Related papers: Random Ancestor Trees
The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…
Phylogenetic networks are directed acyclic graphs that depict the genomic evolution of related taxa. Reticulation nodes in such networks (nodes with more than one parent) represent reticulate evolutionary events, such as recombination,…
Motivated by questions in social networks, distributed computing and probabilistic combinatorics, the last few years have seen increasing interest in network evolution models where new vertices entering the system need to make decisions…
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…
In a deterministic or random tree, a notion of ancestral diversity can be defined as follows. Sample independently $n$ groups of $k$ leaves and count the number $N_n(k)$ of distinct most recent common ancestors of each of the groups. As $n$…
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…
We study structural properties of trees grown by preferential attachment. In this mechanism, nodes are added sequentially and attached to existing nodes at a rate that is strictly proportional to the degree. We classify nodes by their depth…
We consider growing random networks $\{\mathcal G_n\}_{n \ge 1}$ where, at each time, a new vertex attaches itself to a collection of existing vertices via a fixed number $m \ge 1$ of edges, with probability proportional to an attachment…
We consider the set of random Bienaym\'e-Galton-Watson trees with a bounded number of offspring and bounded number of generations as a statistical mechanics model: a random tree is a rooted subtree of the maximal tree; the spin at a given…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considers both: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their…
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites which link to earlier sites with a probability A_k which depends on the number of…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
In networks that grow by isotropic redirection (IR), a new node selects an initial target node uniformly at random and attaches to a randomly chosen neighbor of the target. The emerging networks exhibit leaf proliferation, in which the…
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…
We introduce a new oriented evolving graph model inspired by biological networks. A node is added at each time step and is connected to the rest of the graph by random oriented edges emerging from older nodes. This leads to a statistical…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
We introduce a new class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability 1-r or to the ancestor of the target with probability r,…
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…