Related papers: Scale Free Networks from Self-Organisation
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the…
In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected…
We offer an example of an network model with a power law degree distribution, P(k) ~ k^{-alpha}, for nodes but which nevertheless has a well-defined geography and a nonzero threshold percolation probability for alpha>2, the range of…
Both empirical and theoretical investigations of scale-free network models have found that large degrees in a network exert an outsized impact on its structure. However, the tools used to infer the tail behavior of degree distributions in…
The impact of inhomogeneous arrangement of nodes in space on network organization cannot be neglected in most of real-world scale-free networks. Here, we wish to suggest a model for a geographical network with nodes embedded in a fractal…
In this work, a growing network model that can generate a random network with finite degree in infinite time is studied. The dynamics are governed by a rule where the degree increases under a scheme similar to the Malthus-Verhulst model in…
We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each…
Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the…
The scale-free (SF) structure that commonly appears in many complex networks is one of the hot topics related to social, biological, and information sciences. The self-organized generation mechanisms are expected to be useful for efficient…
We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
We study the following paradox associated with networks growing according to superlinear preferential attachment: superlinear preference cannot produce scale-free networks in the thermodynamic limit, but there are superlinearly growing…
Networks with a scale-free degree distribution are widely thought to promote cooperation in various games. Herein, by studying the well-known prisoner's dilemma game, we demonstrate that this need not necessarily be true. For the very same…
We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…