标题： 图与复杂网络中的通信熔化 显示英文标题

标题： Communication Melting in Graphs and Complex Networks

摘要： 复杂网络是许多复杂系统中相互作用的代表性图。通常，这些相互作用是系统单元之间通信/扩散通道的抽象。真实的复杂网络，例如交通网络，表现出由系统动态应力所支配的不同运行阶段。在这里，我们展示了如何利用可传递性这一拓扑描述符，该描述符通过这些扩散路径揭示网络功能的效率，从而揭示上述转变。通过考虑在给定温度（应力）下图/网络中节点和边的振动模型，我们表明可传递性函数在谐波振子网络中起着热格林函数的作用。随后，我们分析证明了每个简单图的可传递性结构中存在普遍的相变。这种转变类似于固体中的熔化过程。例如，类似于晶体的规则图在较低温度下熔化，并且在连接结构与断开结构之间表现出比类似非晶固体的随机空间图更尖锐的转变。最后，我们计算研究了某些现实世界网络中的图熔化过程，并观察到图的熔化速率随着反温度呈指数或幂律变化。在局部层面，我们发现节点熔化的主驱动因素是相应节点的特征向量中心性，特别是在反温度的关键值接近零时。这些普遍结果为许多在网络中呈现转变的动态扩散过程提供了见解，如交通堵塞、通信丢失或故障级联。 显示英文摘要

摘要： Complex networks are the representative graphs of interactions in many complex systems. Usually, these interactions are abstractions of the communication/diffusion channels between the units of the system. Real complex networks, e.g. traffic networks, reveal different operation phases governed by the dynamical stress of the system. Here we show how, communicability, a topological descriptor that reveals the efficiency of the network functionality in terms of these diffusive paths, could be used to reveal the transitions mentioned. By considering a vibrational model of nodes and edges in a graph/network at a given temperature (stress), we show that the communicability function plays the role of the thermal Green's function of a network of harmonic oscillators. After, we prove analytically the existence of a universal phase transition in the communicability structure of every simple graph. This transition resembles the melting process occurring in solids. For instance, regular-like graphs resembling crystals, melts at lower temperatures and display a sharper transition between connected to disconnected structures than the random spatial graphs, which resemble amorphous solids. Finally, we study computationally this graph melting process in some real-world networks and observe that the rate of melting of graphs changes either as an exponential or as a power-law with the inverse temperature. At the local level we discover that the main driver for node melting is the eigenvector centrality of the corresponding node, particularly when the critical value of the inverse temperature approaches zero. These universal results sheds light on many dynamical diffusive-like processes on networks that present transitions as traffic jams, communication lost or failure cascades.