Spatial clustering and anisotropy

[cbueth]

Calculate for high betweenness nodes

• add config parameter to set the percentile

Spatial clustering and Anisotropy of high ($\theta$-percentile) $C_B$ nodes

$$\begin{aligned} C_\theta & =\frac{1}{N_\theta\langle X\rangle} \sum_{i=1}^{N_\theta}\left|x_i-x_{\mathrm{cm}, \theta}\right| & A_\theta=\frac{\lambda_1}{\lambda_2} & \\ \text { with }\langle X\rangle & =\frac{1}{N} \sum_{i=1}^N\left|x_i-x_{\mathrm{cm}, \theta}\right| & \mathrm{cov}\left[X_\theta\right]=\lambda_i, & \lambda_1 \leq \lambda_2 \end{aligned}$$

Kirkley, A., Barbosa, H., Barthelemy, M. & Ghoshal, G. From the betweenness centrality in street networks to structural invariants in random planar graphs. Nat Commun 9, 2501 (2018).