Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Metric Space of Networks   We study the question of reconstructing a weighted, directed network up to
isomorphism from its motifs. In order to tackle this question we first relax
the usual (strong) notion of graph isomorphism to obtain a relaxation that we
call weak isomorphism. Then we identify a definition of distance on the space
of all networks that is compatible with weak isomorphism. This global approach
comes equipped with notions such as completeness, compactness, curves, and
geodesics, which we explore throughout this paper. Furthermore, it admits
global-to-local inference in the following sense: we prove that two networks
are weakly isomorphic if and only if all their motif sets are identical, thus
answering the network reconstruction question. Further exploiting the
additional structure imposed by our network distance, we prove that two
networks are weakly isomorphic if and only if certain essential associated
structures---the skeleta of the respective networks---are strongly isomorphic.

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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat