## 3 System Model Design
### Community Structure Contraction Strategy  
In opportunistic social networks, information transmission relies on the movements of the nodes and the importance of measuring the significance of nodes is pivotal. After dividing the network into several communities, the nodes in the opportunistic networks coalesce from scattered nodes into individual community structures. However, in these community structures, the significance of each node is also different. It is important to measure the importance of nodes in community structures. If you do not measure the importance of popular nodes, it will probably lead to network congestion. Therefore, we measure the importance of nodes after the division of communities to reduce the number of inefficient nodes. The measurement of node importance is generally divided into two aspects, including the influence of nodes on information flow and the interaction between nodes. The influence of nodes on information flow in networks is defined as the ratio of the number of paths through node \(V_{i}\) in all shortest paths in the network, to all shortest paths. If the network has \(S\) nodes, the influence of node on information flow is expressed as:  
\[S_{b}\left(v_{i}\right)=\sum\
olimits_{m<n}\frac{\gamma_{mn}\left(v_{i} \right)}{l_{mn}} \tag{3}\]  
In the formula, \(\gamma_{mn}\left(v_{i}\right)\) is defined to be the ratio of the number of paths through node \(v\) to all shortest paths in the network. \(l_{mn}\) represents the number of shortest paths between node \(v_{m}\) and \(v_{n}\). In this network, for a given node \(v_{i}\), the maximum influence of nodes on information flow is \(\left[N-1\right]\left[N-2\right]/2\), so the index can be normalized to:  
\[S_{B}\left(v_{i}\right)=S_{b}\left(v_{i}\right)/\left[\left(N-1\right)\left[N -2\right]/2\right] \tag{4}\]  
The importance of nodes is not only related to the number of edges connected, but also to the importance of connected nodes. Nodes can enhance their importance in the network by connecting to nodes that are more important. In a network of \(S\) nodes, \(A\) represents the network connection matrix, and \(\alpha_{1},\alpha_{2},...,\alpha_{S}\) represent the \(N\) characteristic values of \(A\). Suppose \(\alpha_{1}\) is the main characteristic value of the matrix \(A\). The corresponding characteristic vector is \(e=\left(e_{1},e_{2},...,e_{s}\right)^{T}\), and then:  
\[\alpha e_{i}=\sum\
olimits_{j=1}^{S}a_{ij}e_{j} \tag{5}\]  
The characteristic vector indices of nodes can be defined as:  
\[S_{c}\left(v_{i}\right)=\alpha^{-1}\sum\
olimits_{j=1}^{S}a_{ij}e_{j} \tag{6}\]  
Figure 3: This picture shows the result of community division of the network structure shown in Figure 1.  
The overall importance of the nodes is expressed as:  
\[S_{IMP}\left(v_{i}\right)=\beta S_{B}\left(v_{i}\right)+\delta S_{c}\left(v_{i}\right) \tag{7}\]  
In this formula, \(\beta\) and \(\delta\) are variable parameters, representing the weight of \(S_{B}\left(v_{i}\right)\) and \(S_{C}\left(v_{i}\right)\) when we calculate the importance of nodes, respectively. A threshold is set here to measure whether the importance of nodes is within an acceptable range. If the node is less important than the threshold value \(\tau\), directly remove the node from its community. According to the actual application scenario, if the degree of bias in two aspects is reasonably evaluated, then determine the values of parameter \(\beta\) and \(\delta\), \(\beta+\delta=1\) (in this paper, \(\beta=0.5\), \(\delta=0.5\)). After removing the less important nodes, the community structure changes. However, the community can continue to shrink to reduce the size of the network. In this case, we use the cohesion of the nodes to recontract the community structure.