Parameter | Definition | References |
---|---|---|
Nodes | Premises or slaughterhouses | [57] |
Edge | The link between two nodes | |
Degree | This is a node-level metric where we count the number of unique contacts to and from a specific node. When the directionality of the animal movement is considered, the in-going and out-going contacts are defined: out-degree is the number of contacts originating from a specific premises, and in-degree is the number of contacts coming into a specific premises | |
Movements | The number of animal movements | Â |
Diameter | The longest geodesic distance between any pair of nodes using the shortest possible walk from one node to another considering the direction of the edges | [57] |
PageRank | A link analysis algorithm that produces a ranking based on the importance for all nodes in a network with a range of values between zero and one. The PageRank calculation considers the in-degree of a given premise and the in-degree of its neighbors. Here a Google PageRank measure was used | [58] |
Betweenness | This is a node-level network metric where 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 | [57] |
Clustering coefficient | Measures the degree to which nodes in a network tend to cluster together (i.e., if A \(\to\) B and B \(\to\) C, what is the probability that A \(\to\) C), with a range of values between zero and one. Here, we implemented the global cluster coefficient where the number of closed triplets (or 3 × triangles) in the network was divided over the total number of triplets (both open and closed) | [57] |
Giant weakly connected component (GWCC) | The proportion of nodes that are connected in the largest component when directionality of movement is ignored | [57] |
Giant strongly connected component (GSCC) | The proportion of the nodes that are connected in the largest component when directionality of movement is considered | [57] |
Centralization | A general method for calculating a graph-level centrality score based on a node-level centrality measure. The formula for this is C(G) = sum(max(c(w), w) −  c(v),v), where c(v) is the centrality of node v normalized by dividing by the maximum theoretical score for a graph. This essentially quantifies the extent to which the network is structured around a minority of nodes, and is quantified as the summed deviation between the maximum value recorded and the values recorded for all other nodes. Values range from 0 to 1, with higher values indicating more extreme centralization, illustrating a relative reliance or concentration of off- and onto-farm shipments from/to a nodal farm at the macro-level of the entire network |