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The study of probability distributions over graphs. For example, the Erdős–Rényi model where each edge occurs independently with equal probability.

1 vote
0 answers
163 views

Locally "unshortable" paths in graphs

Setup: Consider a connected graph G, with diameter "d". Informally: Trivially (by definition of diameter), taking any path $P$ any nodes $P(i) , P(i+k)$ for $k>d$ can be connected by a SHORTER path. …
6 votes
1 answer
301 views

Citations graphs: what is known?

There has been much research related to web graphs and social graphs. They can be thought of as a kind of random graphs, but the point is that they are different from the well-known Erdős–Rényi model. …
23 votes
4 answers
972 views

What nodes of a graph should be vaccinated first?

Consider a graph, choose some "p: 0<p<1" (probability to infect the neighbor node). Choose some random number "K" of nodes which are "infected" initially. So we can generate epidemic model on a graph …
1 vote
1 answer
179 views

Survey/references on random geometric $K$-NN – $K$-nearest-neighbour graphs?

[Edit:] Some related info on number of connected components of NN-graphs can be found here: https://cstheory.stackexchange.com/a/47037/2408 Sample $N$ points in $\mathbb{R}^d$ from some distributio …