k_{nn}(k) = \frac{\sum_{i:d_i= d}k_{nn,i} }{\sum_{i:d_i= d}1}$$

Considering the example shown in Figure \[fig:1\], Equation \[neighbor\] brings to $k_{nn} = 2.9$, Equation \[knni\] brings to $k_{nn, 1} = 3.0$, $k_{nn, 2} = 3.0$, $k_{nn, 3} = 3.5$, $k_{nn, 4} = 2.5$, $k_{nn, 5} = 2.5$ and $k_{nn, 6} = 3.0$, while Equation \[knnd\] to $k_{nn}(2) = 3.0$ for the set of nodes of degree 2, $k_{nn}(3) = 3.0$ for the set of nodes of degree 3 and $k_{nn}(4) = 2.5$ for the set of nodes of degree 4.

$k_{nn}(k)$ nature highlights two distinctive structural network properties with reference to the presence of degree correlation. If $k_{nn}(k)$ is an increasing function of $k$, such setting identifies [*assortative mixing*]{}, showing that high-degree nodes are preferentially connected to high-degree nodes, while the low ones to low ones. On the other hand, a decreasing trend of $k_{nn}(k)$ identifies [*disassortative mixing*]{} showing nodes with high connections having neighbours with lower ones.

Neighbours’ Information patrimony {#NIP}
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In this section, we introduce our definition of Neighbours’ Information Patrimony ($NIP$).

To this purpose, we start from the concept of “network value” which has been mostly defined on the basis of Metcalfe’s law. Comparing the weight of a 