If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?

Category: QuestionsIf a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?
Editor">Editor Staff asked 4 weeks ago

If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?
 
(a) n-1
 
(b) values greater than n are possible
 
(c) values less than n-1 are possible
 
(d) insufficient Information is given
 
My question is taken from Incidence Matrix and Graph Structured Stack topic in section Graph of Data Structures & Algorithms I
 
This question was posed to me by my college professor while I was bunking the class.

1 Answers
Editor">Editor Staff answered 4 weeks ago

The correct option is (a) n-1
 
The best I can explain: Every column of the incidence matrix may contain only +1 and -1 as non zero entries rank would be less than n.