341 research outputs found
Characterization of L1-norm Statistic for Anomaly Detection in Erdos Renyi Graphs
International audienceWe devise statistical tests to detect the presence of an embedded Erdos-Renyi (ER) subgraph inside a random graph, which is also an ER graph. We make use of properties of the asymptotic distribution of eigenvectors of random graphs to detect the subgraph. This problem is related to the planted clique problem that is of considerable interest
A spectral method for community detection in moderately-sparse degree-corrected stochastic block models
We consider community detection in Degree-Corrected Stochastic Block Models
(DC-SBM). We propose a spectral clustering algorithm based on a suitably
normalized adjacency matrix. We show that this algorithm consistently recovers
the block-membership of all but a vanishing fraction of nodes, in the regime
where the lowest degree is of order log or higher. Recovery succeeds even
for very heterogeneous degree-distributions. The used algorithm does not rely
on parameters as input. In particular, it does not need to know the number of
communities
Testing Cluster Structure of Graphs
We study the problem of recognizing the cluster structure of a graph in the
framework of property testing in the bounded degree model. Given a parameter
, a -bounded degree graph is defined to be -clusterable, if it can be partitioned into no more than parts, such
that the (inner) conductance of the induced subgraph on each part is at least
and the (outer) conductance of each part is at most
, where depends only on . Our main
result is a sublinear algorithm with the running time
that takes as
input a graph with maximum degree bounded by , parameters , ,
, and with probability at least , accepts the graph if it
is -clusterable and rejects the graph if it is -far from
-clusterable for , where depends only on . By the lower
bound of on the number of queries needed for testing graph
expansion, which corresponds to in our problem, our algorithm is
asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201
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