Related papers: Quasistatic Scale-free Networks
We study the mean length $\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law…
We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. We derive the general expression for the connectivity distribution of…
The origin of scale-free degree distributions in the context of networks is addressed through an analogous non-network model in which the node degree corresponds to the number of balls in a box and the rewiring of links to balls moving…
This paper establishes a relation between scale-free networks and Markov chains, and proposes a computation framework for degree distributions of scale-free networks. We first find that, under the BA model, the degree evolution of…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…
A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being…
Complex networks across various fields are often considered to be scale free -- a statistical property usually solely characterized by a power-law distribution of the nodes' degree $k$. However, this characterization is incomplete. In…
There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
The degree distribution of a real world network -- the number of links per node -- often follows a power law, with some hubs having many more links than traditional graph generation methods predict. For years, preferential attachment and…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
Hierarchical models of scale free networks are introduced where numbers of nodes in clusters of a given hierarchy are stochastic variables. Our models show periodic oscillations of degree distribution P(k) in the log-log scale. Periods and…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…
In this paper we present a deterministic vertex spawning model that yields a scale-free network. The model specifies that a parent vertex produces a child vertex in a time interval approximately proportional to the current time and…
We investigate a class of weighted planar stochastic lattice (WPSL1) created by random sequential nucleation of seed from which a crack is grown parallel to one of the sides of the chosen block and ceases to grow upon hitting another crack.…
We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct…
A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively…
Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…