**Aligning two metabolic networks with and without compression.** Top figures (a-c) illustrate the steps of

alignment without

compression. Bottom figures (d-g) demonstrate different phases of

alignment with

compression using our framework. (a) Two hypothetical

metabolic networks with 5 and 4 reactions respectively. Directed edges represent the neighborhood relations between the reactions. (b) Support matrix of size 20

*×*20 needed for the

alignment if

compression is not used. We only show the non-zero entries of a single row that corresponds to topological support given by

*b *-

*b' *mapping to possible mappings of its backward and forward neighbors. Five such mappings supported equally are denoted by

in the matrix, namely

*a *-

*a' *mapping for the backward neighbors and

*c *-

*c'*,

*c *-

*d'*,

*d *-

*c' *and

*d *-

*d' *mappings for the forward neighbors. (c) The resulting reaction mappings of

alignment without

compression. (d) Query networks shown in (a) in compressed domain after one level of

compression. (e) Support matrix of size 6

*×*6 needed for the

alignment with

compression. We only show the entries for the mappings supported by the

*a*,

*b *-

*a'*,

*b' *mapping. (f) The resulting mappings from the

alignment in compressed domain. (g) The resulting reaction mappings after refinement phase of our framework.

## PubMed Commons