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Table 1 Description of network analysis terminology and metrics

From: Multiple species animal movements: network properties, disease dynamics and the impact of targeted control actions

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

 

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

[22, 57]