Related papers: Asymptotic degree distributions in random threshol…
In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…
It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
We propose a random graph model with preferential attachment rule and \emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random…
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite…
We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph ensemble with exponentially decaying random disconnection probabilities determined by an i.i.d. field of variables with heavy tails and infinite mean associated to the vertices of…
We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root…
Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g…
A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in…
Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs…
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…
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…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
We investigate the role of degree correlation among nodes on the stability of complex networks, by studying spectral properties of randomly weighted matrices constructed from directed Erd\"{o}s-R\'enyi and scale-free random graph models. We…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
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 obtain a complete description of anisotropic scaling limits of random grain model on the plane with heavy tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both…