# social network

## Assortative mixing in networks

$\sum_{jk}e_{jk}=1 \quad \sum_je_{jk}=q_k$

$q_k=\frac{(k+1)p_{k+1}}{\sum_jjp_j}$

$r=\frac{\sum_{jk}jk(e_{jk}-q_jq_k)}{\sigma_q^2}$

$r=\frac{\sum_{jk}jk(e_{jk}-q^{in}_jq^{out}_k)}{\sigma_{in}\sigma_{out}}$

$r=\frac{\sum_ij_ik_i-M^{-1}\sum_ij_i\sum_{i^}k_{i^}}{\sqrt{[\sum_ij_i^2-M^{-1}(\sum_ij_i)^2][\sum_ik_i^2-M^{-1}(\sum_ik_i)^2]}}$

r的统计误差用$\sigma_r^2$来衡量$\sigma_r^2=\sum_{i=1}^M(r_i-r)^2$

[1] M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2002)". the remaining degree means the number of edges leaving the vertex other than the one we arrived along.

[2] M.E.J. Newman, S.H. Strogatz, and D.J. Watts, Phys. Rev. E 64, 026118 !2001". Random Graphs with Arbitrary Degree Distributions and Their Applications