Hierarchical network model

These systems generally differ in the structure of the initial cluster as well as in the degree of expansion which is often referred to as the replication factor of the model.

[5] In contrast to the other scale-free models (Erdős–Rényi, Barabási–Albert, Watts–Strogatz) where the clustering coefficient is independent of the degree of a specific node, in hierarchical networks the clustering coefficient can be expressed as a function of the degree in the following way: It has been analytically shown that in deterministic scale-free networks the exponent β takes the value of 1.

Defining links as appearance as a synonym in the Merriam-Webster dictionary a semantic web of 182,853 nodes with 317,658 edges was constructed.

[1] By mapping the www.nd.edu domain a network of 325,729 nodes and 1,497,135 edges was obtained whose degree distribution followed a power law with γout=2.45 and γin=2.1 for the out- and in-degrees, respectively.

The sample distribution of the clustering coefficients was fitted by the scaling function C(k)~k−0.75 whose exponent is (in absolute terms) somewhat smaller than the theoretical parameter for deterministic scale-free networks.