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The simple weight of each edge is represented by the distance between two nodes, as the length of the edge.
We model all channel gains between two nodes as Rayleigh fading channels with free space propagation path loss.
The RP is investigated by simulating the behavior of p r N as a function of SNR threshold and relative distance between two nodes as shown in Figure 2a.
We model the block flat fading channel coefficient between two nodes as h i j = 1 d i j p h ~ i j, (38) Figure 2 Geometrical model: primary transmitter ( P TX ), secondary transmitter ( S TX ), primary receiver ( P RX ), and secondary receiver ( S RX ).
We define P ¯ cat, c l as the probability of unavailability of a single channel of type l among c l channels between two nodes as follows: P ¯ cat, c l = P ¯ cat c l = 1 - p 2 c l (3).
We define P ¯ cat, T l as the probability of unavailability of a single channel of type l among c l channels between two nodes as follows: P ¯ cat, T l = P ¯ cat c l = 1 − p 2 c l (6).
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The betweenness centrality measures how often a node sits on the geodesic between two nodes, acting as an intermediary (e.g., in communication).
Another property, here important to mention, is that scale-free graphs are ultra-small: the average distance between two nodes goes as ∼ log ( log ( N ) ), where N is the number of nodes in the network.
The optimum MAP detection requires the exhaustive search of the space ({mathcal {B}}^{N}), and the complexity grows exponentially with the node number, N. In a practical environment, the correlation between two nodes decreases as their distance increases.
Since the average path length does not change with network size, we can conclude that the number of alternative routes between two nodes increases as the network size increases.
Molecules are represented as nodes, and a biological relationship between two nodes is represented as an edge (line).
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