Related papers: Analysis of large sparse graphs using regular deco…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Given a connected undirected weighted graph, we are concerned with problems related to partitioning the graph. First of all we look for the closest disconnected graph (the minimum cut problem), here with respect to the Euclidean norm. We…
K-core decomposition is a commonly used metric to analyze graph structure or study the relative importance of nodes in complex graphs. Recent years have seen rapid growth in the scale of the graph, especially in industrial settings. For…
We consider the question of averaging on a graph that has one sparse cut separating two subgraphs that are internally well connected. While there has been a large body of work devoted to algorithms for distributed averaging, nearly all…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
Electronic data is growing at increasing rates, in both size and connectivity: the increasing presence of, and interest in, relationships between data. An example is the Twitter social network graph. Due to this growth demand is increasing…
We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small…
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…
Large graphs are difficult to represent, visualize, and understand. In this paper, we introduce "gate graph" - a new approach to perform graph simplification. A gate graph provides a simplified topological view of the original graph.…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
In this note, we test the performance of six algorithms from the family of graph-based splitting methods [SIAM J. Optim., 34 (2024), pp. 1569-1594] specialized to normal cones of linear subspaces. To do this, we first implement some…
Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…
Edge-centric distributed computations have appeared as a recent technique to improve the shortcomings of think-like-a-vertex algorithms on large scale-free networks. In order to increase parallelism on this model, edge partitioning -…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing 'Local Separators' of graphs. Applications…