#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 ncohen):
Yoooooooooooo !
> 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.
Hmmmmm... Well, if the terminology isn't even set, should it become a
Graph method ? I am trying to keep my graph functions out of the graph
class when I believe that their are not of very wide use.
When you type "zeta function graphs" in Google (http://goo.gl/SM8aLb) the
first result I get is the following :
http://math.ucsd.edu/~aterras/snowbird.pdf
Which hints that there may be quite a lot of Zeta functions defined on
graphs. And they do mention the one you implement, saying that it may be
weighted too. What about `.zeta_ihara` if you want the name to begin with
`zeta` ?
> 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.
Like when you do `DiGraph(a_graph)` ?
> 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.
Oh. Well, I still do not understand what your two loops exactly do, but it
looks like you are computing a bit too much. It feels like you are
interested in the edges which share a vertex, except when they represent
the same edge.
...
Hey, aren't you just computing the adjacency matrix of the line graph,
which can be obtained by `G.line_graph().adjacency_matrix()` ?
Nathann
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Ticket URL: <http://trac.sagemath.org/ticket/15662#comment:5>
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