Figure 1.

A comparison of the completely heterogeneous networks (see text) with $N=4$, 5, 6 and 7. In each case, all the possible k-values from 1 to $(N-1)$ are present in the network as shown. One degree (one k-value) has to be shared by two nodes since the Nth node will have the degree of any one of other nodes. It is empirically shown that this degree of Nth node, denoted by $k^{\ast }$, is automatically fixed (if the network has all possible degrees from 1 to $(N-1)$) and is $N/2$ if N is even and $(N-1)/2$ if N is odd. For example, for $N=4$ and 5, $k^{\ast }=2$ and for $N=6$ and 7, $k^{\ast }=3$ and so on.