Sensitivity Analysis of Centralities on Unweighted Networks

Murai, Shogo; Yoshida, Yuichi

doi:10.1145/3308558.3313422

Cited by 21 publications

(12 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we used a rank correlation to quantify the robustness. Future studies may examine whether similar results occur for other measures of robustness like overlap and top metrics (Borgatti et al, 2006;Murai & Yoshida, 2019).…”

Section: Conclusion and Final Remarksmentioning

confidence: 69%

“…In the following, we focus on the degree centrality, as it is the most accessible for an analytical perspective (Platig et al, 2013;Tsugawa & Ohsaki, 2015;Murai & Yoshida, 2019). First (Section 5.1), we derive an expression for the robustness based on the interpretation of the robustness as a probability.…”

Section: Analysis and Discussion Of The Degree Centralitymentioning

confidence: 99%

See 1 more Smart Citation

On the impact of network size and average degree on the robustness of centrality measures

Martin¹,

Niemeyer²

2020

Net Sci

View full text Add to dashboard Cite

Measurement errors are omnipresent in network data. Most studies observe an erroneous network instead of the desired error-free network. It is well known that such errors can have a severe impact on network metrics, especially on centrality measures: a central node in the observed network might be less central in the underlying, error-free network. The robustness is a common concept to measure these effects. Studies have shown that the robustness primarily depends on the centrality measure, the type of error (e.g., missing edges or missing nodes), and the network topology (e.g., tree-like, core-periphery). Previous findings regarding the influence of network size on the robustness are, however, inconclusive. We present empirical evidence and analytical arguments indicating that there exist arbitrary large robust and non-robust networks and that the average degree is well suited to explain the robustness. We demonstrate that networks with a higher average degree are often more robust. For the degree centrality and Erdős–Rényi (ER) graphs, we present explicit formulas for the computation of the robustness, mainly based on the joint distribution of node degrees and degree changes which allow us to analyze the robustness for ER graphs with a constant average degree or increasing average degree.

show abstract

Section: Conclusion and Final Remarksmentioning

confidence: 69%

Section: Analysis and Discussion Of The Degree Centralitymentioning

confidence: 99%

On the impact of network size and average degree on the robustness of centrality measures

Martin¹,

Niemeyer²

2020

Net Sci

View full text Add to dashboard Cite

show abstract

“…Then, we have for any probability 0 ≤ p ≤ 1. 24and an inequality (26), it follows that the network average clustering coefficient of G ′ is underestimated with an expected relative error 1 − τ p given a set of randomly missing nodes.…”

Section: Resultsmentioning

confidence: 99%

“…The broad effects of missing network data on graph properties have long been studied 17,[21][22][23][24][25][26][27][28][29][30] . In particular, measurement errors due to incomplete data between the properties of an original network and the collected…”

mentioning

confidence: 99%

Measurement error of network clustering coefficients under randomly missing nodes

Nakajima

Shudo

2021

Sci Rep

View full text Add to dashboard Cite

The measurement error of the network topology caused by missing network data during the collection process is a major concern in analyzing collected network data. It is essential to clarify the error between the properties of an original network and the collected network to provide an accurate analysis of the entire topology. However, the measurement error of the clustering coefficient, which is a fundamental network property, has not been well understood particularly from an analytical perspective. Here we analytically and numerically investigate the measurement error of two types of clustering coefficients, namely, the global clustering coefficient and the network average clustering coefficient, of a network that is randomly missing some proportion of the nodes. First, we derive the expected error of the clustering coefficients of an incomplete network given a set of randomly missing nodes. We analytically show that (i) the global clustering coefficient of the incomplete network has little expected error and that (ii) conversely, the network average clustering coefficient of the incomplete network is underestimated with an expected error that is dependent on a property that is specific to the graph. Then, we verify the analytical claims through numerical simulations using three typical network models, i.e., the Erdős–Rényi model, the Watts–Strogatz model, and the Barabási–Albert model, and the 15 real-world network datasets consisting of five network types. Although the simulation results on the three typical network models suggest that the measurement error of the clustering coefficients on graphs with considerably small clustering coefficients may not behave like the analytical claims, we demonstrate that the simulation results on real-world networks that typically have enough high clustering coefficients sufficiently support our analytical claims. This study facilitates an analytical understanding of the measurement error in network properties due to missing graph data.

show abstract

“…A closely related problem is that of estimating eigenvector centrality without observing any edge but only signals on nodes (Roddenberry and Segarra 2019;He and Wai 2020). A different but related research direction is to question the stability of centrality measures under perturbations (Segarra and Ribeiro 2015;Han and Lee 2016;Murai and Yoshida 2019). In the case of PageRank score, and more recently for Katz centrality as well (Lin et al 2019), the focus of similar lines of research is based on the different objective of estimating single nodes' scores or approximating the external information missing for reliable within-sample estimation (Sakakura et al 2014;Chen et al 2004; Davis and Dhillon 2006), rather than estimating the relative ranking of nodes within a sample as we do here.…”

Section: Related Workmentioning

confidence: 99%

Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

Ruggeri

Bacco

2020

Appl Netw Sci

View full text Add to dashboard Cite

We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other topological quantities. Our goal is on one hand to extend the analysis of the behavior of TCEC (Ruggeri and De Bacco, in: Cherifi, Gaito, Mendes, Moro, Rocha (eds) Complex networks and their applications VIII, Springer, Cham, pp 90–101, 2020), a theoretically-grounded sampling method for eigenvector centrality estimation. On the other hand, to demonstrate more broadly how sampling can impact the estimation of relevant network properties like centrality measures different than the one aimed at optimizing, community structure and node attribute distribution. In addition, we analyze sampling behaviors in various instances of network generative models. Finally, we adapt the theoretical framework behind TCEC for the case of PageRank centrality and propose a sampling algorithm aimed at optimizing its estimation. We show that, while the theoretical derivation can be suitably adapted to cover this case, the resulting algorithm suffers of a high computational complexity that requires further approximations compared to the eigenvector centrality case. Main contributions (a) Extensive empirical analysis of the impact of the TCEC sampling method (optimized for eigenvector centrality recovery) on different centrality measures, community structure, node attributes and statistics related to specific network generative models; (b) extending TCEC to optimize PageRank estimation.

show abstract

Sensitivity Analysis of Centralities on Unweighted Networks

Cited by 21 publications

References 23 publications

On the impact of network size and average degree on the robustness of centrality measures

On the impact of network size and average degree on the robustness of centrality measures

Measurement error of network clustering coefficients under randomly missing nodes

Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

Contact Info

Product

Resources

About