gathering all the comments so far we obtain the value of $IP$ for the generic node $i$ as:

$$\label{nsi}
IP_i = \frac{d_i}{2m}$$

It is worth noting that we are reducing the market extension to its real dimension and in case of a complete network $m = n(n-1)/2$, thus the denominator of Equation (\[nsi\]) becomes again proportional to $n^2$, as postulated by the original definition of Metcalfe’s law.

Summarising, we are tailoring Metcalfe Law’s with a view to estimating the current value of a network, such as $\mathcal{V} \propto 2m$ and the value $\mathcal{V} \propto n^2$ remain still valid for a complete network.

Uncorrelated networks
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It is now possibile to introduce the collective effects of alters and we therefore define the [*Neighbours’ Information Patrimony*]{} $NIP_i$ of node $i$ as the sum of its information patrimony with the information patrimonies of all its alters, i.e. the nodes $j$ in its neighbourhood $N(i)$. In formula:

$$\label{CMS1}
NIP_i = IP_i + \sum_{j \in N(i)}IP_j = \frac{d_i}{2m} + \sum_{j \in N(i)}IP_j = \frac{d_i}{2m} + \frac{1}{2m}\sum_{j \in N(i)}d_j$$

In Equation (\[CMS1\]) we approximate the information patrimony of $N(i)$ as $\sum_{j \in N(i)}d_j \simeq d_i \cdot k_{nn}$, that is $d_i$ time the average degree of a 