## Appendix A
Let us see the same example of calculation as before for connected devices \(\{A,B,C,D,F\}\), from \(G_{7}\) as shown in Figure 4, but now using the new closeness equation (Equation (15)):  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]2  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]3  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]4  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]5  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]6  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]7  
The new ranking of devices based on their closeness index, which is determined by using the sum of reciprocal distances instead of the reciprocal sum of distances, is in line with the ranking obtained by using the traditional equation (Equation (11)) on a network that is well-connected (Equation (12)):  
\[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]8  
To maintain clarity in the example illustrated in Figure 1, we opt for a value of 0.5 when assessing the closeness of the devices. This choice ensures that the Closeness measure and its dynamics carry equal relative weight. \[DTE_{T}(B)=0.5\cdot(-0.0788)+(1-0.5)\frac{(4+1+2+4)}{10}=(-0.0394)+0.55=0.5106\]9  
\[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]0  
\[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]1  
\[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]2  
\[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]3  
\[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]4The new ranking of nodes according to their Dynamic Closeness index is as follows:  
\[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]5  
The best path from device \(A\) to device \(B\) in Figure 5 is then determined using the opportunistic-based shortest path method. Table A1 presents the findings of this investigation. \[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]6 \[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]7 \[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]8 \[DTE_{T}(C)=0.5\cdot 0.1151+(1-0.5)\frac{(5+3+3+2+4)}{10}=0.05755+0.85=0.90755\]9 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]0 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]1 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]2 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]3 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]4 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]5 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]6 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]7 \[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]8  
\[DTE_{T}(D)=0.5\cdot(-0.0788)+(1-0.5)\frac{(7+3+2)}{10}=(-0.0394)+0.6=0.5606\]9 \[DTE_{T}(E)=0.5\cdot(-0.0182)+(1-0.5)\frac{(3+3+5)}{10}=(-0.0091)+0.55=0.5409\]0 \[DTE_{T}(E)=0.5\cdot(-0.0182)+(1-0.5)\frac{(3+3+5)}{10}=(-0.0091)+0.55=0.5409\]1 \[DTE_{T}(E)=0.5\cdot(-0.0182)+(1-0.5)\frac{(3+3+5)}{10}=(-0.0091)+0.55=0.5409\]2The path \(\{A,B\}\) represents the shortest distance, but it possesses the lowest \(ORI_{T}(A,B)\) value among all routes. On the other hand, the path \(\{A,E,F,B\}\) has the longest path distance with a \(ORI_{T}(A,E,F,B)\) value of 4.2362 (the sum of the three \(ORI_{T}\)), which is the second lowest. Comparatively, both the paths \(\{A,C,B\}\) and \(\{A,D,B\}\) share the same path distance, with \(ORI_{T}(A,C,B)=ORI_{T}(A,D,B)=9\). However, \(Cost_{opp}(A,C,B)\) is lower than \(Cost_{opp}(A,D,B)\).