Related papers: Random graphs and their subgraphs

In this paper, we first discuss the origin of preferential attachment. Then we establish the generalized preferential attachment which has two new properties; first, it encapsulates both the topological and weight aspects of a network,…

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to…

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…

Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However,…

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

Dynamic graph learning has gained significant attention as it offers a powerful means to model intricate interactions among entities across various real-world and scientific domains. Notably, graphs serve as effective representations for…

The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…

We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…

In statistical mechanical investigations on complex networks, it is useful to employ random graphs ensembles as null models, to compare with experimental realizations. Motivated by transcription networks, we present here a simple way to…

Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…

Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…

Graph neural networks have been widely used for learning representations of nodes for many downstream tasks on graph data. Existing models were designed for the nodes on a single graph, which would not be able to utilize information across…

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…

Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…

Many real-world networks exhibit correlations between the node degrees. For instance, in social networks nodes tend to connect to nodes of similar degree. Conversely, in biological and technological networks, high-degree nodes tend to be…