Related papers: On Automorphism Groups of Networks
We show that, in contrast to classical random graph models, many real-world complex systems -- including a variety of biological regulatory networks and technological networks such as the internet -- spontaneously self-organize to a richly…
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,…
Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many…
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…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…
We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Data-driven analysis of large social networks has attracted a great deal of research interest. In this paper, we investigate 120 real social networks and their measurement-calibrated synthetic counterparts generated by four well-known…
Urban road networks are typical complex systems, which are crucial to our society and economy. In this study, topological characteristics of a number of urban road networks based on purely physical roads rather than routes of vehicles or…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…