I am calculating the average minimum path length of Erdős–Rényi graphs. I am using the $G(N,n)$ model whereby a $N$ node graph with $n$ edges are generated uniformly.

I found the expected average minimum path length here

$$l_{ER} = \frac{\ln(N) - \gamma}{\ln(\langle k \rangle)} + \frac{1}{2} = \frac{\ln(N) - \gamma}{\ln(2n) - \ln(N)} + \frac{1}{2}{}$$

Where $\gamma$ is the Euler–Mascheroni constant and the average degree $\langle k \rangle = 2n/N$ is an obvious corollary of the handshaking lemma.

Is there is an estimate for the variance of average minimum path length for Erdős–Rényi graphs?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.