Statistical test finds when networks have meaningful central nodes
Testing Central Structure for Complex Networks
Machine Learning
Summary
Sometimes networks rank their important parts even when differences happen just by chance. This paper studies whether a network truly has a special central structure or if what looks central is just natural variation. The authors propose a way to test this by comparing the network to many random versions. They check how likely the observed centrality is real by using statistics and different models of randomness. Their tests show that the chance of finding central parts depends on how the random networks are created.
What this means in practice
- •For network analysts: Identify when central nodes in networks represent statistically significant structures rather than random variation.
- •For social media data teams: Validate whether detected influential users in social networks reflect real central roles instead of noise from structural randomness.
Authors
Qilong Wu, Yuxiao Li, Simeng Zhang, Xinying Liu, Yan Liu, Zengyou He
Abstract
Centrality measures rank nodes even when the observed differences can be explained by ordinary structural variation. We therefore study a preceding question: whether a network contains a statistically identifiable central structure at all. We formulate this question as a network-level hypothesis testing issue using the adjacency spectral radius as the test statistic and estimate an empirical p-value from randomized networks generated under a specified null model. The framework is evaluated using G(N,M), Chung-Lu, and two implementations of the configuration model on simulated benchmarks and 55 real networks. Controlled experiments further vary the number and connection weights of designated central nodes while holding network size and density fixed. The results show a clear negative association between central-structure strength and the empirical p-value. They also demonstrate that rejection decisions depend substantially on the structural properties preserved by the null model: the detected network sets are not simply nested across models.