Related papers: Basic models and questions in statistical network …
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these…
Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
Communities are a common and widely studied structure in networks, typically under the assumption that the network is fully and correctly observed. In practice, network data are often collected by querying nodes about their connections. In…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to…
Researchers interested in statistically modeling network data have a well-established and quickly growing set of approaches from which to choose. Several of these methods have been regularly applied in research on political networks, while…
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links.…
The statistical inference of stochastic block models as emerged as a mathematicaly principled method for identifying communities inside networks. Its objective is to find the node partition and the block-to-block adjacency matrix of maximum…
1. The birth of network science. 2. What are random networks? 3. Adjacency matrix. 4. Degree distribution. 5. What are simple networks? Classical random graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated…
We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide a guide to available methodology and…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
We study the hierarchy of communities in real-world networks under a generic stochastic block model, in which the connection probabilities are structured in a binary tree. Under such model, a standard recursive bi-partitioning algorithm is…
Community detection, a fundamental task for network analysis, aims to partition a network into multiple sub-structures to help reveal their latent functions. Community detection has been extensively studied in and broadly applied to many…
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…