_{ij}=\delta _{ij}$ and $S_{i}\left( n\right) =0$. We can also define a measure of the global complexity as an arithmetic mean over all the sites, $$G\left( n\right) =\frac{1}{N}\sum_{i=1}^{N}S_{i}\left( n\right) =-\frac{1}{N}\sum_{i=1}^{N}\sum_{j=1}^{N}\left( \mathbb{M}^{n}\right) _{ij}\ln \left( 
\mathbb{M}^{n}\right) _{ij}\ ,  \label{Ent2}$$ outlining a *global mean entropy*.

Model I: Illustration with numbers
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In the four sites network (digraph of Fig. \[fig01\]) we assume that there are, for instance, initially, $10\ 000$, $2\ 500$, $11\ 000$ and $13\ 000$ vehicles; the matrix (\[A1\]) with numbers in its entries is diagonal and is more conveniently expressed as the vector (\[A22\]), $$\mathbb{U}^{\mathrm{T}}\left( 0\right) =\left( 
\begin{array}{cccc}
10000 & 2500 & 11000 & 13000\end{array}\right) ,  \label{B02}$$ and the total number of vehicles in the network is $$Y=\sum_{i=1}^{4}U_{i}\left( 0\right) =36\ 500.  \label{B1b}$$ At a given moment the vehicles begin to circulate through the arteries and after few days (or at several moments of one day) of observation the average number of the vehicles that remain circulating (or parked) within each site (the vertices) are assumed *ad hoc* to be $3\ 000$, $1\ 000$, $4\ 000$, and $4\ 500$, while the remaining vehicles are on their way traveling to the other sites, characterized in the digraph by the values associated to the 