a random distribution, and values near $-1$ to a checkered pattern (every other cell occupied). Usually, polycentric distributions have relatively small positive $I$ values, depending on the size and distance between centers.

#### Network performance

Due to the branching nature of the growth algorithm, the network of roads $G$ cannot contain any other loops than the ones initially present in $G_0$. Therefore, notions of “clustering coefficient” or “robustness” (with respect to node removal) are not relevant here. On the other hand, since $G$ is intended to simulate a *mobility* network, we can evaluate its performance by defining a *relative speed* [@banos2012towards] $S$, representing the “detours” imposed by $G$ with respect to direct, straight travels: $$S(t)=\left(\frac{1}{\sum_{i,j}\delta(i,j,t)}\!\!\sum_{\scriptstyle i,j=1\atop\scriptstyle\delta(i,j,t)\neq0}^N\!\!\left(\frac{d_3(i,j,t)}{e_3(i,j,t)}\right)^{p_S}\right)^{1/p_S}$$ where $p_S\geq 1$ (also 3), and $e_3(i,j,t)$ is the direct Euclidean distance between cell $(i,j)$ and the nearest city center over the network, i.e. the one that realizes the value of $d_3(i,j,t)$. Note that $S\ge1$ and is actually higher for more convoluted networks (thus it is a measure of “slowness”, but we still employ “speed”).

#### Functional accessibility

The global functional accessibility $A$ to city centers is another $p$-norm (also 3), based on the relative local accessibility from each cell, which is $d_4$ over 