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通过对社会生态网络邻域和团块复合体的 Q 分析来研究高阶相互作用的结构。

Structure of higher-order interactions in social-ecological networks through Q-analysis of their neighbourhood and clique complex.

机构信息

Department of Mathematics, School of Natural Sciences, Shiv Nadar Institution of Eminence (Deemed to be University), Greater Noida, Uttar Pradesh, India.

Department of Zoology, School of Life Sciences, Sikkim University (A Central University), Gangtok, Sikkim, India.

出版信息

PLoS One. 2024 Aug 26;19(8):e0306409. doi: 10.1371/journal.pone.0306409. eCollection 2024.

DOI:10.1371/journal.pone.0306409
PMID:39186487
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11346666/
Abstract

This paper studies higher-order interactions in social-ecological networks, which formally represent interactions within the social and ecological units of an ecosystem. Many real-world social ecosystems exhibit not only pairwise interactions but also higher-order interactions among their units. Therefore, the conventional graph-theoretic description of networks falls short of capturing these higher-order interactions due to the inherent limitations of the graph definition. In this work, a mathematical framework for capturing the higher-order interactions of a social-ecological system has been given by incorporating notions from combinatorial algebraic topology. In order to achieve this, two different simplicial complexes, the clique and the neighbourhood complex, have been constructed from a pairwise social-ecological network. As a case study, the Q-analysis and a structural study of the interactions in the rural agricultural system of southern Madagascar have been done at various structural levels denoted by q. The results obtained by calculating all the structural vectors for both simplicial complexes, along with exciting results about the participation of facets of the clique complex at different q-levels, have been discussed. This work also establishes significant theorems concerning the dimension of the neighbourhood complex and clique complex obtained from the parent pairwise network.

摘要

本文研究了社会生态网络中的高阶相互作用，这些相互作用形式上代表了生态系统中社会和生态单元内部的相互作用。许多真实的社会生态系统不仅表现出了二元相互作用，而且还表现出了单元之间的高阶相互作用。因此，由于图定义的固有局限性，传统的图论网络描述方式无法捕捉到这些高阶相互作用。在这项工作中，通过结合组合代数拓扑学的概念，提出了一种用于捕捉社会生态系统高阶相互作用的数学框架。为了实现这一点，从二元社会生态网络中构建了两个不同的单纯复形，即团复形和邻域复形。作为一个案例研究，在不同的结构水平 q 下，对马达加斯加南部农村农业系统的 Q 分析和相互作用的结构研究进行了研究。讨论了通过计算两个单纯复形的所有结构向量所获得的结果，以及关于团复形的不同 q 水平的面的参与的令人兴奋的结果。这项工作还建立了关于从父对网络获得的邻域复形和团复形的维数的重要定理。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e730/11346666/9506e992d38c/pone.0306409.g009.jpg
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Full reconstruction of simplicial complexes from binary contagion and Ising data.从二元传播和伊辛数据中对单纯复形进行完全重构。
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