Related papers: On Random Graph Properties
We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…
Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or…
We study the problem of detecting the presence of an underlying high-dimensional geometric structure in a random graph. Under the null hypothesis, the observed graph is a realization of an Erd\H{o}s-R\'enyi random graph $G(n,p)$. Under the…
We consider core-periphery structured graphs, which are graphs with a group of densely and sparsely connected nodes, respectively, referred to as core and periphery nodes. The so-called core score of a node is related to the likelihood of…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…
Probabilistic generative models of graphs are important tools that enable representation and sampling. Many recent works have created probabilistic models of graphs that are capable of representing not only entity interactions but also…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…
Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…
Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…
We study some properties of graphs (or, rather, graph sequences) defined by demanding that the number of subgraphs of a given type, with vertices in subsets of given sizes, approximatively equals the number expected in a random graph. It…
We prove that the treewidth of an Erd\"{o}s-R\'{e}nyi random graph $\rg{n, m}$ is, with high probability, greater than $\beta n$ for some constant $\beta > 0$ if the edge/vertex ratio $\frac{m}{n}$ is greater than 1.073. Our lower bound…
A random 2-cell embedding of a connected graph $G$ in some orientable surface is obtained by choosing a random local rotation around each vertex. Under this setup, the number of faces or the genus of the corresponding 2-cell embedding…
We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…
Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature…