2.4.1. Hierarchy

Hierarchy can characterize the rank of urban nodes in the network and degree, whereby degree distribution can measure the hierarchy of nodes in the urban network structure [41]. Nevertheless, this has the drawback of ignoring the functional relationship among urban nodes. Therefore, the weighted degree and weighted degree distribution are used to measure the hierarchical resilience of the urban network structure considering the urban network weights. The formula for this is [32]:

$$\mathcal{W}\_i = \mathbb{C}(\mathcal{W}\_I^\*)^a \tag{9}$$

The formula is processed as follows:

$$\ln(\mathcal{W}\_i) = \ln(\mathbb{C}) + \operatorname{aln}(\mathcal{W}\_i^\*) \tag{10}$$

where *Wi* is the weighted degree of city *i*, *Wi\** is the ranking of the weighted degree of city *i* in the network, *C* is a constant, and a is the slope of the weighted degree distribution curve. The higher the slope, the more evident the hierarchy of the urban network [32].
