相关论文: Influence of the seed in affine preferential attac…
We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…
We study the influence of the seed graph in the preferential attachment model, focusing on the case of trees. We first show that the seed has no effect from a weak local limit point of view. On the other hand, we conjecture that different…
We provide a local probabilistic description of the limiting statistics of large preferential attachment trees in terms of the ordinary degree (number of neighbors) but augmented with information on leafdegree (number of neighbors that are…
We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
We find assimpotics for the first $k$ highest degrees of the degree distribution in an evolving tree model combining the local choice and the preferential attachment. In the considered model, the random graph is constructd in the following…
We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible…
We study two models of growing recursive trees. For both models, initially the tree only contains one vertex $u_1$ and at each time $n\geq 2$ a new vertex $u_n$ is added to the tree and its parent is chosen randomly according to some rule.…
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…
Many networks exhibit scale free behavior where their degree distribution obeys a power law for large vertex degrees. Models constructed to explain this phenomena have relied on preferential attachment where the networks grow by the…
We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…
In this paper, a random graph process ${G(t)}_{t\geq 1}$ is studied and its degree sequence is analyzed. Let $(W_t)_{t\geq 1}$ be an i.i.d. sequence. The graph process is defined so that, at each integer time $t$, a new vertex, with $W_t$…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We consider a preferential attachment model that incorporates an anomaly. Our goal is to understand the evolution of the network before and after the occurrence of the anomaly by studying the influence of the anomaly on the structural…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
We study a new class of preferential attachment trees with \emph{self-reinforcement}. At each time, each vertex is assigned a weight equal to the cumulative sum over past times of an affine function of its degree. A new vertex attaches…
We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
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 introduce a model of evolving preferential attachment trees where vertices are assigned weights, and the evolution of a vertex depends not only on its own weight, but also on the weights of its neighbours. We study the distribution of…