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Carlos Gómez-Ambrosi and Violeta Calleja-Solanas, arRxiv 2025.01.13.XXXXX

Abstract

With improvements in data resolution and quality, researchers can now construct detailed representations of complex systems as signed, weighted, and directed networks. In this article, we introduce a framework for measuring net and indirect effects without simplifying these information-rich networks. Building on a generalization of Katz centrality, this framework captures both direct and indirect interactions, the effect of the whole network on a node and its reverse, the effect of a node on the whole network, while accommodating the complexity of signed, weighted, and directed edges. To contextualize our contribution, we propose a taxonomy that unifies existing approaches and measures from the literature. We then apply our measure to ecological networks, where net and indirect effects remain critical yet difficult to quantify factors influencing coexistence. Specifically, we observe a strong correlation between negative net effects and species extinction in generalized Lotka-Volterra dynamics. Additionally, we test our framework on a real-world social network, where it effectively identifies informative importance rankings, providing insights into influence propagation and power dynamics.