## Maximal and Minimal AMI

If the flows are constrained to follow a given path, then knowing that a particle is leaving compartment i also tells us that it will enter compartment j. In this case, there is no uncertainty about the fate ofthe particle, the information we possess is the highest and, consequently, AMI assumes the maximum possible value. If, on the other hand, each compartment of a network communicates with all the others by means of equally efficient channels (fluxes of the same magnitude), the uncertainty about which route the particle will take is maximal (HI 0 = Hj — H0) and AMI equals to 0.

Intermediate configurations will lead to different values ofAMI, that will be bounded by 0 (minimal AMI), and HI,O (maximal AMI). Figure 5 depicts two graphs that represent the topological configurations that give rise to the minimum (left) and maximum (right) values for AMI. The former network yields HI O = 16(—0.062 5 log2(0.062 5)) = 4 bits and AMI = 0 bits, while the latter's joint entropy equals to HI,0 = 4(—0.25 log2(0.25)) = 2 bits, which is also the value for AMI.

Figure 5 Minimal (left) and maximal (right) AMI (and ascendency) for a simple network composed by four nodes.

Figure 5 Minimal (left) and maximal (right) AMI (and ascendency) for a simple network composed by four nodes.

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