Related papers: Cover Edge-Based Novel Triangle Counting

A recent result of Eden, Levi, and Ron (ECCC 2015) provides a sublinear time algorithm to estimate the number of triangles in a graph. Given an undirected graph $G$, one can query the degree of a vertex, the existence of an edge between…

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…

We propose data-driven one-pass streaming algorithms for estimating the number of triangles and four cycles, two fundamental problems in graph analytics that are widely studied in the graph data stream literature. Recently, (Hsu 2018) and…

We develop an algorithm that finds the consensus of many different clustering solutions of a graph. We formulate the problem as a median set partitioning problem and propose a greedy optimization technique. Unlike other approaches that find…

Seeding then expanding is a commonly used scheme to discover overlapping communities in a network. Most seeding methods are either too complex to scale to large networks or too simple to select high-quality seeds, and the non-principled…

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…

Connected components is a fundamental kernel in graph applications. The fastest existing parallel multicore algorithms for connectivity are based on some form of edge sampling and/or linking and compressing trees. However, many combinations…

Triangle counting is a fundamental problem in the analysis of large graphs. There is a rich body of work on this problem, in varying streaming and distributed models, yet all these algorithms require reading the whole input graph. In many…

Data-intensive, graph-based computations are pervasive in several scientific applications, and are known to to be quite challenging to implement on distributed memory systems. In this work, we explore the design space of parallel algorithms…

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…

Subgraph counting aims to count occurrences of a template T in a given network G(V, E). It is a powerful graph analysis tool and has found real-world applications in diverse domains. Scaling subgraph counting problems is known to be memory…

The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and…

We propose a novel algorithm for enumerating and listing all minimal cutsets of a given graph. It is known that this problem is NP-hard. We use connectivity properties of a given graph to develop an algorithm with reduced complexity for…

Triangle Counting (TC) is a procedure that involves enumerating the number of triangles within a graph. It has important applications in numerous fields, such as social or biological network analysis and network security. TC is a…

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…

Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such…

Massively parallel architectures such as the GPU are becoming increasingly important due to the recent proliferation of data. In this paper, we propose a key class of hybrid parallel graphlet algorithms that leverages multiple CPUs and GPUs…

Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…

Higher-order interactions beyond pairwise relationships in large complex networks are often modeled as hypergraphs. Analyzing hypergraph properties such as triad counts is essential, as hypergraphs can reveal intricate group interaction…

Graphs are used to model interactions in a variety of contexts, and there is a growing need to quickly assess the structure of such graphs. Some of the most useful graph metrics are based on triangles, such as those measuring social…