Chapter 5 Relational measures
5.1 Reciprocity
## [1] 0.5779819The reciprocity of a directed network reflects the proportion of edges that are symmetrical. That is, the proportion of outgoing edges that also have an incoming edge. It is commonly used to determine how inter-connected directed networks are. The reciprocity of th US Politician Network is 0.598, meaning that the 57.8% of the communication relationships between politicians is reciprocal, leading to a flow of (potentially) exchanging information.
## [1] 0.5779819Other indexes commonly used to evaluate the structure of a network are related to the degree of global and local connectivity through the analysis of triads (three nodes connected by at least three edges). In a directed network such as the US Political Network, a triangle can have from three to six edges.
## [1] "billy long" "mike johnson" "trent kelly" "john rose"
## [5] "cindy hyde-smith" "tom reed"Transitivity measures whether the relationship between two nodes in a network is transitive. Perfect transitivity implies that, if the node x is connected to the node y, and the node y is connected to the node z,the node x is connected to \(z\) as well. It implies that each component forms a clique. The global transitivity of the network is the proportion of all closed triangles in the network over all possible triangles between vertices. Of all possible closed trianges between vertices in the US Political Network, 60.5% of them are closed, suggesting that the US Political Network is semi-sparse.
## [1] 60.55.2 Local Transitivity
It is also possible to determine the number of triangles a single vertex is part of a.k.a. their local transitivity. It is computed by dividing the actual number of closed triangles the node is a part of by the total possible triangles it could be a part of.
In the US Political Network, the nodes with the highest local transitivity are:
## [1] "larry bucshon" "greg walden" "gerald edward connolly"
## [4] "sharice davids" "rob woodall" "scott peters"