物理学中的图与网络理论
Graph and Network Theory in Physics
摘要：
一本书的章节包括一些主要领域的研究图论应用于物理学。它包括凝聚态理论中的图形，如紧束缚和哈伯德模型。它遵循图论和统计物理的研究通过分析波茨模型。然后，我们考虑使用图多项式求解费曼积分，图形和电网络，振动分析网络系统和随机图。第二部分涉及复杂网络的研究，包括“小世界”模型、“无标度”模型、网络模体、中心性度量、统计力学在网络分析和网络可通信性研究中的应用以及网络社区的研究。本章的最后一章讨论了网络上的一些动力学模型，如一致性分析、耦合振子的同步和网络上的传染病模型。
英文摘要：
A book Chapter consisting of some of the main areas of research in graph theory applied to physics. It includes graphs in condensed matter theory, such as the tight-binding and the Hubbard model. It follows the study of graph theory and statistical physics by means of the analysis of the Potts model. Then, we consider the use of graph polynomials in solving Feynman integrals, graphs and electrical networks, vibrational analysis in networked systems and random graphs. The second part deals with the study of complex networks and includes the models of "small-world", "scale-freeness", network motifs, centrality measures, the use of statistical mechanics for the analysis of networks and network communicability and the study of communities in networks. The chapter is finished by considering some dynamical models on networks, such as the consensus analysis, synchronization of coupled oscillators and epidemic models on networks.
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