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

Abstract

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.

Layer reconstruction and missing link prediction of a multilayer network with maximum a posteriori estimation

“…Recent results in [41][42][43][44] present some methods to estimate the eigenvector centralities based on nodal data without requiring the network structure. Recall that SimHash algorithm is based on the eigenvector centrality obtained from the target layer.…”