Degree of bipartite graph

Question

I have a bipartite graph whose sets of nodes have $N_1$ and $N_2$ nodes respectively.

What is the average degree of the two sets ($\bar{k_1}$ and $\bar{k_2})$?

I know that: $$\bar{k}=\frac{2L}{N_1+N_2}$$ where $L$ is the number of links of the network.

Is there an expression connecting $N_1$, $N_2$, $\bar{k_1}$ and $\bar{k_2}$?

Thanks

Answer 1

Call the vertex classes $S_1$ and $S_2$ and call their degree sums $s_1$ and $s_2$. As the graph is bipartite, each edge connects a vertex in $S_1$ to a vertex in $S_2$. So $s_1 = s_2 = L$.

As $\bar{k}_1 = s_1/N_1$ and $\bar{k}_2 = s_2/N_2$, this gives $N_1 \bar{k}_1 = N_2 \bar{k}_2$.