The paper defines a new theoretical measure Total Influence, of a node as well as a set of nodes in the social network. Total influence uses probabilistic theory to obtain the expected size of the information spreading in the social network under the independent cascade model of diffusion. In order to quantify the size of the spreading practically, the paper proposes a new hybrid simulation methodology for the independent cascade model. The hybrid method uses rough set theory and defines rough knowledge agents around all the seed nodes from which the information is propagating. The lower approximation is calculated using the probabilistic approach, while the size of influence in the boundary region is quantified by Monte-Carlo simulation on a reduced network. The reduce network is formed by compacting all the nodes in the lower approximate region as a super-node. Experimental results on two synthetically generated directed network show that the hybrid method runs magnitude faster than its counterpart with a similar accuracy of the spreading size. © 2020 IEEE.