Definition of an abstract, combinatorial graph
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I have $0$ background in graph theory. I was recently reading an overview/history article of loop quantum gravity here: And in Appendix A, we state that, among other things, a basis state in the Hilbert space for LQG is characterized by a (abstract, combinatorial graph). I am looking for a precise mathematical definition of these terms (tried googling around but couldn't find anything concrete), or if I need a lot of background to understand it, maybe a text recommendation at an introductory level.
graph-theory mathematical-physics
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
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add a comment |
$begingroup$
I have $0$ background in graph theory. I was recently reading an overview/history article of loop quantum gravity here: And in Appendix A, we state that, among other things, a basis state in the Hilbert space for LQG is characterized by a (abstract, combinatorial graph). I am looking for a precise mathematical definition of these terms (tried googling around but couldn't find anything concrete), or if I need a lot of background to understand it, maybe a text recommendation at an introductory level.
graph-theory mathematical-physics
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
$endgroup$
add a comment |
$begingroup$
I have $0$ background in graph theory. I was recently reading an overview/history article of loop quantum gravity here: And in Appendix A, we state that, among other things, a basis state in the Hilbert space for LQG is characterized by a (abstract, combinatorial graph). I am looking for a precise mathematical definition of these terms (tried googling around but couldn't find anything concrete), or if I need a lot of background to understand it, maybe a text recommendation at an introductory level.
graph-theory mathematical-physics
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
$endgroup$
I have $0$ background in graph theory. I was recently reading an overview/history article of loop quantum gravity here: And in Appendix A, we state that, among other things, a basis state in the Hilbert space for LQG is characterized by a (abstract, combinatorial graph). I am looking for a precise mathematical definition of these terms (tried googling around but couldn't find anything concrete), or if I need a lot of background to understand it, maybe a text recommendation at an introductory level.
graph-theory mathematical-physics
graph-theory mathematical-physics
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
asked Dec 2 '18 at 5:30
staedtlerrstaedtlerr
1537
1537
add a comment |
add a comment |
1 Answer
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I think you may relax, because, as far as I know, by an abstract, combinatorial graph is understood
a usual graph. The words abstract and combinatorial belong not to a formal mathematical definition, but remark that we consider a graph as a set of vertices and edges, and we are not tied to its concrete realization, for instance, to a drawing on a plane.
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
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1 Answer
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active
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votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I think you may relax, because, as far as I know, by an abstract, combinatorial graph is understood
a usual graph. The words abstract and combinatorial belong not to a formal mathematical definition, but remark that we consider a graph as a set of vertices and edges, and we are not tied to its concrete realization, for instance, to a drawing on a plane.
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
$endgroup$
add a comment |
$begingroup$
I think you may relax, because, as far as I know, by an abstract, combinatorial graph is understood
a usual graph. The words abstract and combinatorial belong not to a formal mathematical definition, but remark that we consider a graph as a set of vertices and edges, and we are not tied to its concrete realization, for instance, to a drawing on a plane.
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
$endgroup$
add a comment |
$begingroup$
I think you may relax, because, as far as I know, by an abstract, combinatorial graph is understood
a usual graph. The words abstract and combinatorial belong not to a formal mathematical definition, but remark that we consider a graph as a set of vertices and edges, and we are not tied to its concrete realization, for instance, to a drawing on a plane.
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
$endgroup$
I think you may relax, because, as far as I know, by an abstract, combinatorial graph is understood
a usual graph. The words abstract and combinatorial belong not to a formal mathematical definition, but remark that we consider a graph as a set of vertices and edges, and we are not tied to its concrete realization, for instance, to a drawing on a plane.
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
answered Dec 3 '18 at 3:44
Alex RavskyAlex Ravsky
39.6k32181
39.6k32181
add a comment |
add a comment |
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