We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory footprint…
Motivated by community detection, we characterise the spectrum of the non-backtracking matrix $B$ in the Degree-Corrected Stochastic Block Model. Specifically, we consider a random graph on $n$ vertices partitioned into two equal-sized clusters. T…
In this section we present the proof of the lower bound for Theorem 1.1. To prove the lower bound, it suffices to show that for any ε>0, there exists w.h.p. two vertices u and v such that
We would like to thank Andrea Montanari and Guilhem Semerjian for explaining us a key idea for the proof of Lemma 12, as well as Nikolaos Fountoulakis, David Gamarnik, James Martin and Johan Wästlund for interesting discussions.
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