Is there a general way to crack this graph cipher?
As stated by @tylo, this cipher can be cracked by simply finding the greatest common divisor for your numbers.

Continuing from your example: if i am encrypting the message HELLO using the key 605, while following along the graph (or what is essentially a matrix) with the intention to spell out my message, i only actually need the calculations for the first two letters to find the key:


H: 805030 * 605 = 487043150
E: 505040 * 605 = 305549200


Taking these numbers one can trivially find gcd(487043150, 305549200)—gcd being the greatest common divisor—e.g. by using a tool like WolframAlpha, which finds the gcd to be 6050 (6050 rather than 605 due to both of the numbers multiplied with the key ending in a zero, thus for this purpose having an unnecessary extra power of magnitude. Removing these zeros would give 605 directly).