Influence models are currently studied by researchers working in the field of social network analysis. The basic assumption in the existing literature is that the degree of interpersonal influence among two experts can be determined in a single meeting. The second presumption is that the degree of interpersonal influence determined in this meeting is stagnant and will not change in the subsequent meetings. In this paper, we assert that degree of interpersonal influence among two or more experts can change over time. One may not find the other person equally assertive in the second or third meeting. The idea is that it may take several meetings to finally be able to declare the degree to which an expert is influenced by others. We define a composition function for the matrix of interpersonal influence and use it to define the evolution process that this matrix goes through after every meeting. We also state the conditions under which the matrix of interpersonal influence converges in the long run.