k_i\rangle}=\frac{\sum_{j\ne i}\sum_{k\ne j}p_{ij}p_{jk}}{\sum_{j\ne i} p_{ij}},$$ $$\label{BCCe}
\langle c_i(W) \rangle \equiv\frac{\sum_{j\neq i}\sum_{k\ne i,j}p_{ij}p_{jk}p_{ki}}{\sum_{j\neq i}\sum_{k\ne i,j}p_{ij}p_{ki}}$$ where, by construction, $\langle k_i\rangle \equiv k_i$ for all $i$. For the expected value of ${s}^{nn}_i$ we have [@mastrandrea2013enhanced; @mybosefermi]: $$\langle {s}^{nn}_i(W) \rangle \equiv\frac{\sum_{j\ne i}p_{ij}{\langle s}_j\rangle}{\langle k_i\rangle}=\frac{\sum_{j\ne i}\sum_{k\ne j}p_{ij}\langle w_{jk}\rangle}{\sum_{j\ne i} p_{ij}}$$ where $\langle s_i \rangle \equiv s_i$, $\forall i$. Finally, the expected value of $c^w_i$ is $$\langle{c}_i^w(W)\rangle=\frac{\sum_{j\neq i}\sum_{k\ne i,j}
\langle{w}_{ij}^{1/3}\rangle
\langle{w}_{jk}^{1/3}\rangle
\langle{w}_{ki}^{1/3}\rangle}{\sum_{j\neq i}\sum_{k\ne i,j}p_{ij}p_{ki}}
\label{eq:cw}$$

[![image](KnnKBosMix){width="40.00000%"}]{} [![image](CKBosMix){width="40.00000%"}]{} [![image](SnnSBosMix){width="40.00000%"}]{} [![image](CWKBosMix){width="40.00000%"}]{}

In fig. \[AggBUN\] we show, for the snapshot in year 2002, the scatter plots between node degree ($k_i$) and higher-order binary properties ($k^{nn}_i, c_i$), as well as those between node strength ($s_i$) and higher-order weighted properties ($s^{nn}_i, c^w_i$). From an economic point of view, $k^{nn}_i$ and $c_i$ give information about indirect interactions over paths of length $2$ and $3$ respectively, since terms of the form $a_{ij}a_{jk}$ and $a_{ij}a_{jk}a_{ki}$ are involved in the definitions of these quantities. In accordance with the existing literature, we find decreasing trends of both $k_i^{nn}$ and $c_i$ versus $k_i$. This confirms that it is very likely to find nodes with many trade partners connected to nodes with small degree (disassortativity), while trade partners of poorly connected nodes are highly inter-connected. Similar considerations 