Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph spectra and the detectability of community structure in networks   We study networks that display community structure -- groups of nodes within
which connections are unusually dense. Using methods from random matrix theory,
we calculate the spectra of such networks in the limit of large size, and hence
demonstrate the presence of a phase transition in matrix methods for community
detection, such as the popular modularity maximization method. The transition
separates a regime in which such methods successfully detect the community
structure from one in which the structure is present but is not detected. By
comparing these results with recent analyses of maximum-likelihood methods we
are able to show that spectral modularity maximization is an optimal detection
method in the sense that no other method will succeed in the regime where the
modularity method fails.

14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th