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In this paper, we propose a general model for collaboration networks. Depending on a single free parameter "{\bf preferential exponent}", this model interpolates between networks with a scale-free and an exponential degree distribution. The…
The percolation threshold of the network model by Barabasi and Albert (BA-model) [Science 286, 509 (1999)] has thus far only been 'guessed' based on simulations and comparison with other models. Due to the still uncertain influence of…
The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with…
The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or…
In a highly influential paper twenty years ago, Barab\'asi and Albert [Science 286, 509 (1999)] showed that networks undergoing generic growth processes with preferential attachment evolve towards scale-free structures. In any finite…
We introduce and study a general model of social network formation and evolution based on the concept of preferential link formation between similar nodes and increased similarity between connected nodes. The model is studied numerically…
We develop and test a rewiring method (originally proposed by Newman) which allows to build random networks having pre-assigned degree distribution and two-point correlations. For the case of scale-free degree distributions, we discretize…
This paper presents an evolution model of weighted networks in which the structural growth and weight dynamics are driven by human behavior, i.e. passenger route choice behavior. Transportation networks grow due to people's increasing…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
We introduce a growing network evolution model with nodal attributes. The model describes the interactions between potentially violent V and non-violent N agents who have different affinities in establishing connections within their own…
In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create…
Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on…
In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous…
We propose a model of a growing network, in which preferential linking is combined with partial inheritance of connectivity (number of incoming links) of individual nodes by new ones. The nontrivial version of this model is solved exactly…
Many networks are complex dynamical systems, where both attributes of nodes and topology of the network (link structure) can change with time. We propose a model of co-evolving networks where both node at- tributes and network structure…
In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…
Analytical results are presented for the structure of networks that evolve via a preferential-attachment-random-deletion (PARD) model in the regime of overall network growth and in the regime of overall contraction. The phase transition…
We introduce a network growth model in which the preferential attachment probability includes the fitness vertex and the Euclidean distance between nodes. We grow a planar network around its barycenter. Each new site is fixed in space by…