Urban retail location: Insights from percolation theory and spatial interaction modeling - Fig 4

<p>(<b>a</b>) We have overlapped a snapshot of the road network clusters for <i>τ</i> = 130 with the retail clusters {<i>w</i>^eq} for <i>α</i> = 1.5. The colours indicate the size of the clusters in a logarithmic scale. We can see how most of retail clusters fall on road clusters, and there is good agreement between the spatial distribution of the ranks. In (<b>b</b>)-(<b>c</b>) We show how Θ(<i>α</i>, <i>τ</i>) varies with <i>τ</i> for several values of <i>α</i>, on the full network and not considering the giant cluster. The dashed black line indicates the values obtained from the data. We can see that the model for <i>α</i> ≤ 1.9 constantly produces higher values, with and without the giant cluster, while for <i>α</i> = 2.3 we can see how the giant cluster plays a fundamental role. This is because for that value of <i>α</i> the floorspace is mostly concentrated in the giant cluster (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0185787#pone.0185787.g002" target="_blank">Fig 2</a>). (<b>d</b>)-(<b>e</b>) We show the <i>f</i>_in(<i>α</i>, <i>τ</i>) with and without the giant cluster. The results are in line with that said for the previous figures.