# 网络|PH30098 Networks代写

$$E=-\sum_{i j} p_{i j} \ln p_{i j}$$
where
$$p_{i j}=t_{i j} / O_{i}$$
In $p_{i j}, t_{i j}$ is the number of commuters between districts $i$ and $j$, while $O_{i}$ is the outflows of district $i$.

## PH30098 COURSE NOTES ：

$y_{i u}+y_{i j} \geq 2 y_{i j}$ for all $i, j$
$\sum_{i j} \sum_{j \dot{i}} y_{i j}=k(k-1)$
$y_{i j} \in{0,1}$ for all $i, j$
The first constraint implies that if $y_{i j}=1$, then $y_{u}=y_{j}=1$. The second constraint imposes the correct number of connections. Consequently, if $y_{i i}=y_{i j}=1$, then $y_{i j}=1$.