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Andrei M. Raigorodskii

Publications and source records attributed to Andrei M. Raigorodskii.

4 recordsLinked to original sources
arXiv2026

Topological measures in weighted hypergraphs

Higher-order interactions introduce an additional structural dimension to complex networks, requiring consistent generalizations of classical topological measures. In hypergraphs, the definition of distance between nodes is not unique: beyond the conventional measure derived from clique projection, an alternative formulation that explicitly incorporates the sizes of hyperedges, those of their intersection and their weights has been recently proposed. Here, we generalize three distance-based topological measures, namely closeness centrality, betweenness centrality and node eccentricity, using this new hypergraph distance. Trough tractable illustrative examples, we demonstrate that the differences between results obtained with the two distances are systematic and arise from structurally meaningful features of the higher-order networks. Also, analyzing a series of real-world datasets, we show that hypergraphs can be divided into three distinct classes, corresponding to the possible dominance of specific orders of interaction over their general metric structure. This provides practical guidance on the possibility of limiting the analysis to only some specific interaction orders, reducing its complexity while maintaining the full information of the system.

physics.soc-ph↗
arXiv2023

A note on Borsuk's problem in Minkowski spaces

In 1993, Kahn and Kalai famously constructed a sequence of finite sets in $d$-dimensional Euclidean spaces that cannot be partitioned into less than $(1.203\ldots+o(1))^{\sqrt{d}}$ parts of smaller diameter. Their method works not only for the Euclidean, but for all $\ell_p$-spaces as well. In this short note, we observe that the larger the value of $p$, the stronger this construction becomes.

math.MG↗
arXiv2022

Vector Centrality in Hypergraphs

Identifying the most influential nodes in networked systems is of vital importance to optimize their function and control. Several scalar metrics have been proposed to that effect, but the recent shift in focus towards network structures which go beyond a simple collection of dyadic interactions has rendered them void of performance guarantees. We here introduce a new measure of node's centrality, which is no longer a scalar value, but a vector with dimension one lower than the highest order of interaction in a hypergraph. Such a vectorial measure is linked to the eigenvector centrality for networks containing only dyadic interactions, but it has a significant added value in all other situations where interactions occur at higher-orders. In particular, it is able to unveil different roles which may be played by the same node at different orders of interactions -- information that is otherwise impossible to retrieve by single scalar measures. We demonstrate the efficacy of our measure with applications to synthetic networks and to three real world hypergraphs, and compare our results with those obtained by applying other scalar measures of centrality proposed in the literature.

physics.soc-ph↗