Permutation-based parallel-by-serial calculation of resistance in a circuit
The terms 'phase conductivity' and 'order conductivity' don't appear in standard EE for computing resistances. EE doesn't do permutations of components, or average conductivities of assemblies of components. 

When a set of components is assembled into any network of any topology, and they can be any component, resistors, capacitors etc, there are techniques to solve what impedance the composite circuit presents to external terminals, and what it does when voltages and currents are applied. If you permute the order of components, then you have a different circuit, with different behaviour.

It might be an interesting intellectual puzzle 'if you shake out a box of components and solder them where they fall, what do you get on average?' You'd go about solving that question by writing a program to permute your components, then solve each circuit, and then aggregate the results. But it would be no more than an interesting pass-time.