Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Imagine one generates some form of random graph (e.g. a random geometric graph) and via simulation, calculates the probability that there exists an edge-wise path between all vertices in the graph as a function of the number of vertices and/or the allowed edge lengths in an area of fixed size (e.g. a square or circle). Is there a technical term for this "connected graph" threshold? How does this relate to to the percolation threshold where we look for a giant connected component?

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

The technical term is just that: "connectivity threshold" or "threshold for connectivity".

In general, the connectivity threshold and the giant component threshold are different. Take, for example, the percolation thresholds on the path $P_{n/2} + K_{n/2}$. In this case, the giant component threshold is $p = 1/n$ but the connectivity threshold is $p = 1$.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.