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Results tagged with graph-theory
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user 2672
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
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Another betweenness centrality measure: neighbourhood centrality
Among the many centrality measures that I have heard of, I miss the following (but maybe I'm just blind).
Consider a graph $G$ with $k$ connected components $G_i$ of size $|G_i|$. The number of node p …
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2
votes
3
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225
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Random graphs defined by a set of tiles
Related to this question, which I asked at MSE, I'd like to ask this one here:
Consider a (large) graph $G$ and its multi-set of tiles $T$, i.e. the multi-set of its vertex-induced subgraphs, i.e. the …
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4
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3
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421
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How to show that random graphs cannot be embedded with short edges
For each (not necessarily planar) embedding of a graph in $\mathbb{R}^k$ one can calculate the ratio
$$\gamma = \frac{\textsf{mean Euclidean length of edges}}{\textsf{mean Euclidean distance between n …
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0
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0
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139
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Graph theory: Closed neighourhoods and generalized clustering coefficients
The neighbourhood of node $v$ in graph $G$ is the subgraph of $G$ induced by all vertices adjacent to $v$.
The number of edges between neighbours divided by the number of pairs of neighbours is th …
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5
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4
answers
2k
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The distance distribution of graphs
The degree distribution of a graph is of main importance, especially for large graphs, and namely random graphs. Its expected value and its higher moments tell a lot about a graph – but of course not …
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2
votes
1
answer
54
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Uniform closure of a neighbourhood complex in the tritetragonal tiling
Consider a neighbourhood complex of eight vertices (red) with vertex configuration $(3.4)^3$ which gives rise to the tritetragonal tiling of the hyperbolic plane:
Not knowing if this complex can be u …
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3
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0
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Distance spectra of uniform tilings
Let a uniform tiling be defined by a vertex configuration $(n_1.n_2.\cdots.n_k)^m$, which is either spherical, Euclidean or hyperbolic. Assume that the tiling is vertex-transitive, especially that eac …
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4
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1
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Structures for random graphs with structure
Background[You may skip this and go immediately to the Definitions.]
Crucial features of a (random) graph or network are:
the degree distribution $p(d)$ (exponential, Poisson, or power law)
the mean …
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3
votes
1
answer
154
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Hyper-degree sequences: How to count them and how to construct hyper-graphs from them?
From an answer to this question I have learned how to ask this question properly.
Consider a $k$-uniform hypergraph on $n$ nodes, i.e. a family of $k$-subsets of $[n]= \{1,2,\dots,n\}$ (the hyperedges …
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3
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0
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202
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Two kinds of generating functions
Sorry for a possibly off-the-topic question, but I am afraid to gain the necessary overview to give an answer (supposed the question is not ill-posed) is beyond my capabilities.
In the course of creat …
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3
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1
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223
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Yet another graph characteristic
I wonder if the following graph-theoretical concepts have been considered before, and if so, under which name.
Consider a directed graph $G$ with $n$ nodes.
Let the cycle number $\gamma(\nu)$ be …
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0
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0
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85
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Generalized concept of subgraph (input/output graphs)
The usual definition of a vertex-induced subgraph goes like this:
A vertex-induced subgraph1 is a subset of the vertices of a graph $G$
together with any edges with both endpoints in this subse …
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5
votes
2
answers
474
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Another graph characteristic
This question concerns a method of drawing graphs and a graph characteristic about which I want to learn more.
Consider a connected directed graph with at least one node with in-degree 0 and one node …
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6
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2
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906
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Human brains considered as directed graphs
I assume that human brains can be considered as directed graphs with neurons as nodes and synapses as edges. I explicitly don't want to consider the weights, the dynamics of neural activity (based on …
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4
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1
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Fuzzy layers in graphs and neural networks
I wonder if the following statistical description of the layer architecture of finite graphs has been considered before and where I can find some references (especially under which name).
Consider a h …
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