@vs140580 Yes, it can be done with an easy modification of the above code if n and m are not too large. But I don't understand your usage of n-1 instead of n. K[n] by definition has n vertices, not n-1.

Your list L is a list of SETS of sets. I emphasized the first "SETS" because I think that your Question doesn't quite make sense if sets are used at that level (although sets are fine to represent edges). And it doesn't quite make sense because you've emphasized the sequential aspect of those sets, but the order of those sets is completely determined by Maple's automatic simpification of sets and it has nothing to do with any graph-related property. Indeed, if one of your sets contains {0, 1} as an element, then that's guaranteed to be the first element (unless perchance you allow self-loops). There's no way that you can use sets in Maple and impose upon them some order that is useful for your purpose.

Why do you ask "Is this a bug?" so often? Why do you constantly make comparisons with Mathematica? I'm extremely suspicious about your motivation for posting to MaplePrimes. You seem to have a sufficiently high level of programming skill that you could determine whether something is a bug, and you can read the code of MatrixPower to figure out why it is slow.

If you're so dissatisfied with Maple, then don't use it.

@Christopher2222 I agree absolutely that the default quality should be 100%; any other default is ridiculous. 

@mmcdara Here is what I think that the OP means by "suppressing function dependencies": If f is a Maple symbol or name---not a procedure^[*1]---then f(), f(0), f(x), f(x,y), etc., are all what Maple calls functions. I think that the OP would like all such instances to prettyprint display as simply f. By "prettyprint display", I mean that the way that they are displayed in a Standard worksheet (at default interface settings) is to be changed without altering Maple's internal (kernel) representation of the objects or its mathematical or computational understanding of them.

[*1] It's also possible (and indeed very common) for a procedure named f to return a function whose 0th operand is f via the syntax return 'procname'(args) or other closely related syntax.

Would you please attach a picture or PDF of a schematic diagram of the circuit? You could put it in the worksheet, but that's not essential at this point. A hand drawing would be sufficient. 

If I understand your worksheet correctly, then all resistors have 1 unit of resistance, all capacitors have one 1 unit of capacitance, and all inductors have 1 unit of inductance. Is that correct?

@Christopher2222 Add the option quality= 100 to the Write command. This indicates 100% of the original quality. The default is 75.

@nm If we can presume to know that the singularity (i.e., vertical-slope point) is at x= - exp(-1), then we can use the sample option to make sure that x-value is specifically used. Adding the adaptive option makes it plot extra points as the magnitude of the slope increases.

plots:-display(
    plot~(
        [LambertW(x), LambertW(-1, x)], x= -1..4, sample= [-1, -exp(-1), 4],
        color=~ [red, blue], adaptive= 8, view= [-1..4, -3.5..1.5]
    )
);

@mmcdara Was I wrong in saying that the system had derivatives with respect to bn?

It's so curious that there are a large number of both good and bad edges. I think that's a key piece of evidence. Let's look at the numeric plot structures of both types edges and try to figure out the key difference. 

@C_R When we're talking/writing casually of Maple programming, the words "function" and "procedure" are often used interchangeably. But when these words are used as keywords for types in Maple code, they are very different; indeed, they are disjoint. The f in your procedure header is declared function. This won't work. You can make that procedure or appliable (which is a supertype of procedure).

@Christopher2222 Reversing the order of the exponentiations (and, here, just using symbolic variables to emphasize the generality) we have

(x^r)^n = x^(r*n); simplify(%) assuming n::integer;

for any x and r and any integer n.

Your title "Cube root to the third...." states this reverse-order case. I think that you meant the title to be "Cube root of the third power doesn't simplify."

@NurinFYP No, it's not the same error message! The latest error is because you used beta[1] in the equations when you should've used beta__1.

All of your errors have been very simple errors that I could spot in seconds without even seeing your actual worksheet. I'm not saying that you should be able to spot them in seconds, but these trivial typos are not something worth giving up about.

@Jamie128 Surprisingly, I don't think that there's a simple way to get forget to forget everything (i.e., all "remember tables").

@NurinFYP You should change all the uppercase Zeta in your equations to lowercase zeta, or simply use another variable.