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A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
A temporal random geometric graph is a random geometric graph in which all edges are endowed with a uniformly random time-stamp, representing the time of interaction between vertices. In such graphs, paths with increasing time stamps…
I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
Group-based brain connectivity networks have great appeal for researchers interested in gaining further insight into complex brain function and how it changes across different mental states and disease conditions. Accurately constructing…
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…
A framework based on generalized hierarchical random graphs (GHRGs) for the detection of change points in the structure of temporal networks has recently been developed by Peel and Clauset [1]. We build on this methodology and extend it to…
This paper reviews, classifies and compares recent models for social networks that have mainly been published within the physics-oriented complex networks literature. The models fall into two categories: those in which the addition of new…
We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…
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…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
As a representation of relational data over time series, longitudinal networks provide opportunities to study link formation processes. However, networks at scale often exhibits community structure (i.e. clustering), which may confound…
Recent advances in graph learning have paved the way for innovative retrieval-augmented generation (RAG) systems that leverage the inherent relational structures in graph data. However, many existing approaches suffer from rigid, fixed…
The microbiome constitutes a complex microbial ecology of interacting components that regulates important pathways in the host. Measurements of microbial abundances are key to learning the intricate network of interactions amongst microbes.…
We consider the community recovery problem on a one-dimensional random geometric graph where every node has two independent labels: an observed location label and a hidden community label. A geometric kernel maps the locations of pairs of…
The theory of random graphs goes back to the late 1950s when Paul Erd\H{o}s and Alfr\'ed R\'enyi introduced the Erd\H{o}s-R\'enyi random graph. Since then many models have been developed, and the study of random graph models has become…
Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a…
Finding communities in networks is a problem that remains difficult, in spite of the amount of attention it has recently received. The Stochastic Block-Model (SBM) is a generative model for graphs with "communities" for which, because of…
The Blume-Emery-Griffiths model with a random crystal field is studied in a random graph architecture, in which the average connectivity is a controllable parameter. The disordered average over the graph realizations is treated by replica…
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is…