Relating Network Topology to the Robustness of Centrality Measures

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 deteriorate and ultimately converges.

An empirical study of the Mexican banking system’s network and its implications for systemic risk

“…In order to test the robustness of centrality measures Frantz and Carley (2005) perform simulations where an initial network is generated and a copy with perturbations is created. Perturbations consist of creation and elimination of arcs and nodes.…”

“…The study reported here is similar to the one proposed in Frantz and Carley (2005). Networks with 100 nodes were generated using the Bollobas model with parameters α = 0.2, β = 0.6, γ = 0.2, δ − = 0.01, δ + = 4.45.…”

“…The arcs for elimination were selected randomly from a uniform distribution, and created arcs were also randomly created from a uniform distribution. After the perturbation of the original network, the centrality measures were computed and, in order to compare such measures, we used the criteria proposed in Frantz and Carley (2005). Such congruence measures are:…”

The robustness of keystone indices in food webs

“…We would like to answer these questions in A c c e p t e d m a n u s c r i p t 4 this study and to provide some guidance for deciding which index to choose, if the network model might include construction errors. Although these questions have already arisen in sociometry (Borgatti el al., 2006;Costenbader and Valente, 2003;Frantz and Carley, 2005) and, most recently, in connection with animal social networks (Wey et al, 2008), the findings could not be directly used in food web analysis. This is because topology, that may be substantially different in sociometric and trophic networks, affects robustness profiles of centrality measures (Frantz and Carley, 2005).…”

“…Although these questions have already arisen in sociometry (Borgatti el al., 2006;Costenbader and Valente, 2003;Frantz and Carley, 2005) and, most recently, in connection with animal social networks (Wey et al, 2008), the findings could not be directly used in food web analysis. This is because topology, that may be substantially different in sociometric and trophic networks, affects robustness profiles of centrality measures (Frantz and Carley, 2005). Moreover, these studies are not problemoriented, in the sense that apart from providing a global measure of robustness, they do not offer guidance to decide what difference in node centrality can be considered significant.…”