*3.3. Clustering Coefficient*

Given a node *i* in the network, all nodes associated with the node *i* form a sub-network. *cs* is the ratio of the number of arcs in the sub-network to the number of all possible arcs in the sub-network, and *c* is the average of all *cs*.

The clustering coefficient can show the aggregation of nodes in the network, i.e., how close is the network. In real-world networks, especially in specific networks, nodes tend to establish a tight set of organizational relationships due to the relative high-density connection points. In public transportation networks, the distribution of the clustering coefficient means the bus lines' intensity near each station, and the average of the clustering coefficient depicts the intensity of the bus lines in the entire transportation network. Doragovtsev [43] pointed out that there are three different parameters for measuring cohesion characteristics, namely:

(1) Local clustering coefficient *<sup>C</sup>*(*k*). In Equation (4), *mnn*(*k*) denotes the average connections between neighbors of the node with degree *k*.

(2) Average clustering coefficient. In Equation (5), *P*(*k*) is the distribution of the node degree *k*.

(3) Clustering coefficient. In Equation (6), - *k*2 shows the second moment of node degree, while *k* indicates the average node degree. This manuscript uses the average clustering coefficient to measure the aggregation characteristics of urban public transit networks.

$$\mathcal{C}(k) = \frac{\langle m\_{nn}(k) \rangle}{k(k-1)/2} \tag{4}$$

$$\overline{\mathcal{C}} = \sum\_{k} P(k)\mathcal{C}(k) \tag{5}$$

$$\mathcal{C} = \frac{\sum\_{k} P(k) \langle m\_{\text{nn}}(k) \rangle}{\sum\_{k} P(k) k (k-1)/2} = \frac{\sum\_{k} k(k-1) P(k) \mathcal{C}(k)}{\langle k^2 \rangle - \overline{k}} \tag{6}$$
