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

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] |