Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform sampling of undirected and directed graphs with a fixed degree
  sequence   Many applications in network analysis require algorithms to sample uniformly
at random from the set of all graphs with a prescribed degree sequence. We
present a Markov chain based approach which converges to the uniform
distribution of all realizations for both the directed and undirected case. It
remains an open challenge whether these Markov chains are rapidly mixing.
  For the case of directed graphs, we also explain in this paper that a popular
switching algorithm fails in general to sample uniformly at random because the
state graph of the Markov chain decomposes into different isomorphic
components. We call degree sequences for which the state graph is strongly
connected arc swap sequences. To handle arbitrary degree sequences, we develop
two different solutions. The first uses an additional operation (a
reorientation of induced directed 3-cycles) which makes the state graph
strongly connected, the second selects randomly one of the isomorphic
components and samples inside it. Our main contribution is a precise
characterization of arc swap sequences, leading to an efficient recognition
algorithm. Finally, we point out some interesting consequences for network
analysis.

27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin