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

3 DYOGENE - Dynamics of Geometric Networks
Inria de Paris, CNRS - Centre National de la Recherche Scientifique : UMR 8548, DI-ENS - Département d'informatique de l'École normale supérieure
Abstract : We consider a degree-corrected planted-partition model: a random graph on $n$ nodes with two equal-sized clusters. The model parameters are two constants $a,b > 0$ and an i.i.d. sequence $(\phi_i)_{i=1}^n$, with second moment $\Phi^2$. Vertices $i$ and $j$ are joined by an edge with probability $\frac{\phi_i \phi_j}{n}a$ whenever they are in the same class and with probability $\frac{\phi_i \phi_j}{n}b$ otherwise. We prove that the underlying community structure cannot be accurately recovered from observations of the graph when $(a-b)^2 \Phi^2 \leq 2(a+b)$.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01258194
Contributor : Marc Lelarge <>
Submitted on : Monday, January 18, 2016 - 5:26:09 PM
Last modification on : Tuesday, May 14, 2019 - 10:13:58 AM

### Identifiers

• HAL Id : hal-01258194, version 1
• ARXIV : 1511.00546

### Citation

Lennart Gulikers, Marc Lelarge, Laurent Massoulié. An Impossibility Result for Reconstruction in a Degree-Corrected Planted-Partition Model. 2016. ⟨hal-01258194⟩

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