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In this paper a weighted complex network is used to detect communities of basketball players on the basis of their performances. A sparsification procedure to remove weak edges is also applied. In our proposal, at each removal of an edge the best community structure of the "giant component" is calculated, maximizing the modularity as a measure of compactness within communities and separation among communities. The "sparsification transition" is confirmed by the normalized mutual information. In this way, not only the best distribution of nodes into communities is found, but also the ideal number of communities as well. An application to community detection of basketball players for the NBA regular season 2020–2021 is presented. The proposed methodology allows a data driven decision making process in basketball. [ABSTRACT FROM AUTHOR]

We investigate the impact of borders on the topology of spatially embedded networks. Indeed territorial subdivisions and geographical borders significantly hamper the geographical span of networks thus playing a key role in the formation of network communities. This is especially important in scientific and technological policy-making, highlighting the interplay between pressure for the internationalization to lead towards a global innovation system and the administrative borders imposed by the national and regional institutions. In this study we introduce an outreach index to quantify the impact of borders on the community structure and apply it to the case of the European and US patent co-inventors networks. We find that (a) the US connectivity decays as a power of distance, whereas we observe a faster exponential decay for Europe; (b) European network communities essentially correspond to nations and contiguous regions while US communities span multiple states across the whole country without any characteristic geographic scale. We confirm our findings by means of a set of simulations aimed at exploring the relationship between different patterns of cross-border community structures and the outreach index. [ABSTRACT FROM AUTHOR]