# System Model

This section introduces a system model which includes social network, mobility model, and node selfishness.

## Social Network

We study the crowd sensing with mobile nodes in the environment of mobile social networks, where the system structure is shown by Fig. 3.1. It is assumed that there are *N* users denoted by *n _{1}, n_{2},...,n_{N}* moving around within a region all the time. The information can be shared between two users only when they meet and have social relations.

The social network consists of opportunistic network and social network. It is modeled by an unweighted and undirected graph *G* (*V, E).* The symbol *V* is defined as the set of nodes, and *E* denotes the set of edges. The nodes represent users, and their social ties (e.g., friendship and relatives) are denoted by the edges. Thus, we

Fig. 3.1 **System structure**

have *V =* (ni, *n _{2},..., n*

_{N}}. To study the impact of selfishness, the distribution of relationship should be acquired. The probability of a node having

*k*friends is defined by

*P(k),*where the degree of the node is

*k.*Related works show that

*P(k)*follows the power-low distribution in the mobile social network [36]. Therefore,

*P(k)*[27] can be obtained as follows:

Here, the smallest degree of the network is m, the skewness of the degree distribution is y, and the normalization constant is *C(m, y).*