Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Globally and Locally Minimal Weight Spanning Tree Networks   The competition between local and global driving forces is significant in a
wide variety of naturally occurring branched networks. We have investigated the
impact of a global minimization criterion versus a local one on the structure
of spanning trees. To do so, we consider two spanning tree structures - the
generalized minimal spanning tree (GMST) defined by Dror et al. [1] and an
analogous structure based on the invasion percolation network, which we term
the generalized invasive spanning tree or GIST. In general, these two
structures represent extremes of global and local optimality, respectively.
Structural characteristics are compared between the GMST and GIST for a fixed
lattice. In addition, we demonstrate a method for creating a series of
structures which enable one to span the range between these two extremes. Two
structural characterizations, the occupied edge density (i.e., the fraction of
edges in the graph that are included in the tree) and the tortuosity of the
arcs in the trees, are shown to correlate well with the degree to which an
intermediate structure resembles the GMST or GIST. Both characterizations are
straightforward to determine from an image and are potentially useful tools in
the analysis of the formation of network structures.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph