Identifying key actors or nodes in a network is a relevant task regarding many applications. In general, the real-valued function that evaluates the nodes is called node centrality measure. Performing a relevance-based ranking on the list of nodes is also of high practical importance, since the most central nodes by a measure usually provide the highest contribution in explaining the behavior of the whole network. Stability of centrality measures against graph perturbation is an important concept, especially in the analysis of real world—often noise contaminated—datasets from different domains. In this paper, with the utilization of the formal definition of stability introduced by Segarra and Ribeiro (IEEE Trans Signal Process 64(3):543–555, 2015), we discuss three main perturbation categories and experimentally analyze the stability of several node centrality measures.

In this paper, we provide a simple forward-looking approach to compare rating methods with respect to their stability over time. Given a rating vector of entities involved in the comparison and a ranking indicated by the rating, the stability of the methods is measured by the change in rating vector and ranks of the entities over time from a forward-looking perspective. We investigate various linear algebraic rating methods and use the Euclidean distance and Kendall tau rank correlation to measure their stability in rating and ranking, respectively. The investigations are based on both rolling and expanding window approaches. We apply the methodology to sports as a widely known ranking and rating environment. The results suggest that PageRank and Massey rating methods provide better rating and ranking stability than simple methods, such as winning percentage, and more advanced ones, such as Colley’s least square and Keener’s eigenvector-based method. Finally, a simple way to examine the potential predictive power of the rating methods is also provided.

In this paper a novel ranking method which may be useful in sports like tennis, table tennis or American football, etc. is introduced and analyzed. In order to rank the players or teams, a time-dependent PageRank based method is applied on the directed and weighted graph representing game results in a sport competition. The method was examined on the results of the table tennis competition of enthusiastic sport-loving researchers of the Institute of Informatics at the University of Szeged. The results of our method were compared by several popular ranking techniques. We observed that our approach works well in general and it has a good predictive power.

In their previous work, the authors considered the concept of random spanning tree intersection of complex networks (London and Pluhár, in: Cherifi, Mantegna, Rocha, Cherifi, Micciche (eds) Complex networks and their applications XI, Springer, Cham, 2023). A simple formula was derived for the size of the minimum expected intersection of two spanning trees chosen uniformly at random. Monte Carlo experiments were run for real networks. In this paper, we provide a broader context and motivations for the concept, discussing its game theoretic origins, examples, its applications to network optimization problems, and its potential use in quantifying the resilience and modular structure of complex networks.