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Results tagged with random-graphs
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user 2672
The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.
2
votes
3
answers
225
views
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 …
- 9,720
1
vote
Random graphs defined by a set of tiles
To whom it may be of interest: Find here a short paper where I describe a graph generation model that takes a set of ego-networks and ties them together in a systematic (and possibly realistic) way. T …
- 9,720
4
votes
1
answer
279
views
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 …
- 9,720
1
vote
0
answers
71
views
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 …
- 9,720
3
votes
1
answer
154
views
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 …
- 9,720
3
votes
0
answers
202
views
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 …
- 9,720
4
votes
3
answers
421
views
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 …
- 9,720