Relating Network Topology to the Robustness of Centrality Measures

Terrill L Frantz,Kathleen M Carley

doi:10.2139/ssrn.2726774

Abstract

Abstract : This paper reports on a simulation study of social networks that investigated how network topology relates to the robustness of measures of system-level node centrality. This association is important to understand as data collected for social network analysis is often somewhat erroneous and may, to an unknown degree, misrepresent the actual true network. Consequently, the values for measures of centrality calculated from the collected network data may also vary somewhat from those of the true network, possibly leading to incorrect suppositions. To explore the robustness, i.e., sensitivity, of network centrality measures in this circumstance, we conduct Monte Carlo experiments whereby we generate an initial network, perturb its copy with a specific type of error, then compare the centrality measures from two instances. We consider the initial network to represent a true network, while the perturbed represents the observed network. We apply a six-factor full-factorial block design for the overall methodology. We vary several control variables (network topology, size and density, as well as error type, form and level) to generate 10,000 samples each from both the set of all possible networks and possible errors within the parameter space. Results show that the topology of the true network can dramatically affect the robustness profile of the centrality measures. We found that across all permutations that cellular networks had a nearly identical profile to that of uniform-random networks, while the core-periphery networks had a considerably different profile. The centrality measures for the core-periphery networks are highly sensitive to small levels of error, relative to uniform and cellular topologies. Except in the case of adding edges, as the error increases, the robustness level for the 3 topologies deteriorates and ultimately converges.

Highlights

The term robustness as it pertains to social networks has two related, albeit different connotations
While we present only selected charts chosen to augment the five observations, the entire set of result-data tables for the 100/50% true network experiments are provided in the Appendix and the data for all experiments are available from the authors
We consider this approach suitable since the 100/50% case provides a neutral configuration for comparing the sensitivity of the centrality measures; Borgatti, Carley and Krackhardt establish that when evaluating robustness 50% density is an impartial point relative to the type of errors

Summary

Introduction

The term robustness as it pertains to social networks has two related, albeit different connotations. The robustness of a network, is concerned with the reliability (Kim & Médard, 2004) and continued functioning of a network following an intervention. The robustness of a network is relevant in communication-type and flow-oriented networks. The purpose for understanding robustness of a network has more of a management of the network connotation. Another connotation of the term robustness—the one in which we are primarily concerned —is the robustness of the measures of a network. Studying the robustness of a measure of a network can be referred to as conducting a sensitivity analysis on the measure. In keeping with the terminology of the most-recently published research in this area, in lieu of using the term sensitivity, we too will use the robustness term, the terms can be used interchangeably

Methods

Results

Discussion

Conclusion