A new notion of vertex independence and rank for finite graphs
  A new notion of vertex independence and rank for a finite graph G is introduced. The independence of vertices is based on the boolean independence of columns of a natural boolean matrix associated to G. Rank is the cardinality of the largest set of independent columns. Some basic properties and some more advanced theorems are proved. Geometric properties of the graph are related to its rank and independent sets. 
John Rhodes and Pedro V. Silva
math.CO cs.DM math.RT