Related papers: Detecting degree symmetries in networks

We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads…

Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…

We define a new measure of network symmetry that is capable of capturing approximate global symmetries of networks. We apply this measure to different networks sampled from several classic network models, as well as several real-world…

We give sufficient conditions under which a random graph with a specified degree sequence is symmetric or asymmetric. In the case of bounded degree sequences, our characterisation captures the phase transition of the symmetry of the random…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…

Many real networks have been found to have a rich degree of symmetry, which is a very important structural property of complex network, yet has been rarely studied so far. And where does symmetry comes from has not been explained. To…

The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…

Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…

Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy.…

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few…

Precisely quantifying the heterogeneity or disorder of a network system is very important and desired in studies of behavior and function of the network system. Although many degree-based entropies have been proposed to measure the…

Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…

Quantification of symmetries in complex networks is typically done globally in terms of automorphisms. Extending previous methods to locally assess the symmetry of nodes is not straightforward. Here we present a new framework to quantify…

Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…

Virtually all network analyses involve structural measures between pairs of vertices, or of the vertices themselves, and the large amount of symmetry present in real-world complex networks is inherited by such measures. This has practical…