MO412/2021s1 - Tiago da Silva Almeida

The clustering coefficient is an important metric for a network. For example, the metric allows to measuring how many people are related and the potential transmission of some disease. Regarding this, consider an undirected network with five nodes (A, B, C, D, and E), and the following links: (A, B), (A, C), (A, D), (A, E), (B, C), (C, D), (C, E), and (D, E). Also, consider the following sentences: I) The clustering coefficient of a node takes count the degree of that node. The degree of a link v in a network G is the number of links of G incident with v , each loop counting as two edges. For example, node C has a clustering coefficient of 2/3. II) The average clustering coefficient is just an arithmetic average of the clustering coefficient of all nodes. For this network is 21/30. III) The global clustering coefficient is based on triplets of nodes. A triplet is three nodes that are connected by either two (open triplet) or three (closed triplet) undirected ties. For this network i...