Related papers: An efficient counting method for the colored triad…
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…
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…
The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important…
Characterizing graph properties is fundamental to the analysis and to our understanding of real-world networked systems. The local clustering coefficient, and the more recently introduced, local closure coefficient, capture powerful…
Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
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…
Hypergraphs, which use hyperedges to capture groupwise interactions among different entities, have gained increasing attention recently for their versatility in effectively modeling real-world networks. In this paper, we study the problem…
Given a graph stream, how can we estimate the number of triangles in it using multiple machines with limited storage? Specifically, how should edges be processed and sampled across the machines for rapid and accurate estimation? The count…
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…
Collaborating teams of robots show promise due in their ability to complete missions more efficiently and with improved robustness, attributes that are particularly useful for systems operating in marine environments. A key issue is how to…
Triangle counting in a graph is a fundamental problem with wide-ranging applications. It is crucial for understanding graph structure and serves as a basis for more advanced graph analytics. One key application is truss decomposition, a…
Counting and finding triangles in graphs is often used in real-world analytics to characterize cohesiveness and identify communities in graphs. In this paper, we propose the novel concept of a cover-edge set that can be used to find…
On signed social networks, balanced and unbalanced triangles are a critical motif due to their role as the foundations of Structural Balance Theory. The uses for these motifs have been extensively explored in networks with known edge signs,…
We consider the fundamental problems of approximately counting the numbers of edges and triangles in a graph in sublinear time. Previous algorithms for these tasks are significantly more efficient under a promise that the arboricity of the…
In this note we introduce a new randomized algorithm for counting triangles in graphs. We show that under mild conditions, the estimate of our algorithm is strongly concentrated around the true number of triangles. Specifically, if $p \geq…
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…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
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,…
Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of a graph. Some of the most useful graph metrics, especially those measuring social cohesion, are based on…