#A graph is called *cactus graph* if it is connected and every pair of
simple cycles have at most one common vertex.

# Special cases
if self.order() < 4: #Number of vertices
    return True

# Every cactus graph is outerplanar
if not self.is_circular_planar():
    return False

if not self.is_connected():
    return False

# the number of faces is 1 plus the number of blocks of order > 2
B = self.blocks_and_cut_vertices()[0]
return len(self.faces()) == sum(1 for b in B if len(b) > 2) + 1