What is rigidity?

Answer: Rigidity is defined as the property of a solid that changes its shape. In other words, the shape does not change even if an external force is applied to the solid material. 

This indicates that the particles are tightly packed and the gravitational pull between these particles is very strong.  It is the strongest attraction between particles.  This property makes the solid rigid.  Rigidity gives the solid its perfect shape, and the particles in the solid are tightly packed.