Algorithm 1:generate the optimal rigidity graph between cluster heads
Input:location of the cluster head node p,number of cluster head nodes n,maximum UV LED communication radius R
Output:final set of communication links,the final UV LED communication radius communication radius
1 calculate the weight of communication links between all cluster head nodes
2 all links are listed in ascending order by weight
3 stiffness matrix is established according to the sorting results M
4 initialize M',that is M'=M(1)
5 for1:n(n-1)/2 search all links
6 whilerank(M')≤2n-3
7 add the next row of M to M' form a new matrix Mj
8 ifMj is nonsingular
9 M'=Mj
10 record the link corresponding to the row
11 else delete the row
12 end
13 end
14 end
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