Find x
Answer: FAKE LIFE

Each graph encodes the numbers 1-26 in the non-black nodes, with each section using a different number system. These numbers can then be converted to letters A-Z as usual. Solvers must use the structure of the graph, along with the given "X", to determine which letter corresponds to "x". Putting these x values within each section gives a string spelling out a number in that system, which can then in turn be converted back to a letter:

Number systemx valuesAs decimalLetter
A-Z (effectively base 26)THEANSWERIS--
decimalSIX6F
binaryONE1A
ternaryONEZEROTWO11K
balanced ternaryPOSNEGNEG5E
factorial baseTWOZEROZERO12L
base -4ONETWOONE9I
roman numeralsVI6F
Fibonacci baseONEZEROZEROZERO5E

The answer is FAKE LIFE.