相关论文: Network synchronizability analysis: the theory of …

Graph theoretical approach has proved an effective tool to understand, characterize and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the…

Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…

In this letter, we propose high order layered complex networks. The synchronization is discussed in detail. The relations of synchronization, individual coupling matrices and the intrinsic function of the uncoupled system are given. As…

A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…

In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…

The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…

We show that the degree distributions of graphs do not suffice to characterize the synchronization of systems evolving on them. We prove that, for any given degree sequence satisfying certain conditions, there exists a connected graph…

Whether comparing networks to each other or to random expectation, measuring dissimilarity is essential to understanding the complex phenomena under study. However, determining the structural dissimilarity between networks is an ill-defined…

Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as…

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

The contradiction between the fact that many empirical networks possess power-law degree distribution and the finding that network of heterogeneous degree distribution is difficult to synchronize has been a paradox in the study of network…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…

A new family of graphs, {\it entangled networks}, with optimal properties in many respects, is introduced. By definition, their topology is such that optimizes synchronizability for many dynamical processes. These networks are shown to have…

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of…

In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…

The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…

We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…

Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…

We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…