Consider the following taxonomy for graphs (expressed in prolog):

node/1 - predicates of the form node(X) are read as: "X is a node".

edge/2 - predicates of the form edge(X,Y) are read as: "There is an edge from X to Y".

Define a series of rules for the following relations:

path/3 - predicates of the form path(X,Y,Z) are read as: "Z is a list of nodes which defines a path from X to Y"

connected/2 - predicates of the form connected(X,Y) are read as: "there exists a path from node X to node Y"

cyclic - the predicate cyclic is true if there exists a cycle in the given graph