Related papers: The age-dependent random connection model
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…
We study geometric random graphs defined on the points of a Poisson process in $d$-dimensional space, which additionally carry independent random marks. Edges are established at random using the marks of the endpoints and the distance…
In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…
Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected…
When modeling a directed social network, one choice is to use the traditional preferential attachment model, which generates power-law tail distributions. In a traditional directed preferential attachment, every new edge is added…
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…
We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function $nf(\cdot)$, where $n\in \mathbb{N}$, and $f$ is a probability density…
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,\ldots$, with probability $\pi_1>0$ a new vertex with one…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…
Consider a homogeneous Poisson point process in a compact convex set in $d$-dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point…
We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether…