相关论文: Scalable Generation of Scale-free Graphs

This article addresses the degree distribution of subnetworks, namely the number of links between the nodes in each subnetwork and the remainder of the structure (cond-mat/0408076). The transformation from a subnetwork-partitioned model to…

Scaled relative graphs have been originally introduced in the context of convex optimization and have recently gained attention in the control systems community for the graphical analysis of nonlinear systems. Of particular interest in…

We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…

Recently there has been increasing interest in developing and deploying deep graph learning algorithms for many tasks, such as fraud detection and recommender systems. Albeit, there is a limited number of publicly available graph-structured…

Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of…

Random graphs with power-law degrees can model scale-free networks as sparse topologies with strong degree heterogeneity. Mathematical analysis of such random graphs proved successful in explaining scale-free network properties such as…

What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…

We prove the existence of a large complete subgraph w.h.p. in a preferential attachment random graph process with an edge-step. That is, we prove that the random graph $G_{t}$ produced by the so-called GLP model at time $t$ contains a…

Graphs are a prevalent tool in data science, as they model the inherent structure of the data. They have been used successfully in unsupervised and semi-supervised learning. Typically they are constructed either by connecting nearest…

Graph learning algorithms have attained state-of-the-art performance on many graph analysis tasks such as node classification, link prediction, and clustering. It has, however, become hard to track the field's burgeoning progress. One…

Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…

The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the…

Graph simulation has recently received a surge of attention in graph processing and analytics. In real-life applications, e.g. social science, biology, and chemistry, many graphs are composed of a series of evolving graphs (i.e., temporal…

We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is…

Subgraphs reveal information about the geometry and functionalities of complex networks. For scale-free networks with unbounded degree fluctuations, we obtain the asymptotics of the number of times a small connected graph occurs as a…

Significant progress has been made in training large generative models for natural language and images. Yet, the advancement of 3D generative models is hindered by their substantial resource demands for training, along with inefficient,…

The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of…

We present a simple mechanism for generating undirected scale-free networks using random walkers, where the network growth is determined by choosing parent vertices by sequential random walks. We show that this mechanism produces scale-free…

In many networks of scientific interest we know that the link between any pair of vertices conforms to a specific probability, such as the link probability in the Barab\'asi-Albert scale-free networks. Here we demonstrate how the…

In this paper we present a possible model of adaptive grids for numerical resolution of differential problems, using physical or geometrical properties, as viscosity or velocity gradient of a moving fluid. The relation between the values of…