Related papers: Triangle Counting Through Cover-Edges
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…
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,…
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…
Given all pairwise weights (distances) among a set of objects, filtered graphs provide a sparse representation by only keeping an important subset of weights. Such graphs can be passed to graph clustering algorithms to generate hierarchical…
The problem of finding dense components of a graph is a widely explored area in data analysis, with diverse applications in fields and branches of study including community mining, spam detection, computer security and bioinformatics. This…
Breadth-First Search (BFS) is a building block used in a wide array of graph analytics and is used in various network analysis domains: social, road, transportation, communication, and much more. Over the last two decades, network sizes…
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…
We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\tilde{O}(n^{1/2})$ rounds. In contrast, the previous…
From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks at both the global macro-level as well as the local micro-level. While graphlets have witnessed a…
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…
The $k$-truss, introduced by Cohen (2005), is a graph where every edge is incident to at least $k$ triangles. This is a relaxation of the clique. It has proved to be a useful tool in identifying cohesive subnetworks in a variety of…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. Using binary indexed tree data structure, we improve algorithms for calculating the size and the number of…
We present a new parallel algorithm for $k$-clique counting/listing that has polylogarithmic span (parallel time) and is work-efficient (matches the work of the best sequential algorithm) for sparse graphs. Our algorithm is based on…
An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into \emph{bundles}. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between…
Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks,…
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.…
In the distributed triangle detection problem, we have an $n$-vertex network $G=(V,E)$ with one player for each vertex of the graph who sees the edges incident on the vertex. The players communicate in synchronous rounds using the edges of…
Graphs are a fundamental data structure used to represent relationships in domains as diverse as the social sciences, bioinformatics, cybersecurity, the Internet, and more. One of the central observations in network science is that…
The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer…
Although community detection has drawn tremendous amount of attention across the sciences in the past decades, no formal consensus has been reached on the very nature of what qualifies a community as such. In this article we take an…