arXiv subjects

Enric Monsó

Publications and source records attributed to Enric Monsó.

2 recordsLinked to original sources

arXiv2026

Principal Component Analysis and Power Indices

Measuring the influence of a player in a simple game is a widely studied topic. Shapley-Shubik power index is perhaps the maximum exponent in terms of relevance. Furthermore, other power indexes have been proposed over time. In this paper, we propose yet another power index, defined in terms of winning coalitions. We show that this index coincides with eigenvalues obtained with the Principal Component Analysis method, a broadly used technique in data science to determine the influence of different features given a dataset. Furthermore, we provide a characterization of this proposed index in terms of four properties.

cs.GT↗

arXiv2016

Effective resistances and Kirchhoff Index in subdivision networks

We define a subdivision network $Γ^S$ of a given network $Γ,$ by inserting a new vertex in every edge, so that each edge is replaced by two new edges with conductances that fulfill electrical conditions on the new network. In this work, we firstly obtain an expression for the Green kernel of the subdivision network in terms of the Green kernel of the base network. Moreover, we also obtain the effective resistance and the Kirchhoff index of the subdivision network in terms of the corresponding parameters on the base network. Finally, as an example, we carry out the computations in the case of a wheel.

math.CO↗