Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How tree-based is my network? Proximity measures for unrooted
  phylogenetic networks   Tree-based networks are a class of phylogenetic networks that attempt to
formally capture what is meant by "tree-like" evolution. A given non-tree-based
phylogenetic network, however, might appear to be very close to being
tree-based, or very far. In this paper, we formalise the notion of proximity to
tree-based for unrooted phylogenetic networks, with a range of proximity
measures. These measures also provide characterisations of tree-based networks.
One measure in particular, related to the nearest neighbour interchange
operation, allows us to define the notion of "tree-based rank". This provides a
subclassification within the tree-based networks themselves, identifying those
networks that are "very" tree-based. Finally, we prove results relating
tree-based networks in the settings of rooted and unrooted phylogenetic
networks, showing effectively that an unrooted network is tree-based if and
only if it can be made a rooted tree-based network by rooting it and orienting
the edges appropriately. This leads to a clarification of the contrasting
decision problems for tree-based networks, which are polynomial in the rooted
case but NP complete in the unrooted.

29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th