Fig. 4: Cross-temporal cluster analysis, carried out for cross-sections of the MSA variables in intervals of 25 years.
From: A century of decoupling size and structure of urban spaces in the United States
a Size-related variables (NUMBUPROP, NETBUI, BUAREA), and b form-related variables (NUMPATCH, SCAT, MAXPATCHPROP). Each node of the depicted networks represents a cluster of MSAs, node sizes correspond to the number of MSAs per cluster, and node colors represent the location of the cluster center (i.e., medoid) in the respective attribute spaces, using RGB color-coding. The legend for the attribute color-coding is shown in c. The width of the links (grey lines) between clusters identified in subsequent years represent the number of MSAs transitioning between clusters over time ("cluster flows"). Line plots show measures of cluster separation (blue) and within-cluster variance (orange) over time for: d size-based clusters, and e form-based clusters. Dashed lines show cluster separation and within-cluster variances for form variables in size-based clusters (d), and vice-versa in e, indicating the disentanglement of size and form over time.
