Consistency and differences between centrality measures across distinct classes of networks (1805.02375v2)

Abstract: The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different centrality measures have been proposed, but the degree to which they offer unique information, and such whether it is advantageous to use multiple centrality measures to define node roles, is unclear. Here we calculate correlations between 17 different centrality measures across 212 diverse real-world networks, examine how these correlations relate to variations in network density and global topology, and investigate whether nodes can be clustered into distinct classes according to their centrality profiles. We find that centrality measures are generally positively correlated to each other, the strength of these correlations varies across networks, and network modularity plays a key role in driving these cross-network variations. Data-driven clustering of nodes based on centrality profiles can distinguish different roles, including topological cores of highly central nodes and peripheries of less central nodes. Our findings illustrate how network topology shapes the pattern of correlations between centrality measures and demonstrate how a comparative approach to network centrality can inform the interpretation of nodal roles in complex networks.

Centrality Measures Consistency Across Network Classes

The paper "Consistency and differences between centrality measures across distinct classes of networks" by Stuart Oldham et al. explores the complexities of centrality measures within diverse real-world networks. Addressing the core question of whether different centrality measures are unique and informative in defining node roles, the paper explores how these metrics correlate across various network types and densities. A thorough analysis is conducted on 17 centrality measures applied to 212 different networks, highlighting not only the generally positive correlations among these measures but also examining the variability driven by network topologies.

Key Findings and Methodology

The authors utilized a robust methodological approach, incorporating Spearman's correlation to examine the centrality measure correlations (CMCs) across networks. Weighted and unweighted analyses were carried out to draw distinctions between how edge weights influence CMCs. Notably, measures such as Random-Walk Closeness Centrality (RWCC) and Information Centrality (IC) demonstrated high redundancy, exhibiting correlations of nearly 1 across networks irrespective of weights. Similarly, Katz Centrality (KC) and Total Communicability Centrality (TCC) showed consistent high correlations in unweighted networks.

The investigation extended to assessing global network properties—including modularity, spectral gap, and majorization gap—to determine their influence on CMC variability. The findings indicated that modularity notably drives the divergence in CMCs across different networks, weakening the assumptions that majorization and spectral gaps are significant predictors.

Theoretical and Practical Implications

The paper's outcomes have profound theoretical implications. It challenges the predictive capacity of specific network properties like the majorization gap concerning CMCs. The empirical evidence suggests that modular structures within networks can distinctly modify how local and global centrality metrics correlate, thereby affecting the interpretation of nodal roles. Practically, these insights promote the application of a reduced set of centrality measures in network analysis, particularly where redundancy is identified, simplifying computational requirements without losing significant informational content about nodal centrality.

Furthermore, by employing hierarchical clustering of multivariate centrality profiles, the paper effectively distinguishes core nodes—those highly central across metrics—from peripheral nodes, offering a nuanced understanding of node roles across various network topologies. This has practical applications in fields like social network analysis, biology, and urban transportation networks, where understanding the pivotal roles of certain nodes could aid in strategic planning or targeted interventions.

Speculations on Future Developments

Looking forward, the research lays foundational insights for developing automated frameworks to select centrality measures based on network class and topology, optimizing the computational efficiency and interpretability of network analyses in large-scale applications like brain network mapping or infrastructure networks.

Additionally, the paper emphasizes the need for further exploration into the relationship between network modularity and CMCs, encouraging future work to refine modularity detection methods and investigate alternative clustering algorithms that may reveal more intricate node roles.

Overall, the paper by Oldham et al. significantly contributes to our understanding of how centrality measures perform across diverse networks and sets the stage for more refined and targeted network analyses in various scientific and practical domains.