Towards Unbiased BFS Sampling

Abstract—Breadth First Search (BFS) is a widely used approach for sampling large unknown Internet topologies. Its main advantage over random walks and other exploration techniques is that a BFS sample is a plausible graph on its own, and therefore we can study its topological characteristics. However, it has been empirically observed that incomplete BFS is biased toward highdegree nodes, which may strongly affect the measurements. In this paper, we first analytically quantify the degree bias of BFS sampling. In particular, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction f of covered nodes, in a random graph RG(pk) with an arbitrary degree distribution pk. We also show that, for RG(pk), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, Snowball Sampling, RDS) suffer from exactly the same bias. Next, based on our theoretical analysis, we propose a practical BFS-bias correction procedure. It takes as input a coll...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Maciej Kurant, Athina Markopoulou, Patrick Thiran
• Keywords: Bfs Samples, CORR 2011, Correction Procedures, Education, Internet Topologies