If a user u connects to the network (N_1) (LTE) in a sub-zone (C_i) then the number of bandwidth units occupied in this sub-zone passes to (b_{1i}) (b_{1i} + N_{PRB}^k).
Besides, if a user u connects to the network (N_1) (LTE) in sub-zone (C_0) by disconnecting from the same network (N_1) but in a zone (C_i) then the number of bandwidth units occupied in this sub-zone (C_0) of the network (N_1) (LTE) passes from (b_{11}) to (b_{11} + N_{rm PRB}^k) and (b_{1i}) to (b_{1,i}^{k} - N_{rm PRB}^{k}) in sub-zone (C_i).
So the found rate is: begin{aligned} (lambda _{C_0}^{C k)} + lambda _{N_1}^{H k)} cdot left( frac{b_{11}^{k}}{N_{rm PRB}^{k}} + 1 right) cdot left( frac{1}{Delta _{C k)}} + eta _{C_0}^{C_1}right) end{aligned} (2) If a user u connects to the network (N_1) (LTE) in a sub-zone (C_i) then the number of bandwidth units occupied in this sub-zone passes to (b_{1i}) (b_{1i} + N_{PRB}^k).
The next step is to compute c x,τ′, S), by using the values of c x,τ1, S1) and c u,τ2, S2) for every u connected to x, and all feasible set of colors S1 and S2.
Now for every vertex u connected to x in G, and all set of colors S1 and S2⊂[ k] with | S1|=ν τ1′, | S2|=ν τ2′ and S1∩ S2=∅ we recursively find c x,τ1, S1) and c u,τ2, S2).
For convenience, the r subtrees are merged into a forest T0 = (V1∪ … ∪V r, E1∪ … ∪E r ), d u, v) represents the weight of the edge (u, v) connecting node u and node v.
For an edge (u, v) connecting node u and node v, we calculate its ECC by using the common neighbors instead of triangles.
More generally, L ( T | N ) = 0 if T has no fixed points on N ⊂ G. Proof Given a simplex x, the orbit U = { T k ( x ) } is T-invariant and L ( T | U ) = 0. To see this, note that H k ( U ) is trivial for k ≥ 2. There are two possibilities: either U is connected, or U has n > 1 connectivity components.
For a symmetric link ℓ uv connecting nodes u and v, we weigh its quality by (frac {N_{text {fwd}} v)}{N_{text {oh}} v)}).
For a preliminary core C with den(C) < T d, the edge clustering coefficient ECC u, v) of each edge (u, v) connecting the seed vertex v and a rest vertex u is calculated.
