From the perspective of spatial autocorrelation, the nearer the two objects are to each other, the stronger the reliance is between them. Based on the space autocorrelation theory, it is thought that nodes neighboring current nodes contribute more to the importance of the nodes. Existing research has suggested that some characteristics of many complex systems are positively correlated with the degree of the node. Thus, during the node importance evaluation process, the index importance contribution matrix of neighboring nodes is positively correlated with the value of degree.

When, the influence of only one characteristic (such as value of degree) on node importance is considered, the node importance evaluation function of Eq. (19) is introduced in terms of any Node *i*:
$${I}_{i}=a{\delta}_{i}+{b}^{1}\sum _{j\in {\pi}_{i}^{1}}{\delta}_{j}+{b}^{2}\sum _{j\in {\pi}_{i}^{2}}{\delta}_{j}+\cdots +{b}^{m}\sum _{j\in {\pi}_{i}^{m}}{\delta}_{j}$$(19)

Where, *I*_{i} stands for the importance index of Node *i*; *δ* stands for the node attribute value, which can be the degree of node or the network constraint coefficient; a and b are two adjustable parameters, which are used to adjust the degree of reliance of node importance on the node attributes and the neighbouring nodes from the first order to the *n*^{th} order, respectively. From the perspective of autocorrelation, in order to fully consider the contribution of importance of the node and the neighboring nodes, here the value of a and b meets the conditions of
$\overline{k}\cdot b>a>b$ and 1 > *b* > 0, where
$\overline{k}$ stands for the node’s mean degree. From Eq.(19), it can be seen that the evaluation function comprehensively considers the contribution of the node to the importance of the node itself and the neighboring nodes of the m order. Besides, the farther the node is away from Node *i*, the less contribution it is to the importance of Node *i*. Considering the influence of neighboring nodes of the m order on node importance, the location information of the node is utilized. For the convenience of understanding, here, neighboring nodes of the m order to be evaluated are regarded as the depth of neighboring nodes to be observed for the node importance evaluation, and their value should meet the condition of *D* ≥ *m* ≥ 0.

Generally speaking, in real life, when importance of target objects is evaluated, the influence of multiple factors will be taken into consideration. To network nodes, their importance is not fully decided by their degree and structural hole index. The remaining factors should also be accommodated to so as to achieve an accurate evaluation of node importance.Thus, it is assumed that every node selects n evaluation indexes, and that *δ*_{i, j} is used to stand for the *j* index value of Node *i*. Therefore, the importance evaluation model of Node *i* can be defined as below:
$${I}_{i}=A{E}_{i}$$(20)

Where, *I*_{i} stands for the degree of importance of Node *i*; A stands for the evaluation coefficient matrix or the importance degree contribution matrix; *E*_{i} stands for the contribution of the node itself and its neighboring nodes of various orders to the importance of Node *i*. Here, it is assumed that neighboring nodes of the same order contribute the same amount to Node *i*. In other words, their evaluation coefficient is the same. *W* stands for the evaluation index matrix of Node *i*, which includes the index value of Node *I* and various neighboring nodes; *W* stands for the index weight matrix, which is used to stand for the degree of reliance of the importance of Node i on various indexes. Here, the proportion of the weight of n evaluation indexes
is written as, *w*_{1}, *w*_{2}, …, *w*_{n}. Under the multi-factor situation, the single-factor evaluation function is maintained. The method to calculate the contribution of neighboring nodes of the same order to the importance of Node *i* is shown below:
$${\delta}_{i,j}^{m}=\sum _{j\in {\pi}_{i}^{m}}{\delta}_{j,n},$$(21)

Where,
${\delta}_{j,n}^{m}$ stands for the total contribution amount of the set of neighbouring nodes of the m order belonging to Node *i* to the importance of Node *I* under the restriction of the *n* index;
${\delta}_{j,n}(j\in {\pi}_{i}^{m})$ stands for the value of the *n* index of the central node *j* among neighboring nodes of the *m* order belonging to Node *I*. It is assumed that the value of the *n* indexes of Node *i* is {*δ*_{i,1}, *δ*_{i,2}, …*δ*_{i,1}}. Therefore, the evaluation index matrix in Eq. (19) can be expressed as below:
$$\begin{array}{}{E}_{i}& =\left[\begin{array}{cccc}{\delta}_{i,1}^{0}& {\delta}_{i,2}^{0}& \cdots & {\delta}_{i,n}^{0}\\ {\delta}_{i,1}^{1}& {\delta}_{i,2}^{1}& \cdots & {\delta}_{i,n}^{1}\\ \vdots & \vdots & \cdots & \vdots \\ {\delta}_{i,1}^{m}& {\delta}_{i,2}^{m}& \cdots & {\delta}_{i,n}^{m}\end{array}\right]\\ & =\left[\begin{array}{cccc}{\delta}_{i,1}& {\delta}_{i,2}& \cdots & {\delta}_{i,n}\\ \sum _{j\in {\pi}_{i}^{1}}{\delta}_{j,1}& \sum _{j\in {\pi}_{i}^{1}}{\delta}_{j,2}& \cdots & \sum _{j\in {\pi}_{i}^{1}}{\delta}_{j,n}\\ \vdots & \vdots & \cdots & \vdots \\ \sum _{j\in {\pi}_{i}^{m}}{\delta}_{j,1}& \sum _{j\in {\pi}_{i}^{m}}{\delta}_{j,2}& \cdots & \sum _{j\in {\pi}_{i}^{m}}{\delta}_{j,n}\end{array}\right]\end{array}$$(22)

The value scope of different indexes might vary greatly. For example, the degree of the same node might be several hundred, but its network restraint coefficient might be smaller than 1. The physical meaning and the measurement unit of various indexes might not necessarily be the same, thus might lead to a different data dimension and magnitude. Therefore, it is necessary to conduct normalization of the evaluation index matrix. From Eq. (21), it can be seen every column of elements corresponds to one index. There are n indexes in total. The following normalization equation is adopted to process every index value:
$${\delta}_{i,j}^{{}^{\prime}k}=\frac{{\delta}_{i,j}^{k}-min{\delta}_{i,j}^{k}}{max{\delta}_{i,j}^{k}-min{\delta}_{i,j}^{k}},j=1,2,\dots n$$(23)

In order to work out the normalization evaluation index matrix based on the index value after normalization, it is assumed that the importance of any Node *i* in the network can be expressed a
${I}_{i}=A{E}_{i}^{\prime}W,$ namely:
$$\begin{array}{}{I}_{i}& =\left[a,{b}^{1},{b}^{2},...,{b}^{n}\right]\times \left[\begin{array}{cccc}{\delta}_{i,1}^{0}& {\delta}_{i,2}^{0}& \cdots & {\delta}_{i,n}^{0}\\ {\delta}_{i,1}^{1}& {\delta}_{i,2}^{1}& \cdots & {\delta}_{i,n}^{1}\\ \vdots & \vdots & \cdots & \vdots \\ {\delta}_{i,1}^{m}& {\delta}_{i,2}^{m}& \cdots & {\delta}_{i,n}^{m}\end{array}\right]\\ & \times \left[\begin{array}{c}{w}_{1}\\ {w}_{2}\\ \vdots \\ {w}_{\mathrm{\partial}}\end{array}\right]\end{array}$$(24)

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