Table 2.

Network analysis glossary of terms interpreted in the context of pig movements.

Parameter	Definition	Reference
Average path length	Average number of steps along the shortest paths for all possible pairs of nodes, i.e., the number of premises a premise has to trade through, on average, to reach any other premise. It measures the efficiency of infection flow on the network	(37)
Degree (k)	Number of contacts from and to a specific premise. When direction is taken into account, the ingoing and outgoing contacts are separated: the out-degree is the number of contacts originated from a specific premise, i.e., the number of premises receiving pigs from this premise; the in-degree is the number of contacts with direction to a specific premise, i.e., the number of premises that sent pigs to this premise. Nodes with high in-degree are more likely to acquire infection, whereas nodes with high out-degree are more likely to pass infection	(35)
Degree distribution P(k)	Probability distribution of the degrees over the whole network. In several networks, the degree distribution displays a power-law tail P(k) ~ k−γ, where the exponent γ is a constant. The tail of this distribution reflects the presence of hubs, which are nodes that have much higher contacts than the majority of the other nodes	(38)
Density (D)	Proportion of links that are present in the network compared to all possible links, calculated by the equation: D = 2L/N(N − 1). A value of 0 means that there are no links and 1 that all theoretically possible links are present. It informs about the speed at which infection may diffuse among nodes	(35)
Diameter	The largest geodesic distance in the network, i.e., the greatest number of links in the shortest path between two nodes	(35)
Components	Regions of the network where every node can be reached from every other node, either via directed paths (strong components) or ignoring the direction of the links (weak components)	(39)
Isolate	A node that did not send or receive pigs during the study period	(35)
Links (L)	A directed connection between two nodes representing pigs moved between two pig holdings	(35)
Local average clustering coefficient of the network	Average of local clustering coefficient over all nodes. The clustering coefficient of a node is the number of triangles (3-loops) that pass through this node, relative to the maximum number of 3-loops that could pass through the node. It indicates the likelihood that any two nodes with a common neighbor are themselves connected. Direction of the links is ignored and isolated nodes are not included in the averaging	(37)
Nodes (N)	Pig premises (farms, traders, etc.)	(35)
Shortest path	Number of links in the shortest possible walk from a node to another. It is also called geodesic distance	(35)
Weight (${\text{W}}_{\text{ij}}^{\text{A}}$ and ${\text{W}}_{\text{ij}}^{\text{B}}$)	The strength of a link. Two weights were considered in the present study to represent the amount of pig batches ${\text{W}}_{\text{ij}}^{\text{A}}$ and of pigs ${\text{W}}_{\text{ij}}^{\text{B}}$ moved from premise i to premise j during the study period. This parameter is used to better detect community structures	(35)