Related papers: Hybrid of node and link communities for graphon es…
The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here…
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…
In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose…
Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…
Characterizing large-scale organization in networks, including multilayer networks, is one of the most prominent topics in network science and is important for many applications. One type of mesoscale feature is community structure, in…
Stochastic block models (SBMs) are often used to find assortative community structures in networks, such that the probability of connections within communities is higher than in between communities. However, classic SBMs are not limited to…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
We prove identifiability of parameters for a broad class of random graph mixture models. These models are characterized by a partition of the set of graph nodes into latent (unobservable) groups. The connectivities between nodes are…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually…
The community structure of a complex network can be determined by finding the partitioning of its nodes that maximizes modularity. Many of the proposed algorithms for doing this work by recursively bisecting the network. We show that this…
This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are…
Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…
Community detection and hierarchy extraction are usually thought of as separate inference tasks on networks. Considering only one of the two when studying real-world data can be an oversimplification. In this work, we present a generative…
In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or…
The estimation of probabilities of network edges from the observed adjacency matrix has important applications to predicting missing links and network denoising. It has usually been addressed by estimating the graphon, a function that…
Structural changes in a network representation of a system (e.g.,different experimental conditions, time evolution), can provide insight on its organization, function and on how it responds to external perturbations. The deeper…
Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis.…
The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…
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…