Related papers: Evolving networks through deletion and duplication

Real-world networks evolve over time via additions or removals of vertices and edges. In current network evolution models, vertex degree varies or grows arbitrarily. A recently introduced degree-preserving network growth (DPG) family of…

We investigate a model of evolving random network, introduced by us previously {[}{\it Phys. Rev. Lett.} {\bf 83}, 5587 (1999){]} . The model is a generalization of the Bak-Sneppen model of biological evolution, with the modification that…

Background: Duplication of genes is important for evolution of molecular networks. Many authors have therefore considered gene duplication as a driving force in shaping the topology of molecular networks. In particular it has been noted…

Many real world networks, such as social networks, are primarily formed through local interactions between agents. Additionally, in contrast with common network models, social and biological networks exhibit a high degree of clustering.…

We consider a stochastic model for directed scale-free networks following power-laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with growth rate p.…

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of "splitting" nodes of degree $k$ into $k$ nodes of degree 1. Four networks are considered, each…

Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…

The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…

We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…

Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…

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…

We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…

Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these…

Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…

Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…

The evolution of complex networks is governed by both growing rules and internal properties. Most evolving network models (e.g. preferential attachment) emphasize on the growing strategy, while neglecting the characteristics of individual…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

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…