Questions tagged [graph-theory]
DO NOT USE THIS TAG FOR graphs of a function.
33
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Mathematics of the star-mesh transformation
I'm trying to understand the star-mesh transform from a mathematical perspective. This transformation removes a node and by definition, the topology of the network changes, but the resulting network ...
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Entropy of natural networks [duplicate]
How does one define the entropy of a natural network (say for example, a river network, or a morphological skeletal network of a lake in the figure below) ? For example, the following report suggests ...
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Loop counting -- what if the graph is not planar?
It is typically claimed that $\hbar$ counts the number of loops in a connected diagram. E.g., Weinberg's QFT, Vol.II, equation 16.1.10. This rests on the fact that for a diagram with $I$ internal ...
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Line graph of altitude and pressure
Why isn't the graph a straight line but is rather curved ?
user65035
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Signature of Feynman Graphs
We have introduced the signature of Feynman Graph as:
$$
\omega_D(\Gamma)=D|\Gamma|-2E_\Gamma-V_\Gamma
$$
in which $E_\Gamma$ is the number of the edges, $V_\Gamma$ is the number of vertexes and $D$ ...
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Connected Diagrams [duplicate]
The generating functional for the connected part of the Green functions is defined
as
$$iW[j] = \log Z[j].$$
From this the four-point connected Green's function is then given by
$G_c(x_1,x_2,x_3,...
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1
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Why does this derivation/proof of KVL from KCL and Tellegens theorem hold?
I have come across a strange derivation of Kirchhoff's voltage law. You assume that Tellegen's theorem and Kirchhoff's current law both hold.
(Bold letters signify a vector.)
The proof:
Let L be an ...
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2
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Intuition behind Linked Cluster Theorem: connected vs. non-connected diagrams
Within statistical physics and quantum field theory, the linked cluster theorem is widely used to simplify things in the calculation of the partition function among other things.
My question has the ...
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When does a finite size random graph percolate?
Assume we are simulating percolation on a 2d lattice. While the system is of finite size, we say that the critical state appears when a cluster connects two opposing ends of the lattice. The bigger ...
1
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1
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Scalar fields of graphs
I am trying to find literature on the propagation of scalar fields over random graphs.
Think of a network of ideal resistors (with a given degree distribution), with a voltage source at a random node....
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1
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Resistance Distance in large electrical networks
I am not tremendously familiar with electrical circuits (I have some memories, but too long ago) and now I have come accross a problem where I need to compute the resistance distance in a graph.
So, ...
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What are the "balls" that are present in lightning?
Whenever I see a slow-motion video of lightning, I see that there are some sort of balls going around before the real discharge.
My question is.. what are those? (Video for reference: https://vimeo....
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Betti number of Feynman graph
Let $\mathcal{L}$ be a Lagrangian, which contains polynomials of bosonic fields $\phi$. After Wick's rotation we obtain a perturbation expansion od Green's function. In this expansion there are terms ...
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1
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Any fractal physical model that generates time series which demonstrate heavy-tailed (non-Gaussian) behavior in some form?
I know that fractal structures have power-laws in various forms "hidden" in them. I am looking for the most simple fractal model that I can find that generates time series with, say, Pareto-...
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Of the two variables (Q and V) in the equation of capacitor energy, which is better to take the average of?
$U_c = \frac{1}{2}QV$
I understand from the graph which it should be one half but not quarter, or taking the average of both.
But it doesn't really matter to me which variable is on y or x axis? (...
- 1,281
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2
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Writing a proper answer in a velocity-time graph
In a velocity time or any other vs time graph is it necessary,while mentioning an instant of time as 1s,2s,3s that it is from the starting point?Do I always have to say t=2s from the starting point?Is ...
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Dropping vertices of an overdetermined statics system graph
In statics, the problem of determining the tensions of K cables that connect a structure made of N points and keep all points in static equilibrium implies $ND$ systems of equations, where $D$ is the ...
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Examples of application of detour matrices in physics?
Are there any good examples of application of detour matrices in physics?
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Graph Theory and Feynman Integrals
In Vladimir A. Smirnov's book Analytic Tools for Feynman Integrals, Section 2.3, the alpha representation of general Feynman integral takes the form
$$
F_{\Gamma}(q_1,\ldots,q_n;d) = \frac{i^{-a-h}\...
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How to prove useful property of logarithm of generating functional in QFT?
How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.
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Dimension of the space of solutions in an electric circuit
Consider an electric circuit with dc sources ( voltage and current) and resistors. Write down the equations. In the most general case, the solution of the system is not unique. The set of solutions ...
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Understanding the intermediate field method for the $\phi^4$ interaction
In Rivasseau's and Wang's How to Resum Feynman Graphs, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to ...
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Lattice theory in mathematics and physics [closed]
I have undertaken a project examining lattice model and trying to construct algorithm that could work on all lattice (in physical sense, or crystal structure). I notice there is a branch in ...
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What is the difference between scale-free network and small-world network? [closed]
What is the difference between scale-free network and small-world network?
I can't understand from the definitions around the web if they are both the same name for one thing. Do both follow a power-...
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Research on ground state configuration of Ising model
I want to do mathematical research (algorithm construction and mathematical analysis) on Ising model ground state configuration. From what I know, the state of art research is using graph theory ...
3
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Quantum graph theory: complex spectra
In quantum graph theory, what are the properties of a given graph to own complex conjugated complex eigenvalues, either finite or infinite? Spectral graph theory is as far as I know a not completely ...
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Spin Glass Transitions in Random Bond Ising Model (RBIM)
In brief, is there a list of spin glass transition properties for the RBIM on different lattices? Is there any know results about the relationships between these probabilities for a graph and its dual?...
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Book reviewing current state of research on complex networks [closed]
Can anybody recommend a book reviewing the current state of knowledge and active research on complex networks?
Not primarily a textbook but a true review of the field - ideally with references to ...
2
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2
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226
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Graph Invariants and Statistical Mechanics
Many intuitive knot invariants including Jones' polynomial are inspired by statistical mechanics. Further profound connections have been explored between knot theory and statistical mechanics. I was ...
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what is meant by "crossover phenomena"?
In many articles I read the term "crossover phenomena" and a lot of methodology discussed according to it, with little or no description about what is meant by it. Sometimes there is a connection to ...
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Properties of graph of subatomic particle interactions
Say there was some situation where you have a lot of subatomic particles interacting with each other and decided to draw (say, by joining Feynmann diagrams) those interactions- so that you got some ...
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Why are physicists interested in graph theory?
Can you tell me how graph theory comes into physics, and the concept of small world graphs?
(inspired to ask from comment from sean tilson in):
Which areas in physics overlap with those of social ...
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Which areas in physics overlap with those of social network theory for the analysis of the graphs?
I am studying social networks in terms of graph theory and linear algebra. I know that physicists have published and worked a lot in this field. This causes me to assume that there are sub-fields in ...
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