Related papers: Approximate Triangle Counting
We consider the problem of approximate counting of triangles and longer fixed length cycles in directed graphs. For triangles, T\v{e}tek [ICALP'22] gave an algorithm that returns a $(1 \pm \eps)$-approximation in…
Triangle count and local clustering coefficient are two core metrics for graph analysis. They find broad application in analyses such as community detection and link recommendation. Current state-of-the-art solutions suffer from…
How can we accurately estimate local triangles for all nodes in simple and multigraph streams? Local triangle counting in a graph stream is one of the most fundamental tasks in graph mining with important applications including anomaly…
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…
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations forprobabilistic…
Pattern counting in graphs is fundamental to network science tasks, and there are many scalable methods for approximating counts of small patterns, often called motifs, in large graphs. However, modern graph datasets now contain richer…
Estimating the number of triangles in a graph is one of the most fundamental problems in sublinear algorithms. In this work, we provide an algorithm that approximately counts the number of triangles in a graph using only polylogarithmic…
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…
Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which…
Triadic analysis encompasses a useful set of graph mining methods that are centered on the concept of a triad, which is a subgraph of three nodes. Such methods are often applied in the social sciences as well as many other diverse fields.…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
Counting the number of small subgraphs, called motifs, is a fundamental problem in social network analysis and graph mining. Many real-world networks are directed and temporal, where edges have timestamps. Motif counting in directed,…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model generalizes the random geometric…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
Massive sizes of real-world graphs, such as social networks and web graph, impose serious challenges to process and perform analytics on them. These issues can be resolved by working on a small summary of the graph instead . A summary is a…
We study the following combinatorial counting and sampling problems: can we efficiently sample from the Erd\H{o}s-R\'{e}nyi random graph $G(n,p)$ conditioned on triangle-freeness? Can we efficiently approximate the probability that $G(n,p)$…
Graphlet counting is an important problem as it has numerous applications in several fields, including social network analysis, biological network analysis, transaction network analysis, etc. Most of the practical networks are dynamic. A…
In this paper, we propose a novel method to compute triangle counting on GPUs. Unlike previous formulations of graph matching, our approach is BFS-based by traversing the graph in an all-source-BFS manner and thus can be mapped onto GPUs in…
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…
Network reliability is an important metric to evaluate the connectivity among given vertices in uncertain graphs. Since the network reliability problem is known as #P-complete, existing studies have used approximation techniques. In this…