Related papers: Properties of dense partially random graphs
In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…
In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…
We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency…
The spectral and localization properties of heterogeneous random graphs are determined by the resolvent distributional equations, which have so far resisted an analytic treatment. We solve analytically the resolvent equations of random…
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…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
In this work we perform a detailed statistical analysis of topological and spectral properties of random geometric graphs (RGGs); a graph model used to study the structure and dynamics of complex systems embedded in a two dimensional space.…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
This paper investigates the addition of random edges to arbitrary dense graphs; in particular, we determine the number of random edges required to ensure various monotone properties including the appearance of a fixed size clique, small…
When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…
Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the…
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edges are far from independent, and to prove several results…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…
We study crossing numbers of dense graph drawings whose vertices are uniformly distributed either on the unit sphere or in a compact convex planar domain. We prove a sharp inequality for weighted geodesic drawings on $\mathbb S^2$ in a…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
We study the two most common types of percolation process on a sparse random graph with a given degree sequence. Namely, we examine first a bond percolation process where the edges of the graph are retained with probability p and afterwards…
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…