Parameter |
Definition |
Reference |
Nodes |
The unit of interest in network analysis, for example, herds or
municipalities. |
(WASSERMAN; FAUST, 1994) |
Edge |
Link between two nodes in the network. |
|
Degree (k) |
Number of unique contacts to and from a specific node
(e.g., farm location). When the direction is considered, the ingoing and
outgoing contacts are separated: out-degree is the number of contacts
originating from a specific node, and in-degree is the number of
contacts coming into a specific node. |
|
PageRank |
Google PageRank measure, a link analysis algorithm that
produces a ranking of importance for all nodes in a network with a range
of values between zero and one. The PageRank calculation considers the
indegree of a given premises and the indegree of its neighbors. |
(BRIN;
PAGE, 1998) |
Reverse of PageRank
(rev(PageRank)) |
The Google
PageRank algorithm can be typically implemented in an adjacent matrix
\(\mathbf{A}\) as a representation of the directed graph \(g\). Here, we
use a transposed adjacency matrix \(\mathbf{t}(\mathbf{A})\) where
\(\mathbf{t}\left(\mathbf{A}\right)\mathbf{\text{ij}}=\mathbf{1}\ \)
if there exists an edge between the origin node \(\mathbf{i}\) and
destination node \(\mathbf{j}\ \), otherwise
\(\mathbf{t}\left(\mathbf{A}\right)\mathbf{\text{ij}}=\mathbf{0}\)
if the edge does not exist. We then applied the PageRank algorithm using
the \(\mathbf{t}\left(\mathbf{A}\right)\) to obtain the rev(PageRank). |
|
In/out Closeness centrality |
Closeness centrality measures how many
steps are required to access every other vertex from a given node; this
measure can be calculated for incoming or outgoing paths. |
(FREEMAN,
1978) |
Betweenness |
Describes 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. |
|
In/out degree centralization
|
Quantifies the extent to which a minority of the farms are responsible
for a majority of the incoming/outgoing movements.
|
(WASSERMAN; FAUST, 1994)
(WATTS; STROGATZ, 1998)
|
Clustering coefficient |
Measures the degree to which nodes in a network
tend to cluster together (i.e., if A B and B C, what is the probability
that A C), with a range of values between zero and one. |
|
Giant weakly connected component (GWCC) |
Proportion of nodes that are
connected in the largest component when directionality of movement is
ignored |
(WASSERMAN; FAUST, 1994) |
Giant strongly connected component (GSCC). |
Proportion of the nodes
that are connected in the largest component when directionality of
movement is considered |
(WASSERMAN; FAUST, 1994) |