Related papers: Spider networks
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…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
We study a new class of networks, generated by sequences of letters taken from a finite alphabet consisting of $m$ letters (corresponding to $m$ types of nodes) and a fixed set of connectivity rules. Recently, it was shown how a binary…
The sorting number of a graph with $n$ vertices is the minimum depth of a sorting network with $n$ inputs and outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in…
Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on…
A large body of work has been devoted to defining and identifying clusters or communities in social and information networks. We explore from a novel perspective several questions related to identifying meaningful communities in large…
Alternative paths in a network play an important role in its functionality as they can maintain the information flow under node/link failures. In this paper we explore the navigation of a network taking into account the alternative paths…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
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…
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…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
A number of network structural characteristics have recently been the subject of particularly intense research, including degree distributions, community structure, and various measures of vertex centrality, to mention only a few. Vertices…
In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
Ecology and evolution are inseparable. Motivated by some recent experiments, we have developed models of evolutionary ecology from the perspective of dynamic networks. In these models, in addition to the intra-node dynamics, which…