create an AI behavior

I believe in this possibility!!! but i think it’s very difficult, but doesn’t impossible!!
i’ve seen the possible AI behavior but i don’t find one that i want. Then, I want create a new AI creator.
I’d like to have a AI behavior that allows me to follow a random path. Given a graph in which there’re described which node are connected with the other node, the AICharacter follows a random path (to simplify the situation, two point are connected if exists a straight path between the two). Example
A is connected with B and C
B is connected with A and D
C is connected with A and D
D is connected with B and C and E
E is connected with D
the AICharacter starts in point A. it decides if goes in B or in C (a random choice). For example it choices C. When AICharacter is in C, it choices where he goes: A or D. ans so on…
Is it possible ??