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Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
In this paper, we prove a local limit theorem for the distribution of the number of triangles in the Erdos-Renyi random graph $G(n,p)$, where $p \in (0,1)$ is a fixed constant. Our proof is based on bounding the characteristic function…
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…
In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c>3 are present in random Erdos and Renyi graphs only in the limit of diverging average connectivity. Starting…
We consider secure and reliable connectivity in wireless sensor networks that utilize a heterogeneous random key predistribution scheme. We model the unreliability of wireless links by an on-off channel model that induces an…
In a random key graph (RKG) of $n$ nodes each node is randomly assigned a key ring of $K_n$ cryptographic keys from a pool of $P_n$ keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume…
Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…
The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…
The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model generalizes the random geometric…
We introduce two models of inclusion hierarchies: Random Graph Hierarchy (RGH) and Limited Random Graph Hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erd\H{o}s-R\'{e}nyi random…
Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies…
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…