## 3 System Model Design
### Community Structure Contraction Strategy
The information is transmitted by nodes through the reduced structure of communities, and the algorithm not only has fast transmission speed, but also has high transmission efficiency. We may then compare with the Spray and wait algorithm. In the spray process, the node continuously copies the data and assigns it to its neighbors. Its time complexity is O(\(n^{2}\)). It is the same as the SCR algorithm, because nodes are selected by social relationships to form a local cluster. In the EMIST algorithm,nodes transmit messages and save them as a list in their cache, so while its time complexity is O(\(n\)), it has higher routing overhead compared with our work. ## 4 Simulation

We implement the proposed ESR scheme in the OMNET++ simulator [27] and evaluate ESR by performance comparison with the EIMST algorithm, Spray and wait algorithm and SCR algorithm. The simulation time is 12 h, and the simulation area is \(4300\times 1200\) m in the communication area. Our background city is St Paul. The number of involved nodes is 1000. The node distribution is random, and the transmission mode is broadcast. The maximum transmission distance of each node is 10 m, and the transmission speed of a node is 0.5\(\sim\)1.5 m per second. The cache of each node is 10 MB, and the Packet size is 500 KB\(\sim\)1 MB. The specific setting of this simulation scenario is shown in Table 1, and the setting of algorithm parameters is shown in Table 2.

We compared the performance of different routing algorithms in the same scenario and analyzed the effect of varying parameters in the ESR algorithm. In this study, ESR is compared with spray and wait [15], SCR [4], and EMIST [3], which are a classic routing algorithm and two new algorithms published in 2017, respectively. EMIST is an information transmission strategy based on socialization nodes, and SCR is an effective social-based clustering and routing scheme in opportunistic networks. These algorithms were analyzed by three performance indicators, namely packet delivery ratio, transmission delay and routing overhead [28]. The experiment shows that the effective data transmission algorithm based on social relationships in opportunistic mobile social networks has the best comprehensive performance when N = 16, \(\tau\)= 0.17, and \(\varepsilon\) = 0.42. ### Community Division Interval

In a community-based opportunistic social network, the role of the community division interval is important. In a period of time, it can be considered that the status of a node and communities in the network do not change, and data transmission can be stable. If the division interval is relatively small, because the community result is not stable enough, the guiding effect of community division on the routing algorithm is not good, and the packet delivery ratio is low. As the division interval increases, the packet delivery ratio increases correspondingly as shown in Figure 4. When the interval is selected as 900 s, the optimal packet delivery ratio is 80%. As the division interval continues to increase, the packet delivery ratio decreases. At 2700 s, the packet delivery rate is 70%, and the algorithm performance is worse than that at 900 s. This is because when the interval of community division is too long, the true node distribution state is not consistent with the assumed stable state, and previous community segmentation results do not represent the latest community structure well. \begin{table}
\begin{tabular}{c c} \hline \hline
**Environmental Parameter** & **Settings** \\ \hline Simulation time/h & 12 \\ Simulation area & 4300 \(\times\) 1200 m \\ Background city & St Paul \\ Number of nodes & 1000 \\ Velocity of a node/(m/s) & 0.5 1.5 \\ Transmit speed(KB/s) & 250 \\ Maximum transmission distance/m & 10 \\ Transmission mode & broadcast \\ Buffer size/MB & 10 \\ Packet size & 500 KB 1 MB \\ Packet sending intervals/s & 25 35 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Environmental parameter of simulation settings.