Related papers: Fast Generation of Spatially Embedded Random Netwo…
Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
Counting the number of triangles in a graph has many important applications in network analysis. Several frequently computed metrics like the clustering coefficient and the transitivity ratio need to count the number of triangles in the…
Limited data availability in machine learning significantly impacts performance and generalization. Traditional augmentation methods enhance moderately sufficient datasets. GANs struggle with convergence when generating diverse samples.…
Miller et al. \cite{MPVX15} devised a distributed\footnote{They actually showed a PRAM algorithm. The distributed algorithm with these properties is implicit in \cite{MPVX15}.} algorithm in the CONGEST model, that given a parameter $k =…
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
We study the random planar graph process introduced by Gerke, Schlatter, Steger, and Taraz [The random planar graph process, Random Structures Algorithms 32 (2008), no. 2, 236--261; MR2387559]: Begin with an empty graph on $n$ vertices,…
We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols,…
Attributed networks are ubiquitous since a network often comes with auxiliary attribute information e.g. a social network with user profiles. Attributed Network Embedding (ANE) has recently attracted considerable attention, which aims to…
In this paper, we propose Orthogonal Generative Adversarial Networks (O-GANs). We decompose the network of discriminator orthogonally and add an extra loss into the objective of common GANs, which can enforce discriminator become an…
In this paper, we introduce InstantEmbedding, an efficient method for generating single-node representations using local PageRank computations. We theoretically prove that our approach produces globally consistent representations in…
Let $G = (V,E,w)$ be a weighted undirected graph on $|V| = n$ vertices and $|E| = m$ edges, let $k \ge 1$ be any integer, and let $\epsilon < 1$ be any parameter. We present the following results on fast constructions of spanners with…
Graph neural networks have become a staple in problems addressing learning and analysis of data defined over graphs. However, several results suggest an inherent difficulty in extracting better performance by increasing the number of…
We propose an algorithm for deep learning on networks and graphs. It relies on the notion that many graph algorithms, such as PageRank, Weisfeiler-Lehman, or Message Passing can be expressed as iterative vertex updates. Unlike previous…
Despite the recent success of reconciling spike-based coding with the error backpropagation algorithm, spiking neural networks are still mostly applied to tasks stemming from sensory processing, operating on traditional data structures like…