Table 4 Permutation test of contact network structure metrics between the same genotype of HPAI H5N6 virus infected premises linked via vehicle movements based on the Bayesian parameter estimation.

Network metrics	C2 (No. of IPs = 19 (chicken 15, duck 4), Edge density = 0.051)		C3 (No. of IPs = 13 (chicken 13), Edge density = 0.109)		C4 (No. of IPs = 52 (chicken 14, duck 38) Edge density 0.020)
Network metrics	Observed value	Median difference (5–95 PCTL)	Observed value	Median difference (5–95 PCTL)	Observed value	Median difference (5–95 PCTL)
Assortativity by species	1.000	–	NA §	–	0.820	–
Diameter	5	1 (− 3, 3)	5	− 1 (− 4,2)	4	− 4 (− 11, 0)
Average path length	1.071	− 0.771 (− 2.191, − 0.116)	1.653	− 1.007 (− 1.871, − 0.063)	1.258	− 1.825 (− 4.192, − 0.542)
Reciprocity	0.286	0.286 (0.055, 0.286)	0.348	0.257 (0.062, 0.348)	0.231	0.231 (0.151, 0.231)
Assortativity by degree	0.417	0.473 (− 0.003, 0.949)	0.634	0.693 (0.315, 1.094)	0.068	0.084 (− 0.207, 0.347)
Transitivity	0.600	0.600 (0.284, 0.600)	0.200	0.006 (− 0.146, 0.2)	0.333	0.301 (0.229, 0.333)

Networks for permutation test were generated based on the observed number of IPs (nodes) and probability of edge formation between nodes, which was calculated by the observed edge density.
MD, median difference between observed value and 1000 simulated values; 5–95 PCTL 5–95% percentile range of difference.
NA, not available; because all IPs were chicken holdings, the corresponding assortativity were not available.
Diameter is the shortest distance between the two most distant nodes in the network. Average path length is equal to the number of ties along the shortest length of the tie between two nodes. Reciprocity denotes the proportion of nodes in a directed network to be mutually linked. Transitivity refers to the ratio between the observed closed triplets and the maximum possible number of closed triplets in the network.
HPAI, highly pathogenic avian influenza; IPs, infected premises.

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