Related papers: Random Geometric Graphs
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…
Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…
Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
We show that an intricate relation of cluster properties and optimal bipartitions, which takes place in undirected random graphs, extends to directed and mixed random graphs. In particular, the satisfability threshold coincides with the…
We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
We consider a model for random hypergraphs with identifiability, an analogue of connectedness. This model has a phase transition in the proportion of identifiable vertices when the underlying random graph becomes critical. The phase…
Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erd\H{o}s-R\'enyi random graph in large scale is often lack of local…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…
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…
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…