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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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Section: New Results

An Impossibility Result for Reconstruction in a Degree-Corrected Planted-Partition Model

We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on n nodes, having i.i.d. weights (φu)u=1n (possibly heavy-tailed), partitioned into q2 asymptotically equal-sized clusters. The model parameters are two constants a,b>0 and the finite second moment of the weights Φ(2). Vertices u and v are connected by an edge with probability (φuφv/n)a when they are in the same class and with probability (φuφv/n)b otherwise. We prove that it is information-theoretically impossible to estimate the clusters in a way positively correlated with the true community structure when (ab)2Φ(2)q(a+b). As by-products of our proof we obtain (1) a precise coupling result for local neighbourhoods in DC-SBM's, that we use in a follow up paper [Gulikers et al., 2017] to establish a law of large numbers for local-functionals and (2) that long-range interactions are weak in (power-law) DC-SBM's.