#20228: Spectral radius of graphs
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Reporter: vdelecroix | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.1
Component: graph theory | Keywords:
Merged in: | Authors: Vincent Delecroix
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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There are no current way to compute the spectral radius of a graph (the
Perron-Frobenius eigenvalue of its adjacency matrix). We provide a method
`spectral_radius` that provides an interval of floating approximations.
It is much faster than previously available methods (where the exact
methods are unusable because of characteristic polynomial computation)
{{{
sage: G = digraphs.RandomDirectedGNM(10,40)
sage: %timeit max(G.adjacency_matrix().charpoly().roots(AA,
multiplicities=False))
100 loops, best of 3: 6.23 ms per loop
sage: %timeit G.spectral_radius()
1000 loops, best of 3: 178 µs per loop
}}}
And for a larger graph
{{{
sage: G = digraphs.RandomDirectedGNM(400, 6000)
sage: %timeit max(G.adjacency_matrix().charpoly().roots(AA,
multiplicities=False))
1 loop, best of 3: 4.63 s per loop
sage: %timeit G.spectral_radius()
10 loops, best of 3: 13 ms per loop
}}}
The new method `spectral_radius` can be used for much larger graph as soon
as the spectral graph is large enough to ensure the convergence.
--
Ticket URL: <http://trac.sagemath.org/ticket/20228>
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