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Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…

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…

Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…

Understanding how social networks form, whether through reciprocity, shared attributes, or triadic closure, is central to computational social science. Exponential Random Graph Models (ERGMs) offer a principled framework for testing such…

Graphs are widely used for describing systems made up of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination…

Exponential Random Graph Models (ERGMs) are an inferential model for analysing statistical networks. Recent development in ERGMs uses hierarchical Bayesian setup to jointly model a group of networks, which is called a multiple-network…

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…

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…

Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Though early studies of such processes were primarily descriptive, recent…

Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…

Ensemble models of graphs are one of the most important theoretical tools to study complex networks. Among them, exponential random graphs (ERGs) have proven to be very useful in the analysis of social networks. In this paper we develop a…

With the emerging of new networks, such as wireless sensor networks, vehicle networks, P2P networks, cloud computing, mobile Internet, or social networks, the network dynamics and complexity expands from system design, hardware, software,…

Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…

Bayesian inference for exponential family random graph models (ERGMs) is a doubly-intractable problem because of the intractability of both the likelihood and posterior normalizing factor. Auxiliary variable based Markov Chain Monte Carlo…

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…

Exponential family Random Graph Models (ERGMs) can be viewed as expressing a probability distribution on graphs arising from the action of competing social forces that make ties more or less likely, depending on the state of the rest of the…

Graphical models are powerful tools to investigate complex dependency structures in high-throughput datasets. However, most existing graphical models make one of the two canonical assumptions: (i) a homogeneous graph with a common network…

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade the overabundance of certain sub-network patterns, so called motifs, has attracted…

We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network…

Community detection is considered as a fundamental task in analyzing social networks. Even though many techniques have been proposed for community detection, most of them are based exclusively on the connectivity structures. However, there…