Tagged Questions

The tag has no wiki summary.

learn more… | top users | synonyms

6
votes
1answer
56 views

Expected number of maximal cliques in $G(n,p)$

The $G(n,p)$ random graph model creates graphs with $n$ vertices and each possible edge exists independently with probability $p\in (0,1)$. Much is known about the (expected) size of a largest ...
4
votes
2answers
86 views

Generation of random binary trees

Given n, I want to randomly generate a binary tree (unlabelled) that has n end nodes. Could someone kindly provide a reference containing an algorithm for doing that? I attempted to do as follows: ...
6
votes
4answers
263 views

What is a good algorithm for generating random DFAs?

I am generating random DFAs to test a DFA reduction algorithm on them. The algorithm that I'm using right now is as follows: for each state $q$, for each symbol in the alphabet $c$, add $\delta (q, ...
2
votes
1answer
53 views

Mean number of edges between two equal partitions

For a random undirected graph with $n$ nodes, where each node has $k$ incident edges ($nk/2$ edges in total), the vertex set is partitioned into two sets each having $n/2$ nodes. What is the ...
3
votes
1answer
242 views

What is the probability of friendship conditioned on the number of mutual friends

Let Alice and Bob be two users chosen uniformly at random from a social network (e.g. Facebook). What is the probability that they are friends assuming that they share $k$ mutual friends? I am ...
9
votes
1answer
330 views

Number of clique in random graphs

There is a family of random graphs $G(n, p)$ with $n$ nodes (due to Gilbert). Each possible edge is independently inserted into $G(n, p)$ with probability $p$. Let $X_k$ be the number of cliques of ...