Measuring net effects in signed ecological and social network (2501.09190v1)

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.

• The paper introduces a generalized Katz measure framework that quantifies both direct and indirect net effects, integrating sign, weight, and direction in network analysis.
• The methodology employs three rescaling approaches, including a PageRank-inspired and a reverse PageRank method, to ensure convergence and capture nuanced node influences.
• Applications in ecology and social networks reveal that negative net effects correlate with species extinction and emerging social hierarchies, offering predictive insights.

Overview of "Measuring net effects in signed ecological and social networks"

The paper "Measuring net effects in signed ecological and social networks" by Carlos Gómez-Ambrosi and Violeta Calleja-Solanas ventures into the intricate domain of signed, weighted, and directed networks. This paper introduces an exhaustive framework designed to quantify net and indirect effects within complex systems, expanding on the classical Katz centrality measure. The framework is versatile, applicable to ecological and social networks, thus providing profound insights into species coexistence and influence propagation.

Framework and Methodology

The authors endeavor to address the complexities of capturing direct and indirect interactions in signed and weighted networks. By introducing a generalized Katz measure, the framework uses the network's structure to assess node influence bi-directionally: the impact of the network on a node and the node's impact on the network. This approach encompasses signed, weighted, and directed edges, thereby offering a broader perspective than traditional centrality measures.

The paper organizes a taxonomy of current measures, contextualizing their contribution within the broader literature. Three rescaling approaches for the interaction matrix are presented to ensure mathematical convergence and practicality: a global rescaling akin to Katz's original method, a PageRank-inspired local rescaling, and a reverse PageRank approach for network effect symmetry. These methodologies enable quantification of cumulative direct and indirect effects on node dynamics over the network.

Ecological Applications

Applying the framework to ecological networks highlights its ability to elucidate biological interactions that influence species persistence. Through generalized Lotka-Volterra (GLV) dynamics, the paper establishes a correlation between negative net effects and species extinction probabilities. This is a pivotal insight in ecological dynamics, as it highlights the potential for structural network attributes to predict long-term species viability. The paper's simulation results demonstrate that species with negative Katz net effects are prone to extinction, a finding with substantial implications for biodiversity conservation strategies.

Social Network Analysis

In social systems, the framework adeptly measures influence propagation and power dynamics among agents. The application to a well-documented social network—the Sampson monastery—demonstrates the framework's effectiveness in capturing nuanced social hierarchies and influence patterns. By computing and comparing different centrality measures, the research underscores scenarios where indirect influence plays a significant role, such as echo chambers and social cohesion.

Implications and Future Directions

The paper's introduction of a generalized centrality measure signifies a significant advancement in the quantitative analysis of complex networks. The ability to incorporate sign, weight, and direction into the analysis enhances the granularity and scope of structural insights obtainable from network data. The practical applicability to ecological predictions and social influence mapping opens numerous avenues for future research across various domains, including economics and epidemiology.

Further exploration could involve validating the framework with empirical datasets depicting real-world interactions, thereby enhancing the model’s robustness and application potential. Additionally, examining the interplay between structural network attributes and dynamic processes in ecological networks could lead to critical insights into community assembly and species coexistence dynamics.

In conclusion, the framework proposed by Gómez-Ambrosi and Calleja-Solanas is a substantial step forward in the analysis of signed ecological and social networks, providing a robust method for measuring net effects and offering significant implications for both theoretical exploration and practical applications.