Related papers: Duplication Models for Biological Networks
We characterize the tail behavior of the distribution of the PageRank of a uniformly chosen vertex in a directed preferential attachment graph and show that it decays as a power law with an explicit exponent that is described in terms of…
For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…
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…
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…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
We study the evolution of the network properties of a populated network embedded in a genotype space characterised by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…
A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein…
Phylogenetic networks are mathematical structures for modeling and visualization of reticulation processes in the study of evolution. Galled networks, reticulation visible networks, nearly-stable networks and stable-child networks are the…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
Biological networks such as gene regulatory networks possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated…
The study of complex networks has pursued an understanding of macroscopic behavior by focusing on power-laws in microscopic observables. Here, we uncover two universal fundamental physical principles that are at the basis of complex…
Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact. Existing network alignments use…
Combinations of random and preferential growth for both on-growing and stationary networks are studied and a hierarchical topology is observed. Thus for real world scale-free networks which do not exhibit hierarchical features preferential…
We consider two types of random networks grown in blocks. Hooking networks are grown from a set of graphs as blocks, each with a labelled vertex called a hook. At each step in the growth of the network, a vertex called a latch is chosen…
Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…
Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach, Cygan, {\L}acki,…
We consider an evolving network of a fixed number of nodes. The allocation of edges is a dynamical stochastic process inspired by biological reproduction dynamics, namely by deleting and duplicating existing nodes and their edges. The…
Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…