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The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
Social networks are of interest to researchers in part because they are thought to mediate the flow of information in communities and organizations. Here we study the temporal dynamics of communication using on-line data, including e-mail…
For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the…
From interacting cellular components to networks of neurons and neural systems, interconnected units comprise a fundamental organizing principle of the nervous system. Understanding how their patterns of connections and interactions give…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
The study of human interactions is of central importance for understanding the behavior of individuals, groups and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links and we…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…
Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
Driven by growing interest in the sciences, industry, and among the broader public, a large number of empirical studies have been conducted in recent years of the structure of networks ranging from the internet and the world wide web to…
Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has…
This chapter provides an overview of the different techniques and methods that exist for the analysis and visualization of dynamic networks. Basic definitions and formal notations are discussed and important references are cited. A major…
Certain areas of scientific research flourish while others lose advocates and attention. We are interested in whether structural patterns within citation networks correspond to the growth or decline of the research areas to which those…
A simple and accurate relationship is demonstrated that links the average shortest path, nodes, and edges in a complex network. This relationship takes advantage of the concept of link density and shows a large improvement in fitting…