Related papers: Geometric evolution of complex networks
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
A model for growing information networks is introduced where nodes receive new links through j-redirection, i.e. the probability for a node to receive a link depends on the number of paths of length j arriving at this node. In detail, when…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
The step-growth polymerisation of a mixture of arbitrary-functional monomers is viewed as a time-continuos random graph process with degree bounds that are not necessarily the same for different vertices. The sequence of degree bounds acts…
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
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.…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
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,…