sharing of $N(i)$ as $\sum_{j \in N(i)}d_j \simeq d_i \cdot k_{nn, i}$, that is equal to $d_i$ time the average degree of a neighbour of node $i$. Thus, the [*Network Information Patrimony*]{} is:

$$\label{cnei}
NIP_i \simeq \frac{d_i}{2m} + \frac{d_i}{2m} k_{nn} = \frac{d_i}{2m}(1 + k_{nn, i})$$

When we move to sets of nodes for identical degree, we have to consider Equation (\[knnd\]) instead of Equation (\[neighbor\]) and Equation (\[CMS1\]) which becomes:

$$\label{cne1}
NIP_i(d) \simeq \frac{d_i}{2m} + \frac{d_i}{2m} k_{nn}(d_i) = \frac{d_i}{2m}\bigg(1 + k_{nn}(d_i)\bigg)$$

Discussion and implication of the network information patrimony
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In the previous section we introduced three new measures for a given network; one referred to uncorrelated ones (Eq. \[CMS\]) and two to correlated networks (Eq. \[cnei\] and Eq. \[cne1\]). In both cases, we started from the concept of the market share of a node $i$, taking into consideration the average degree of neighbours as a proxy capable to capture the meso-scale connectiveness effects.

Considering a network, the degree correlation is a phenomenon capable to detect the tendency between nodes with similar degree to associate with each other. In a social networks environment, such tendency is called homophily or assortative mixing [@newman2018networks]. A network exhibits assortative mixing if nodes with 