Motif-Based Structural Robustness of Lower- and Higher-Order Networks

XING Zhi-yao; XIANG Lin-ying

doi:10.12263/DZXB.20250683

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Motif-Based Structural Robustness of Lower- and Higher-Order Networks

PAPERS | 更新时间：2026-04-24

- Motif-Based Structural Robustness of Lower- and Higher-Order Networks
- ACTA ELECTRONICA SINICA Vol. 53, Issue 12, Pages: 4592-4606(2025)
- 作者机构：
  
  1.天津工业大学电子与信息工程学院，天津 300387
  2.天津工业大学人工智能学院，天津 300387
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62473284)
- DOI：10.12263/DZXB.20250683
  CLC： TN94;
- Received：05 August 2025，
  
  Accepted：12 December 2025，
  
  Published：25 December 2025
- 稿件说明：
移动端阅览
邢之尧, 项林英. 基于模体的高低阶网络结构鲁棒性[J]. 电子学报, 2025, 53(12): 4592-4606.

XING Zhi-yao, XIANG Lin-ying. Motif-Based Structural Robustness of Lower- and Higher-Order Networks[J]. Acta Electronica Sinica, 2025, 53(12): 4592-4606.
邢之尧, 项林英. 基于模体的高低阶网络结构鲁棒性[J]. 电子学报, 2025, 53(12): 4592-4606. DOI：10.12263/DZXB.20250683

XING Zhi-yao, XIANG Lin-ying. Motif-Based Structural Robustness of Lower- and Higher-Order Networks[J]. Acta Electronica Sinica, 2025, 53(12): 4592-4606. DOI：10.12263/DZXB.20250683

摘要

现实中的多智能体网络系统普遍处于攻击与防御相互博弈的动态环境之中.攻击方通过破坏关键节点或交互结构削弱系统功能，而防御方则采取相应的修复与重构策略以维持系统整体性能，二者交替作用，形成复杂且高度非线性的对抗演化过程.此类多智能体系统通常可抽象为复杂网络模型，其中节点表示智能体，边刻画其相互作用关系.基于传统图结构的建模方法在描述节点之间的二元交互关系方面具有较强优势，已被广泛用于网络鲁棒性分析与攻防博弈研究.然而，该类方法在刻画多智能体之间普遍存在的多元协同、群体交互以及高阶耦合行为时仍存在一定局限，难以全面反映现实系统中复杂的协作机制.近年来，随着复杂系统研究的不断深入，高阶网络建模方法逐渐受到关注，并被引入多智能体系统分析框架中.相较于传统低阶网络，高阶网络为研究多智能体系统中复杂协同行为的形成机制与演化规律提供了更加丰富的结构表征手段.在此背景下，本文从复杂网络低阶结构出发，引入高阶网络建模框架，系统研究多智能体网络在攻防博弈条件下的结构鲁棒性演化问题.首先，围绕多智能体系统可能面临的攻击与防御场景，构建多种典型的攻击与防御策略，并在此基础上分析不同策略组合对高阶网络结构鲁棒性的影响.重点考察在不同攻击模式和防御机制下，高阶网络与对应低阶网络在鲁棒性演化过程中的差异特征，以及高阶结构在提升或削弱系统抗攻击能力中的作用机理.具体而言，本文从模体结构出发，深入分析高阶网络中不同类型模体对系统整体鲁棒性的影响机制，并进一步探讨低阶网络平均度等结构参数对高阶网络鲁棒性的调节作用.研究采用数值仿真与理论分析相结合的方法，选取四类典型低阶网络模型，构建其对应的高阶网络结构.在此基础上，引入四种具有代表性的攻击策略，对智能体节点的失效过程进行模拟，系统刻画攻防交互过程中网络结构的动态演化特征.通过计算网络最大连通分支的相对规模，定量评估不同攻防策略下网络鲁棒性的变化规律.结果表明，与传统低阶网络相比，高阶网络在面对攻击时呈现出显著不同的鲁棒性响应特征.系统鲁棒性不仅依赖于节点之间的二元连接关系，还受到高阶模体结构分布以及低阶网络平均度等因素的共同影响.合理的模体组织形式和适当的低阶结构参数能够在一定程度上增强系统对攻击的抵抗能力.本文的研究结论为揭示多智能体系统中多元协同行为的鲁棒性形成机制提供了新的理论视角，同时也为高阶网络结构设计及攻防策略的优化提供了有价值的参考依据.

Abstract

Real-world multi-agent networked systems are commonly embedded in dynamic environments characterized by the interplay between attacks and defenses. Attackers aim to degrade system functionality by disrupting critical nodes or interaction structures

whereas defenders adopt corresponding repair and reconfiguration strategies to preserve overall system performance. The alternating actions of these two sides give rise to complex and highly nonlinear adversarial evolutionary processes. Such multi-agent systems are typically abstracted as complex networks

where nodes represent individual agents and edges describe their interaction relationships. Traditional graph-based modeling approaches exhibit clear advantages in characterizing pairwise interactions between nodes and have been widely employed in studies of network robustness and attack-defense games. However

these approaches encounter inherent limitations when attempting to capture the ubiquitous multi-agent coordination

group interactions

and higher-order coupling behaviors present in real-world systems

and thus fail to fully reflect the complexity of collective cooperation mechanisms. In recent years

with the rapid advancement of complex systems research

higher-order network modeling approaches have attracted increasing attention and have been incorporated into the analytical framework of multi-agent systems. Compared with conventional lower-order networks

higher-order networks provide richer structural representations for investigating the formation mechanisms and evolutionary dynamics of complex cooperative behaviors in multi-agent systems. In this context

this paper starts from lower-order network structures and introduces a higher-order network modeling framework to systematically investigate the structural robustness evolution of multi-agent networks under attack-defense games. Specifically

multiple representative attack and defense strategies are constructed to reflect realistic adversarial scenarios

and their combined effects on the structural robustness of higher-order network are systematically analyzed. Particular emphasis is placed on examining the differences in robustness evolution between higher-order networks and their corresponding lower-order counterparts under various attack modes and defense mechanisms

as well as on elucidating the role of higher-order structures in enhancing or weakening system resilience against attacks. More concretely

this study focuses on motif-based structures and conducts an in-depth analysis of how different types of motifs in higher-order networks influence overall system robustness. Furthermore

the moderating effects of lower-order structural parameters

such as the average degree of the underlying network

on higher-order network robustness are investigated. A combination of numerical simulations and theoretical analysis is employed. Four representative lower-order network models are selected to generate their corresponding higher-order network structures. On this basis

four typical attack strategies are introduced to simulate agent node failures

enabling a systematic characterization of the dynamic structural evolution of networks during attack-defense interactions. By computing the relative size of the largest connected component

the robustness variations of networks under different attack-defense strategies are quantitatively evaluated. The results demonstrate that

compared with traditional lower-order networks

higher-order networks exhibit distinctly different robustness response characteristics when subjected to attacks. System robustness depends not only on pairwise connections between nodes but is also significantly influenced by the distribution of higher-order motif structures and lower-order structural parameters such as the average degree. Appropriate motif organization and suitable lower-order structural configurations can

to some extent

enhance system resistance to attacks. The findings of this study provide a novel theoretical perspective for understanding the robustness formation mechanisms of multi-agent systems with complex cooperative behaviors and offer valuable insights for the design of higher-order network structures and the optimization of attack-defense strategies.

关键词

Keywords

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