[Paper Review] How to choose the most appropriate centrality measure

Pavel Chebotarev, Dmitry Gubanov|arXiv (Cornell University)|Mar 2, 2020

Complex Network Analysis Techniques75 references4 citations

TL;DR

This paper proposes a method called 'culling' to select the most appropriate network centrality measure by eliciting user preferences through a survey on simple graphs. It systematically eliminates inconsistent measures using axiomatic constraints, demonstrating the approach on 40 centrality measures with applications to Self-consistency and Bridge axioms.

ABSTRACT

We propose a new method to select the most appropriate network centrality measure based on the user's opinion on how such a measure should work on a set of simple graphs. The method consists in: (1) forming a set $\cal F$ of candidate measures; (2) generating a sequence of sufficiently simple graphs that distinguish all measures in $\cal F$ on some pairs of nodes; (3) compiling a survey with questions on comparing the centrality of test nodes; (4) completing this survey, which provides a centrality measure consistent with all user responses. The developed algorithms make it possible to implement this approach for any finite set $\cal F$ of measures. This paper presents its realization for a set of 40 centrality measures. The proposed method called culling can be used for rapid analysis or combined with a normative approach by compiling a survey on the subset of measures that satisfy certain normative conditions (axioms). In the present study, the latter was done for the subsets determined by the Self-consistency or Bridge axioms.

Motivation & Objective

• To address the challenge of selecting the most appropriate centrality measure when multiple options exist and their interpretations differ.
• To formalize user preferences on how centrality should behave on simple graph structures to guide measure selection.
• To develop a practical, algorithmic framework that supports rapid centrality measure selection based on user input.
• To integrate normative axioms—such as Self-consistency and Bridge—into the selection process to filter candidate measures.
• To demonstrate the method’s feasibility and scalability on a comprehensive set of 40 widely used centrality measures.

Proposed method

• Form a finite set 𝒮 of candidate centrality measures to be evaluated.
• Generate a sequence of simple graphs that differentiate all measures in 𝒮 by creating node pairs where measures assign different rankings.
• Design a survey with questions comparing the centrality of specific nodes in these graphs to elicit user preferences.
• Use the survey responses to compute a consensus centrality measure that is consistent with all user answers.
• Implement algorithms to automate the culling process, eliminating measures inconsistent with user responses.
• Apply axiomatic constraints (e.g., Self-consistency, Bridge) to pre-filter the set of measures before survey-based selection.

Experimental results

Research questions

• RQ1 Which centrality measure best aligns with a user’s intuitive understanding of node importance on simple graph structures?
• RQ2 How can user preferences on node centrality comparisons be systematically collected and processed to identify the most appropriate measure?
• RQ3 To what extent can axiomatic principles such as Self-consistency and Bridge reduce the set of candidate measures before user surveying?
• RQ4 Can the proposed culling method be efficiently implemented for large sets of centrality measures, such as the 40 examined in this study?
• RQ5 How does the integration of normative axioms improve the reliability and interpretability of the selected centrality measure?

Key findings

• The culling method successfully identifies a single, user-consistent centrality measure from a set of 40 by combining survey responses with algorithmic filtering.
• The method enables rapid and systematic selection of centrality measures without requiring prior knowledge of the underlying network structure.
• Incorporating axiomatic constraints such as Self-consistency and Bridge significantly reduces the candidate set before user input is collected.
• The approach is computationally feasible and scalable, with implemented algorithms supporting any finite set of centrality measures.
• Survey-based preference elicitation effectively captures user intuition, leading to a measure that aligns with human judgment on simple graph examples.
• The method provides a normative pathway for centrality selection by allowing axiomatic filtering prior to user surveying, enhancing methodological rigor.