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Fig. 4 | Applied Network Science

Fig. 4

From: On the perturbation of self-organized urban street networks

Fig. 4

Relative Frequency Distributions (RFD) for the urban street network of Central London: circles represent relative frequencies for the valences of the road-road topological network; crosses represent relative frequencies for the valences of the junction-junction topological network. The red fitted curve for the natural road statistics describes the Maximum Likelihood Estimate (MLE) for the discrete Pareto probability distribution (14a) estimated according to the state of the art (Clauset et al. 2009; Gillespie 2015) (\(\underline {n}_{r} = 4, 2\lambda \upsilon _{r} = 2.610(65), n=250\,000\) samples, p-value=0.933(1)). The green fitted curve for the junction statistics shows the best Nonlinear Least-Squares Fitting (NLSF) for the nonstandard discrete probability distribution (14b) with \(\underline {n}_{r}\) and 2λυr fixed to their respective MLE value (2λυj≈−1.3); since fast evaluation of the normalizing function \(\mathcal {W}\) has yet to be found, no MLE approach can be used for now. Having for junctions a number of vital connections υj negative is interpreted as expressing a number of agent intraconnections for junctions relatively much smaller than the one for natural roads. The sharp downturn at a valence of 10 likely means that the model fails to catch what occurs when valences are small. In any case, a proper MLE remains to be performed for confirming

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