相关论文: On the influence of the seed graph in the preferen…

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 randomly growing trees governed by the affine preferential attachment rule. Starting with a seed tree $S$, vertices are attached one by one, each linked by an edge to a random vertex of the current tree, chosen with a probability…

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 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 the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…

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 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 study preferential attachment models where vertices enter the network with i.i.d. random numbers of edges that we call the out-degree. We identify the local limit of such models, substantially extending the work of Berger et al.(2014).…

The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

We are interested in the asymptotics of random trees built by linear preferential attachment, also known in the literature as Barab\'asi-Albert trees or plane-oriented recursive trees. We first prove a conjecture of Bubeck, Mossel \& R\'acz…

Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…

We consider the open problem concerning the possible lack of concentration of the degree distribution in preferential attachment graphs with random initial degree, when its distribution is characterized by extremely heavy tails of power-law…

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…

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the…

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 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…

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 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…