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Table 1 Definition and sources of the network analysis terms used in this study

From: Dynamic network measures reveal the impact of cattle markets and alpine summering on the risk of epidemic outbreaks in the Swiss cattle population

Type / Name

Definition

Source

Holding centrality metrics

 In-degree

Number of individual sources providing animals to a specific holding

[14]

 Out-degree

Number of individual recipients obtaining animals from a specific holding

[14]

 Betweenness

The frequency a livestock operation is in the shortest path between pairs of holdings in the network

[47]

 Closeness

The inverse of the sum of the shortest geodesic distances from a source holding to all other reachable holdings in the network

[48]

Static network measures of connectivity

 Geodesic

The shortest path length between two holdings

[49]

 Path length

A path between farm A and farm C is the number of steps required to travel from A to C. In a path, holdings and animal transports cannot be repeated between a source and a destination. Related terms are geodesic and average path length

[49]

 Average path length (APL)

The shortest path, or geodesic, among two holdings averaged over all pairs of holdings in the network

[50]

 Density

Sum of the number of all links divided by the number of possible links in the network

[14]

 Clustering coefficient (CC)

If a neighbour is defined as a the holding in direct contact with the holding of interest, the clustering coefficient represents the proportion of one’s neighbours who are also neighbours of one another

[50]

 Components

Maximally connected subregions of a network in which all pairs of holdings are directly or indirectly linked

[46]

 Giant strongly connected component (GSCC)

The largest component in the network in which all pairs of holdings are linked via directed paths

[43, 46]

 Giant weakly connected component (GWCC)

The largest component in the network in which all pairs of holdings are linked regardless of the direction of the link

[43, 46]

 Assortativity

Correlation between the degrees of linked premises

[51]