Network equilibrium models represent a versatile tool for the analysis of interconnected objects and their relationships. They have been widely employed in both science and engineering to study the behavior of complex systems under various conditions, including external perturbations and damage. In this paper, network equilibrium models are revisited through graph-theory laws and attributes with special focus on systems that can sustain equilibrium in the absence of external perturbations (self-equilibrium). A new approach for the analysis of self-equilibrated networks is proposed; they are modeled as a collection of cells, predefined elementary network units that have been mathematically shown to compose any self-equilibrated network. Consequently, the equilibrium state of complex self-equilibrated systems can be obtained through the study of individual cell equilibria and their interactions. A series of examples that highlight the flexibility of network equilibrium models are included in the paper. The examples attest how the proposed approach, which combines topological as well as geometrical considerations, can be used to decipher the state of complex systems.

中文翻译：

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通过细胞建模分析自平衡网络

网络平衡模型代表了一种用于分析互连对象及其关系的通用工具。它们已被广泛应用于科学和工程领域，以研究复杂系统在各种条件下的行为，包括外部扰动和损坏。在本文中，网络均衡模型通过图论定律和属性重新审视，特别关注可以在没有外部扰动的情况下维持平衡（自平衡）的系统。提出了一种分析自平衡网络的新方法；它们被建模为一组单元格，即预定义的基本网络单元，这些单元在数学上已被证明可以构成任何自平衡网络。最后，复杂自平衡系统的平衡状态可以通过研究单个细胞的平衡及其相互作用来获得。论文中包含了一系列突出网络均衡模型灵活性的例子。这些例子证明了所提出的方法，结合了拓扑和几何考虑，可以用来破译复杂系统的状态。