Related papers: The shortest path to complex networks

The search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…

We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…

Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…

Purpose of our work is to obtain a basic understanding and comparison of the performance and structure of real Knowledge Networks, to identify strengths and weaknesses and to highlight guidelines for improvements. We selected 18 Knowledge…

Many complex networks depend upon biological entities for their preservation. Such entities, from human cognition to evolution, must first encode and then replicate those networks under marked resource constraints. Networks that survive are…

The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…

Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many…

We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with…

Knowledge about the graph structure of the Web is important for understanding this complex socio-technical system and for devising proper policies supporting its future development. Knowledge about the differences between clean and…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

The fractal nature of complex networks has received a great deal of research interest in the last two decades. Similarly to geometric fractals, the fractality of networks can also be defined with the so-called box-covering method. A network…

Complex networks are ubiquitous in nature and play a role of paramount importance in many contexts. Internet and the cyberworld, which permeate our everyday life, are self-organized hierarchical graphs. Urban traffic flows on intricate road…

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabasi-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…

Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…

An important knowledge dimension of science and technology is the extent to which their development is cumulative, that is, the extent to which later findings build on earlier ones. Cumulative knowledge structures can be studied using a…

Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of…