2.7 Hierarchical Modularity
A high clustering coefficient indicates highly interconnected subnetworks (modules) in real-world networks. However, the next question that arises is regarding the way in which these modules are organized in the network.
Ravasz et al.  and Ravasz and Barabási  provided an answer for this question by using the degree-dependent clustering coefficient.
This statistical property is defined as
where Ci is the clustering coefficient of node i (see Eq. 2.19).
Ravasz et al. found that the degree-dependent clustering coefficient follows a power–law function in several real-world networks:
where α is a constant and is empirically equal to about 1.
In a random network, the clustering coefficients of all nodes are p, which is independent of the node degree k, because an edge is drawn between a given node pair with the probability p: Crand(k) = p. Thus, the random network cannot explain this statistical property.
This power–law degree-dependent clustering coefficient indicates that the edge density among neighbors of nodes with a small degree is high and that the edge density among the neighbors of nodes with a large degree is low. In order to explain the relation between this property and the network structure, Ravasz et al. used a simple example, ...