Network size would be the number of actors. Though you might be interested in the count of all network members, you also might want to know how many people are one, two, or three links away. Long before computer networking was invented, psychologists Jeffrey Travers and Stanley Milgram conducted a low-tech experiment that looked directly at this question.Travers, J., & Milgram, S. (1969). An experimental study in the small world problem.