# Adjacency-Information-Entropy-Based Cooperative Name Resolution Approach in ICN
## 3 Model and Theory Fundamental
### Adjacency Information Entropy  
Information entropy was proposed by [PERSON] in 1948 [PERSON] (1948). The advantage of information entropy is that it can characterize the degree of a system disorder embodied in \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Description** \\ \hline \(V\) & the set of nodes that have the potential to place name resolution server \\ \(N\) & the total count of nodes in \(V\) \\ \(E\) & the set of links directly connect between nodes \\ \(W\) & the set of weights of edges \\ \(D\) & an \(N\times N\) matrix, the shortest path latencies between every pair of nodes in \(V\) \\ \(e_{ij}\) & the link between node \(v_{i}\) and node \(v_{j}\) \\ \(w_{ij}\) & the weight between node \(v_{i}\) and node \(v_{j}\) \\ \(d\Big{(}v_{i},\ v_{j}\Big{)}\) & the network latency between node \(v_{i}\) and node \(v_{j}\) \\ \(T\) & the set of upper bounds of name resolution latencies at each level \\ \(L\) & the number of name resolution service levels \\ \(U\) & the set of users in the network \\ \(M^{l}\) & the count of master name resolution node in level \(l\) \\ \(MN_{i}^{l}\) & the \(i\)-th master name resolution node in level \(l\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of notation. the sample space from the uncertainty of the system sample points, using probabilistic and statistical methods, and quantify the local structure of the network nodes and the neighborhood information well. In recent years, information entropy has been widely used in complex systems and complexity theory, and it has become an effective method to solve problems in complex networks, especially in identifying key nodes and quantifying node adjacency structures [43; 44; 45; 46]. The approach proposed in this paper is based on information entropy and involves the following definition of concepts:  
**Definition 1**. _Neighbor node._  
Neighbor nodes refer to the nodes that are directly adjacency to a node in the network topology, neighbor node set of node \(v_{i}\) is defined as Equation (6):  
\[\Gamma_{i}=\left\{v_{j}\big{|}e_{ij}\in E,\ v_{j}\in V\right\} \tag{6}\]  
**Definition 2**. _Adjacency degree._  
Several researchers use the degree of a node as an important indicator to quantify its structural characteristics. However, the degree of a node can only reflect the connection of a node with its direct neighbors, and cannot reflect well the connection of a node with other indirect neighbor nodes. In order to more accurately reflect the local structural characteristics of a node, the adjacency degree is proposed. The adjacency of node \(v_{i}\) is defined as Equation (7):  
\[Q_{i}=\sum_{j\in\Gamma_{i}}k_{j} \tag{7}\]  
where \(k_{j}\) denotes the degree value of node \(v_{j}\). **Definition 3**. _Neighbor probability function._  
The neighbor probability function describes the probability that each node will be selected among its neighbor nodes for operations such as communication. The neighbor probability function of the node \(v_{i}\) is defined as Equation (8):  
\[p_{ij}=\frac{k_{j}}{Q_{i}},\ j\in\Gamma_{i} \tag{8}\]  
where the adjacency degree here cannot equal to zero--otherwise, the relative \(p_{ij}\) is meaningless. **Definition 4**. _Adjacency information entropy._  
In the literature [45], the neighbor probability function is considered to describe the influence of neighbor nodes of different nodes on themselves based on the traditional information entropy, thus proposing the adjacency information entropy, defined as Equation (9):  
\[H_{i}=-\sum_{j\in\Gamma_{i}}\left(p_{ij}\log_{2}p_{ij}\right) \tag{9}\]  
Adjacency information entropy mainly reflects the magnitude of a node's influence on its direct and indirect neighbor nodes. A higher adjacency information entropy of a node indicates that this node has a higher probability of being selected by the node' neighbors for communication or cooperation compared with other indirect neighbor nodes.