Related papers: Birth-Burst in Evolving Networks
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
Complex networks serve as abstract models for understanding real-world complex systems and provide frameworks for studying structured dynamical systems. This article addresses limitations in current studies on the exploration of individual…
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by…
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…
Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs…
We show that the protein-protein interaction networks can be surprisingly well described by a very simple evolution model of duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the…
Networks describing the interaction of the elements that constitute a complex system grow and develop via a number of different mechanisms, such as the addition and deletion of nodes, the addition and deletion of edges, as well as the…
Growing attention has been brought to the fact that many real directed networks exhibit hierarchy and directionality as measured through techniques like Trophic Analysis and non-normality. We propose a simple growing network model where the…
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…
Under preferential attachment (PA) network growth models late arrivals are at a disadvantage with regard to their final degrees. Previous extensions of PA have addressed this deficiency by either adding the notion of node fitness to PA,…
Proteins participating in a protein-protein interaction network can be grouped into homology classes following their common ancestry. Proteins added to the network correspond to genes added to the classes, so that the dynamics of the two…
We introduce a stochastic model of growing networks where both, the number of new nodes which joins the network and the number of connections, vary stochastically. We provide an exact mapping between this model and zero range process, and…
Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. It is not clear, however, how such dramatic evolutionary process has contributed to shape the large scale topology of…
We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law…
Since proteins carry out biological processes by interacting with other proteins, analyzing the structure of protein-protein interaction (PPI) networks could explain complex biological mechanisms, evolution, and disease. Similarly, studying…
A dynamic model for a random network evolving in continuous time is defined where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is…
We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly…
With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has…
The ever-increasing knowledge of the structure of various real-world networks has uncovered their complex multi-mechanism-governed evolution processes. Therefore, a better understanding of the structure and evolution of these networked…
We propose a new preferential attachment-based network growth model in order to explain two properties of growing networks: (1) the power-law growth of node degrees and (2) the decay of node relevance. In preferential attachment models, the…