user, while the adjacency matrix is a table used to gather the relations between all purchase choices expressed by users in a given moment, identifying a formal relationships between them.

In graphs, a usual measure is given by the number of relationships owned by a user. In the case of Figure \[fig:1\], user $1$ has three relationships, namely with users $2, 3$ and $4$. For a generic user $i$, such relations are expressed as a measure called [*degree*]{}, with symbol $d_i$, while the nodes linked to node $i$ are called the [*neighbour*]{} of $i$ (in symbols, $N(i)$). It is clear, that $d_i$ is an integer being zero when the user has no established relations.

All the degrees can be gathered in a vector, whose elements are ordered in a non-decreasing mode. This vector, called [*degree sequence*]{} with symbol $D_G$, is – in our example – $D_G = \{4, 3, 3, 2, 2, 2\}$. On the basis of such sequence, it is possible to compute the traditional average value $\langle d\rangle$, as well as the average of the squared values $\langle d^2\rangle$, that are – in our example – respectively, $\langle d\rangle =  2.67,$ and $\langle d^2\rangle = 7.67$.

In order 