Related papers: The $N$-stars network evolution model
Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges.…
Recently, we introduced a quantity, "node weight", to describe the collaboration sharing or competition gain of the elements in the collaboration-competition networks, which can be well described by bipartite graphs. We find that the node…
We highlight intriguing features of complex networks that are grown by \emph{redirection}. In this mechanism, a target node is chosen uniformly at random from the pre-existing network nodes and the new node attaches either to this initial…
Many real-world complex networks arise as a result of a competition between growth and rewiring processes. Usually the initial part of the evolution is dominated by growth while the later one rather by rewiring. The initial growth allows…
A novel Markovian network evolution model is introduced and analysed by means of information theory. It will be proved that the model, called Network Evolution Chain, is a stationary and ergodic stochastic process. Therefore, the Asymptotic…
Preferential attachment --- by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree --- has become the standard growth model for scale-free networks, where the asymptotic probability of a node…
Genomic duplication-divergence events, which are the primary source of new protein functions, occur stochastically at a wide range of genomic scales, from single gene to whole genome duplications. Clearly, this fundamental evolutionary…
In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Cellular functions are based on the complex interplay of proteins, therefore the structure and dynamics of these protein-protein interaction (PPI) networks are the key to the functional understanding of cells. In the last years, large-scale…
Individual nodes in evolving real-world networks typically experience growth and decay --- that is, the popularity and influence of individuals peaks and then fades. In this paper, we study this phenomenon via an intrinsic nodal fitness…
We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there…
Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs a reference model (null model). One frequently used…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
The distribution of distances in the star graph $ST_n$, ($1<n\in\Z$), is established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given by the distances to the identity…
We study the interplay between evolutionary game and network structure and show how the dynamics of the game affect the growth pattern of the network and how the evolution of the network influence the cooperative behavior in the game.…
Information diffusion in online social networks is affected by the underlying network topology, but it also has the power to change it. Online users are constantly creating new links when exposed to new information sources, and in turn…
We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy $s_i$ of a node $i$ is defined as a total number of all nodes that are younger than $i$ and can be connected to it by a directed path. For a network with…
This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…