Efficient semi-streaming algorithms for local triangle counting in massive graphs

In this paper we study the problem of local triangle counting in large graphs. Namely, given a large graph G = (V;E) we want to estimate as accurately as possible the number of triangles incident to every node υ ∈ V in the graph. The problem of computing the global number of triangles in a graph has been considered before, but to our knowledge this is the first paper that addresses the problem of local triangle counting with a focus on the efficiency issues arising in massive graphs. The distribution of the local number of triangles and the related local clustering coefficient can be used in many interesting applications. For example, we show that the measures we compute can help to detect the presence of spamming activity in large-scale Web graphs, as well as to provide useful features to assess content quality in social networks.

For computing the local number of triangles we propose two approximation algorithms, which are based on the idea of min-wise independent permutations (Broder et al. 1998). Our algorithms operate in a semi-streaming fashion, using O(jV j) space in main memory and performing O(log jV j) sequential scans over the edges of the graph. The first algorithm we describe in this paper also uses O(jEj) space in external memory during computation, while the second algorithm uses only main memory. We present the theoretical analysis as well as experimental results in massive graphs demonstrating the practical efficiency of our approach.