ANSWER:

The guardian or wali is set by Islam to be a woman’s father, paternal grandfather, son, brother, paternal uncle or paternal cousin. If she has no muslim relatives, the muslim ruler, judge or authorized islamic center would act like her guardian. 

We were discussing with my friends and some of them said that one can randomly choose a waliy for herself even if the person is not your family and the wedding will still be valid. I need more clarification on this topic.