Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balance and Frustration in Signed Networks   The frustration index is a key measure for analysing signed networks, which
has been underused due to its computational complexity. We use an exact
optimisation-based method to analyse frustration as a global structural
property of signed networks coming from diverse application areas. In the
classic friend-enemy interpretation of balance theory, a by-product of
computing the frustration index is the partitioning of nodes into two
internally solidary but mutually hostile groups.
  The main purpose of this paper is to present general methodology for
answering questions related to partial balance in signed networks, and apply it
to a range of representative examples that are now analysable because of
advances in computational methods.
  We provide exact numerical results on social and biological signed networks,
networks of formal alliances and antagonisms between countries, and financial
portfolio networks. Molecular graphs of carbon and Ising models are also
considered. The purpose served by exploring several problems in this paper is
to propose a single general methodology for studying signed networks and to
demonstrate its relevance to applications. We point out several mistakes in the
signed networks literature caused by inaccurate computation, implementation
errors or inappropriate measures.

13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom