Related papers: A Preferential Attachment Process Approaching the …

This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…

Every countable graph can be built from finite graphs by a suitable infinite process, either adding new vertices randomly or imposing some rules on the new edges. On the other hand, a profinite topological graph is built as the inverse…

We consider the averaging process on an infinite connected graph with bounded degree and independent, identically distributed starting values or initial opinions. Assuming that the law of the initial opinion of a vertex has a finite second…

We claim that networks are created according to the priority attachment mechanism and we show a simple model which uses the priority attachment to generate both synthetic and close to empirical networks. Priority attachment is a mechanism…

In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between…

A multi-type preferential attachment tree is introduced, and studied using general multi-type branching processes. For the $p$-type case we derive a framework for studying the tree where a type $i$ vertex generates new type $j$ vertices…

We study the number of isolated vertices in a preferential attachment random graph introduced by Dereich and M\"orters in 2009. In this graph model vertices are added over time and newly arriving vertices connect to older ones with…

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

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…

We study a general preferential attachment and Polya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not…

We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…

Since the paper of Kleinberg and Kleinberg, SODA'05, where it was proven that the preferential attachment random graph with degeneracy at least 3 does not obey the first order 0-1 law, no general methods were developed to study logical…

In this paper, we characterise the notion of preferential attachment in networks as action at a distance, and argue that it can only be an emergent phenomenon -- the actual mechanism by which networks grow always being the closing of…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an…

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…

Let $\mathcal{P}$ be a graph property which is preserved by removal of edges, and consider the random graph process that starts with the empty $n$-vertex graph and then adds edges one-by-one, each chosen uniformly at random subject to the…

We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…

Motivated by the complexity of network data, we propose a directed hybrid random network that mixes preferential attachment (PA) rules with uniform attachment (UA) rules. When a new edge is created, with probability $p\in [0,1]$, it follows…

This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…