# System Model

In this section, we present the system model consisting of three parts: MSN-based social graph, opportunistic links and information dissemination mechanism.

## MSN-Based Social Graph

We consider *N* mobile nodes (or users) take smartphones to bi-directionally communicate with others and self-organize an MSN, where there are some physical constraints [36] including battery and channel fading. Hence, it is impractical for each node to spread all information to all nodes. The mobile nodes in MSNs select a part of nodes as their friends and have social ties with them to spread information. An undirected social graph *G(V, E)* is used to represent social ties among the mobile nodes, where *V* denotes the set of nodes, and *E* denotes the set of edges among nodes. Nodes in *G (V, E*) can be the users or devices in MSNs. An edge exists between two nodes if they have a social tie, e.g., relatives, friends, and etc. For simplicity, two nodes which have social ties are considered to be friends in this chapter. The number of the nodes in MSNs is | *V* |= *N*.

To study the impact of social ties, we need to know the distribution of the friendship. Let *P (k)* denote the probability that a node has degree *k,* where the degree of a node in the network refers to the number of its friends. The degree distribution *P (k) *can be calculated by the fraction of nodes in the network with degree *k*. Thus, if there are *N _{k}* nodes having the degree

*k*, we have

*P (k) = N*.

_{k}/NExisting studies have shown that a great number of social networks have scale-free structures [37]. In other words, *P (k)* conforms to a power-law distribution [32]:

where y is called skewness of the degree distribution, and can be adjusted according to the scale of the network. Furthermore, the expectation of the degree distribution can be denoted by *(k) =* ^{-1} *kP(k),* where *m* is the smallest degree of nodes in

the network.