Andrii Snarskii,
Dmytro Lande,
Oleh Dmytrenko
Relaxation Time as Unique Characteristic for Networks Clustering
// Selected Papers of the XXI International Scientific and Practical Conference
"Information Technologies and Security" (ITS 2021) Kyiv, Ukraine, December 9, 2021.
CEUR Workshop Proceedings (ceurws.org).  Vol3241.  pp 1322. ISSN 16130073.
[http://ceurws.org/Vol3241/paper2.pdf]
This paper researches new unique characteristics of networks . a network relaxation time and
an individual node relaxation time, which characterize the stability of a complex network and,
accordingly, each node separately to external perturbations. While researching of the complex
networks, it is assumed that relaxation time is the number of iterative steps of the corresponding
algorithm required to achieve the initial equilibrium numerical values of a certain characteristic
after some external perturbation. In other words, the network relaxation time for each node
characterize the resistance of a complex network and the individual node relaxation time
characterize the resistance of each node to external perturbations, accordingly. In this work, to
compute the relaxation time, the decelerated iterative HITS algorithm is used. It is shown, that
these characteristics are unique numerical characteristic of network nodes, and they can be
used to find the centroids of clusters and combine nodes into groups according to these
characteristics . for complex networks clustering. The approbation of the presented
characteristics of the relaxation time and the individual relaxation time was carried out on the
example of clustering of random networks with clearly expressed clusters. In particular, a
randomly generated matrix with dimension 30.30 and 3 clusters and a matrix with dimension
100.100 and 4 clusters were researched.
Keywords
Complex Network, Network Relaxation Time, Individual Node Relaxation Time, HITS,
PageRank, Clustering, Centroids of Clusters
