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5 votes
1 answer
386 views

Are directed graphs with out-degree exactly 2 strongly connected with probability 1?

Consider a directed graph with out-degree exactly two with $n$ vertices $v_1, v_2 \cdots v_n$ that is constructed as follows: For each vertex $v_i$, one chooses uniformly at random two (not ...
JoshuaZ's user avatar
  • 6,969
6 votes
0 answers
116 views

The properties of almost all directed graphs

A mathematician on the forum previously requested a reference on human brains modelled as directed graphs. This makes sense as neurons are mostly unidirectional and I have been thinking about similar ...
Aidan Rocke's user avatar
  • 3,871
0 votes
1 answer
166 views

Length of longest directed circuit in random tournament

Build a random tournament $T=(V,E)$ on $V=\{1,\ldots, n\}$ in the following fashion: for $i < j\in \{1,\ldots, n\}$ let the probability be $0.5$ whether $(i,j)\in E$ or $(j,i)\in E$ (in a ...
Dominic van der Zypen's user avatar