Related papers: Duplication Models for Biological Networks
Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…
Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected,…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
In this work we study a simple evolutionary model of bipartite networks which its evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary…
While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is…
Research shows that gene duplication followed by either repurposing or removal of duplicated genes is an important contributor to evolution of gene and protein interaction networks. We aim to identify which characteristics of a network can…
Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism…
In this paper we study the macroscopic conduction properties of large but finite binary networks with conducting bonds. By taking a combination of a spectral and an averaging based approach we derive asymptotic formulae for the conduction…
We use mathematical methods from the theory of tailored random graphs to study systematically the effects of sampling on topological features of large biological signalling networks. Our aim in doing so is to increase our quantitative…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
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…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
It is widely believed that the Internet's AS-graph degree distribution obeys a power-law form. Most of the evidence showing the power-law distribution is based on BGP data. However, it was recently argued that since BGP collects data in a…
Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
Gene duplication is a fundamental evolutionary mechanism that contributes to biological complexity and diversity (Fortna et al., 2004). Traditionally, research has focused on the duplication of gene sequences (Zhang, 1914). However,…
Degree distribution of nodes, especially a power law degree distribution, has been regarded as one of the most significant structural characteristics of social and information networks. Node degree, however, only discloses the first-order…
We evaluate analytically and numerically the size of the frozen core and various scaling laws for critical Boolean networks that have a power-law in- and/or out-degree distribution. To this purpose, we generalize an efficient method that…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
We introduce and analyze a model of a multi-directed Eulerian network, that is a directed and weighted network where a path exists that passes through all the edges of the network once and only once. Networks of this type can be used to…