Parameter Definition Reference
Nodes The unit of interest in network analysis, for example, herds or municipalities. (WASSERMAN; FAUST, 1994)
Edge Link between two nodes in the network.
Degree (k) Number of unique contacts to and from a specific node (e.g., farm location). When the direction is considered, the ingoing and outgoing contacts are separated: out-degree is the number of contacts originating from a specific node, and in-degree is the number of contacts coming into a specific node.
PageRank Google PageRank measure, a link analysis algorithm that produces a ranking of importance for all nodes in a network with a range of values between zero and one. The PageRank calculation considers the indegree of a given premises and the indegree of its neighbors. (BRIN; PAGE, 1998)
Reverse of PageRank (rev(PageRank)) The Google PageRank algorithm can be typically implemented in an adjacent matrix \(\mathbf{A}\) as a representation of the directed graph \(g\). Here, we use a transposed adjacency matrix \(\mathbf{t}(\mathbf{A})\) where \(\mathbf{t}\left(\mathbf{A}\right)\mathbf{\text{ij}}=\mathbf{1}\ \) if there exists an edge between the origin node \(\mathbf{i}\) and destination node \(\mathbf{j}\ \), otherwise \(\mathbf{t}\left(\mathbf{A}\right)\mathbf{\text{ij}}=\mathbf{0}\) if the edge does not exist. We then applied the PageRank algorithm using the \(\mathbf{t}\left(\mathbf{A}\right)\) to obtain the rev(PageRank).
In/out Closeness centrality Closeness centrality measures how many steps are required to access every other vertex from a given node; this measure can be calculated for incoming or outgoing paths. (FREEMAN, 1978)
Betweenness Describes the extent to which a node lies on paths connecting other pairs of nodes, defined by the number of geodesics (shortest paths) going through a node.
In/out degree centralization
Quantifies the extent to which a minority of the farms are responsible for a majority of the incoming/outgoing movements.
(WASSERMAN; FAUST, 1994) (WATTS; STROGATZ, 1998)
Clustering coefficient Measures the degree to which nodes in a network tend to cluster together (i.e., if A B and B C, what is the probability that A C), with a range of values between zero and one.
Giant weakly connected component (GWCC) Proportion of nodes that are connected in the largest component when directionality of movement is ignored (WASSERMAN; FAUST, 1994)
Giant strongly connected component (GSCC). Proportion of the nodes that are connected in the largest component when directionality of movement is considered (WASSERMAN; FAUST, 1994)