Table 3.

Network metrics.

Metric	Definition	Formula
In-degree	The number of links a node $i$ receives from other nodes $j$ in moment $t$. In our research, it refers to the number of trucking routes finishing at a given municipality.	$k_i^{in}\left(t\right)=\sum _{j=1}^{N\left(t\right)}{a}_{ij}\left(t\right)$
Out-degree	The number of links a node $i$ sends to other nodes $j$ in moment $t$. In our research, it is the number of trucking routes originating at a given municipality.	$k_i^{out}\left(t\right)=\sum _{j=1}^{N\left(t\right)}{a}_{ji}\left(t\right)$
Degree	The sum of in and out degrees.	$k_i^T\left(t\right)=k_i^{in}\left(t\right)+k_i^{out}\left(t\right)$
Weighted in-degree	In-degree pondered by the weight of each link. In our research, it is pondered by the number of trucking trips received by a municipality.	$W{k}_i^{in}\left(t\right)=\sum _{j=1}^{N\left(t\right)}{a}_{ij}\left(t\right)\ast w_{ij}\left(t\right)$
Weighted out-degree	Out-degree pondered by the weight of each link. In our research, pondered by the number of trucking trips originating at a municipality.	$W{k}_i^{out}\left(t\right)=\sum _{j=1}^{N\left(t\right)}{a}_{ji}\left(t\right)\ast w_{ji}\left(t\right)$
Betweenness centrality	The extent to which a particular municipality $i$ is located on the shortest trucking route connecting other municipalities $j$ and $k$ in the network.	$C_{Bi}=\sum _{k\ne i\ne j\in N}{\sigma }_{kj}\left(i\right)/{\sigma }_{kj}$
Closeness centrality	The extent to which a municipality $i$ is close to all other municipalities$j$ along the shortest routes, reflecting its level of accessibility in the trucking network.	$C_{ci}=\frac{n-1}{{\sum }_{v_j\in V,i\ne j}{d}_{ij}}$

Source: Own elaboration based on Wang et al. (2011) and Calatayud et al. (2017).