Related papers: Cover Edge-Based Novel Triangle Counting
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
Graph analytics for large scale graphs has gained interest in recent years. Many graph algorithms have been designed for vertex-centric distributed graph processing frameworks to operate on large graphs with 100 M vertices and edges, using…
Triangle counting is a fundamental and widely studied problem on static graphs, and recently on temporal graphs, where edges carry information on the timings of the associated events. Streaming processing and resource efficiency are crucial…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…
In this work, we present the first efficient and practical algorithm for estimating the number of triangles in a graph stream using predictions. Our algorithm combines waiting room sampling and reservoir sampling with a predictor for the…
Triangle counting is a building block for a wide range of graph applications. Traditional wisdom suggests that i) hashing is not suitable for triangle counting, ii) edge-centric triangle counting beats vertex-centric design, and iii)…
Triangle counting in hypergraph streams, including both hyper-vertex and hyper-edge triangles, is a fundamental problem in hypergraph analytics, with broad applications. However, existing methods face two key limitations: (i) an incomplete…
Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are…
Recently, considerable efforts have been devoted to approximately computing the global and local (i.e., incident to each node) triangle counts of a large graph stream represented as a sequence of edges. Existing approximate triangle…
Subgraph counting aims to count the occurrences of a subgraph template T in a given network G. The basic problem of computing structural properties such as counting triangles and other subgraphs has found applications in diverse domains.…
We implement exact triangle counting in graphs on the GPU using three different methodologies: subgraph matching to a triangle pattern; programmable graph analytics, with a set-intersection approach; and a matrix formulation based on sparse…
The performance of graph algorithms is often measured in terms of the number of traversed edges per second (TEPS). However, this performance metric is inadequate for a graph operation such as exact triangle counting. In triangle counting,…
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
The rise of graph analytic systems has created a need for new ways to measure and compare the capabilities of graph processing systems. The MIT/Amazon/IEEE Graph Challenge has been developed to provide a well-defined community venue for…
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 study the problem of estimating the number of triangles in a graph stream. No streaming algorithm can get sublinear space on all graphs, so methods in this area bound the space in terms of parameters of the input graph such as the…
Counting the frequency of small subgraphs is a fundamental technique in network analysis across various domains, most notably in bioinformatics and social networks. The special case of triangle counting has received much attention. Getting…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
Triangle counting is an important problem in graph mining. Clustering coefficients of vertices and the transitivity ratio of the graph are two metrics often used in complex network analysis. Furthermore, triangles have been used…
\textsc{Edge Triangle Packing} and \textsc{Edge Triangle Covering} are dual problems extensively studied in the field of parameterized complexity. Given a graph $G$ and an integer $k$, \textsc{Edge Triangle Packing} seeks to determine…