ABSTRACT
These days, people living in a complex and interdependent world make thousands of decisions every day. Before they make a decision, humans tend to pay attention to the viewpoint of their friends, for decision makers usually don’t have enough useful information. Hence, modeling the way in which information is spread on the social network is meaningful. But to do this is very difficult. On the one hand, it is not an easy job to find a model that can express the topology of social network reasonably and precisely. On the other hand, with time goes by, the friendships among individuals are changeable for massive reasons.Thus, this new discipline has not been researched in large scale until the emergence of the well-known random cascade model, which is introduced by Watts (Watts 2002). In the basic Watts’s threshold model, it assumes that people always contact with all their friends in a single duration. However, due to various reasons, an individual can’t contact all of his friends in one step in the reality. It makes the weights of very link change. Taking frequency of contact into account, some assumptions are referred to as follows. We assume the probability that a node with k friends in contact with one of them in one time step as k−α, obviously, the bigger the value of k is, the lower the probability will become. Therefore, the probability that two nodes whose degrees are k1 and k2, respectively, choose to contact with each other can be defined asF(k1,k2) = (k1∗k2)−α . It is common sense that people usually forget a new thing a few days or hours after they are told, if they don’t really remember it. As degree of
forgetfulness is now an additional degree of freedom to be incorporated into the models. In previous work, memory length appeared to be studied in some literatures, however, most of them did it with binary-state threshold models (Watts 2002, Hackett et al. 2011, Liu et al. 2012). It means that the nodes of a network only have two kinds of status: state 0 or state 1, where state 1 represents “susceptible” and state 0 represents infected state. But in the real world, opinions are usually furiously divided as a new thing or idea appears. Therefore, it will be more reasonable if more statuses are added.
