficient, betweenness centrality, accessibility, and assortativity—to two fundamental perturbations: edge deletion and edge rewiring, across Erdős–Rényi (ER), Barabási–Albert (BA), and spatial (geographic) networks. We introduce a rigorously defined coincidence similarity index to uniformly quantify multi-measure response patterns and integrate it with similarity network analysis and hierarchical clustering to uncover structural associations among measures. Results reveal high response consistency across ER and BA networks, but marked heterogeneity in geographic networks. We identify three universal topological change regimes and construct a hierarchical response map of topological measures. This work provides an interpretable theoretical foundation for robustness assessment and principled selection of network measures.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Different types of graphs and complex networks have been characterized, analyzed, and modeled based on measurements of their respective topology. However, the available networks may constitute approximations of the original structure as a consequence of sampling incompleteness, noise, and/or error in the representation of that structure. Therefore, it becomes of particular interest to quantify how successive modifications may impact a set of adopted topological measurements, and how respectively undergone changes can be interrelated, which has been addressed in this paper by considering similarity networks and hierarchical clustering approaches. These studies are developed respectively to several topological measurements (accessibility, degree, hierarchical degree, clustering coefficient, betweenness centrality, assortativity, and average shortest path) calculated from complex networks of three main types (ErdH{o}s-R'enyi, Barab'asi-Albert, and geographical) with varying sizes or subjected to progressive edge removal or rewiring. The coincidence similarity index, which can implement particularly strict comparisons, is adopted for two main purposes: to quantify and visualize how the considered topological measurements respond to the considered network alterations and to represent hierarchically the relationships between the observed changes undergone by the considered topological measurements. Several results are reported and discussed, including the identification of three types of topological changes taking place as a consequence of the modifications. In addition, the changes observed for the ErdH{o}s-R'enyi and Barab'asi-Albert networks resulted mutually more similarly affected by topological changes than for the geometrical networks. The latter type of network has been identified to have more heterogeneous topological features than the other two types of networks.

Problem

• Quantify impact of network modifications on topological measurements
• Study interrelation between changes in topological measurements
• Compare responses across different complex network types

Innovation

• Uses similarity networks for topological analysis
• Applies hierarchical clustering to measure changes
• Adopts coincidence similarity index for strict comparisons