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Questions tagged [graph-theory]

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To calculate the resultant resistance of a circuit can you use all possible paths and assume they're parallel? [duplicate]

To calculate the resultant resistance of a circuit can you use all possible paths and assume they're parallel? Say I have a circuit like this: And I want to determine the resistance between x and y. ...
WilliamHarvey's user avatar
2 votes
1 answer
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Measure of connectivity in Graph States

Given $G = (V,E)$, with the set of vertices $V$ and the set of edges $E$, the corresponding graph state is defined as $$|G\rangle = \prod_{(a,b)\in E} U^{\{a,b\}} |+\rangle ^{\otimes V}$$ where the ...
Young Kindaichi's user avatar
4 votes
2 answers
391 views

Interpreting generating functional as sum of all diagrams

The generating functional is defined as: $$Z[J] = \int \mathcal{D}[\phi] \exp\Big[\frac{i}{\hbar}\int d^4x [\mathcal{L} + J(x)\phi(x)]\Big].$$ I know this object is used as a tool to generate ...
CBBAM's user avatar
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Feynman diagrams with no lines crossing

What does it mean when we say a feynman diagram has no lines crossing? What are some examples of diagrams with and without lines crossing?
Taenyfan's user avatar
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Where can I find the configurations corresponding to the current largest max-cut values on $G$-set graphs?

I am looking for the configurations that are behind the max-cut value in many articles about solving the Ising problem/max-cut problem on graphs, but I can't seem to find any articles with this data ...
Dániel Száraz's user avatar
5 votes
1 answer
369 views

From Feynman diagram to electrical circuit in arXiv:hep-th/0308184 by Rajesh Gopakumar

I am asking this question on behalf of user furious.neutrino. I asked this question at Electrical Engineering Stack Exchange, but it has not received a reply, so I am duplicating it here. I think the ...
Math Keeps Me Busy's user avatar
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0 answers
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General validity of the Linked Cluster Theorem in QFT for arbitrary correlation functions

In QFT, either at zero or finite temperature, the Linked Cluster Theorem (LCT) ensures that all disconnected diagrams appearing in the numerator of the interacting Green's function exactly cancel with ...
Zarathustra's user avatar
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1 answer
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What is the definition of $n$-loop 1PI diagrams in QFT? [closed]

What is the precise definition of a $n$-loop one-particle irreducible ($1$PI) diagram? For example, consider the following diagrams. Is the first diagram a $0$-loop $1$PI diagram? Is the second ...
TaeNyFan's user avatar
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1 vote
0 answers
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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 ...
Paula's user avatar
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2 answers
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Deriving the number of loops and number of lines meeting at a vertex in a diagram

When reading about Superficial Degrees of Divergence (SDOD) I have seen in An Introduction to Field Theory (Chapter 10.1) that for Lagrangians with a $\phi^n$ interaction term we know that: $$\tag{1} ...
user7077252's user avatar
2 votes
1 answer
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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 ...
vbj's user avatar
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4 votes
1 answer
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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 ...
AccidentalFourierTransform's user avatar
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1 answer
4k views

Line graph of altitude and pressure

Why isn't the graph a straight line but is rather curved ?
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0 answers
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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 $D$ ...
Drebin J.'s user avatar
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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,...
amilton moreira's user avatar
1 vote
1 answer
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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 ...
Jure Vreča's user avatar
13 votes
2 answers
6k views

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 ...
KF Gauss's user avatar
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1 vote
0 answers
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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 ...
Dionysios Georgiadis's user avatar
1 vote
1 answer
123 views

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....
Dionysios Georgiadis's user avatar
0 votes
1 answer
595 views

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, ...
excalibur1491's user avatar
2 votes
0 answers
58 views

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....
Goodwine's user avatar
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3 votes
1 answer
254 views

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 ...
mikis's user avatar
  • 512
2 votes
1 answer
93 views

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-...
mt_christo's user avatar
0 votes
1 answer
51 views

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? (...
most venerable sir's user avatar
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2 answers
99 views

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 ...
Harmonic's user avatar
  • 274
3 votes
0 answers
73 views

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 ...
diffeomorphism's user avatar
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0 answers
144 views

Examples of application of detour matrices in physics?

Are there any good examples of application of detour matrices in physics?
qazwsx's user avatar
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6 votes
1 answer
2k views

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}\...
soliton's user avatar
  • 1,681
6 votes
2 answers
2k views

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.
Andrew McAddams's user avatar
4 votes
2 answers
250 views

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 ...
user35303's user avatar
5 votes
0 answers
188 views

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 ...
Huy's user avatar
  • 309
3 votes
0 answers
282 views

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 ...
user40780's user avatar
  • 173
0 votes
1 answer
4k views

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-...
linello's user avatar
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1 vote
1 answer
372 views

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 votes
1 answer
464 views

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 ...
riemannium's user avatar
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3 votes
0 answers
224 views

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?...
Matthew Matic's user avatar
2 votes
0 answers
160 views

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 ...
3 votes
2 answers
243 views

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 ...
DurgaDatta's user avatar
13 votes
6 answers
33k views

What are the different methods for a resistor circuit that isn't parallel or series? [closed]

What are the different approaches to determine the equivalent resistance of nontrivial resistor networks in general, that cannot be reduced by the usual series and parallel rules? (The diagram below ...
Carl Brannen's user avatar
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9 votes
2 answers
5k views

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 ...
Vass's user avatar
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4 votes
1 answer
943 views

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 ...
Tomcat's user avatar
  • 141
24 votes
5 answers
12k views

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 ...
Vass's user avatar
  • 782
15 votes
2 answers
4k views

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 ...
Vass's user avatar
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