d\rangle} - {\langle d\rangle} = ({\langle d^2\rangle} - {\langle d\rangle}^2)/{\langle d\rangle} = \sigma^2/{\langle d\rangle} > 0$, since: (i) the variance is non-negative unless the network shows the same degree for all its nodes; (ii) $\langle d\rangle$ is greater than zero unless all the nodes have zero degree. This holds that ${\langle d^2\rangle}/{\langle d\rangle} > {\langle d\rangle}$, showing a result known as the [*friendship paradox*]{}, according to which your friends have more friends than you do [@feld1991your]. Such bias is due to an over-representation of high-degree nodes in comparison with low-degree ones during the calculation.

Please note that Formula (\[neighbor\]) refers to the general case of uncorrelated degree sequences [@barabasi2016network; @newman2018networks]. Networks generally show a degree-degree correlation which can display a positive degree correlation in the case of social networks or a negative one, for instance, in the case of networks related to technological and innovation research projects. In such context, the average degree of a neighbour of node $i$ is computed as [@pastor2001dynamical]:

$$\label{knni}
k_{nn,i} = \frac{1}{d_i}\sum_{j}d_ja_{ij}$$

A further measure can be expressed considering sets of nodes for identical degree. In this case, the average degree of a neighbour for nodes with degree equal to $k$, is defined as:

$$\label{knnd}
