Consider a bipartite network with N$1$ and N$2$ nodes in the two sets.

$($i$)$ What is the maximum number of edges the network can have?

$($ii$)$ Derive an expression for the number of edges that are prohibited in a bipartite network as compared to a non$-$bipartite network of size $\backslash ($ N$=$N $1+$N $2(2\backslash$mathrm$\{$pts$\})\backslash )$

$($iii$)*$ Find the projections to both the yellow and the blue nodes for the bipartite network shown below.

$*$ You may use the support of a computer. If you do so please add a documented screenshot of your code. No need to upload an extra notebook.