Triangle Counting

How to Count Triangles, without Seeing the Whole Graph

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 scenarios, …

How the Degeneracy Helps for Triangle Counting in Graph Streams

We revisit the well-studied problem of triangle count estimation in graph streams. Given a graph represented as a stream of $m$ edges, our aim is to compute a $(1\pm\varepsilon)$-approximation to the triangle count $T$, using a small space algorithm. …

Towards Tighter Space Bounds for Counting Triangles and Other Substructures in Graph Streams

We revisit the much-studied problem of space-efficiently estimating the number of triangles in a graph stream, and extensions of this problem to counting fixed-sized cliques and cycles, obtaining a number of new upper and lower bounds. For the …