Related papers: How to Count Triangles, without Seeing the Whole G…
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…
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…
The number of triangles in a graph is a fundamental metric, used in social network analysis, link classification and recommendation, and more. Driven by these applications and the trend that modern graph datasets are both large and dynamic,…
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…
There is a trivial $O(\frac{n^3}{T})$ time algorithm for approximate triangle counting where $T$ is the number of triangles in the graph and $n$ the number of vertices. At the same time, one may count triangles exactly using fast matrix…
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…
If we cannot store all edges in a graph stream, which edges should we store to estimate the triangle count accurately? Counting triangles (i.e., cycles of length three) is a fundamental graph problem with many applications in social network…
In network theory, a triad census is a method designed to categorize and enumerate the various types of subgraphs with three nodes and their connecting edges within a network. Triads serve as fundamental building blocks for comprehending…
Triangle counting and sampling are two fundamental problems for streaming algorithms. Arguably, designing sampling algorithms is more challenging than their counting variants. It may be noted that triangle counting has received far greater…
Listing and counting triangles in graphs is a key algorithmic kernel for network analyses including community detection, clustering coefficients, k-trusses, and triangle centrality. We design and implement a new serial algorithm for…
In this paper we present improved results on the problem of counting triangles in edge streamed graphs. For graphs with $m$ edges and at least $T$ triangles, we show that an extra look over the stream yields a two-pass treaming algorithm…
Exploratory analysis over network data is often limited by the ability to efficiently calculate graph statistics, which can provide a model-free understanding of the macroscopic properties of a network. We introduce a framework for…
Counting the number of small patterns is a central task in network analysis. While this problem is well studied for graphs, many real-world datasets are naturally modeled as hypergraphs, motivating the need for efficient hypergraph motif…
Counting triangles in a graph and incident to each vertex is a fundamental and frequently considered task of graph analysis. We consider how to efficiently do this for huge graphs using massively parallel distributed-memory machines.…
We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…
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…
Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…
Listing all triangles is a fundamental graph operation. Triangles can have important interpretations in real-world graphs, especially social and other interaction networks. Despite the lack of provably efficient (linear, or slightly…
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…
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…