#15662: Ihara zeta function of graphs
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Reporter: | Owner:
chapoton | Status: needs_info
Type: | Milestone: sage-6.1
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers:
theory | Work issues:
Keywords: zeta | Commit:
function | b2c1e310c03477183cb3e793103711989955eb57
Authors: | Stopgaps:
Frédéric Chapoton |
Report Upstream: N/A |
Branch: |
u/chapoton/15662 |
Dependencies: |
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Comment (by chapoton):
Hello,
1) I am not quite sure about the name indeed. I would say that this is
usually called the zeta function of a graph. But there are variants, some
of them called weighted zeta functions. I think keeping the name starting
with zeta is good for TAB completion.
2) The algorithm needs to duplicate every edge, by orienting the original
one in a chosen direction, and the new one in the other direction. I take
as orientation the one given by self.edges(). I then use the shift by the
number of edges as the bijection between original edges and their
duplicate-reverse.
3) Some people had needed that function and used another way to do it :
see http://mathoverflow.net/questions/122682/ihara-zeta-function-graph-
theory-coefficients-using-a-line-graph
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Ticket URL: <http://trac.sagemath.org/ticket/15662#comment:4>
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