# Measuring Method of Node Importance of Urban Rail Network Based on H Index
## 2 Preliminaries
### Definitions of \(h\)-Index and \(g\)-Index  
The \(h\)-index skillfully takes into account both the quantity and quality of scholars' papers, and achieves the effect of describing productivity and influence with one index value. However, the \(h\)-index is insensitive to the papers with high citation frequency. Based on this, [PERSON] [17] puts forward the \(g\)-index, which can reflect the evaluation index of the papers with high citation frequency. The \(h\)-index and \(g\)-index are defined as follows:  
**Definition 1**.: _If and only if each of the \(N_{p}\) papers published by a scientist has at least \(h\) citations, and the other \(\left(N_{p}-h\right)\) papers have no more than \(h\) citations, this \(h\) value is the scientist's \(h\)-index [12]._  
For instance, [PERSON]'s own \(h\)-index is \(59\), which means that in his published papers, each paper cited at least \(59\) times has a total of \(59\) papers. [PERSON] believes that the \(h\)-index can accurately reflect a person's academic achievements. The higher the \(h\)-index, the greater the influence of his paper [12]. An important node in an urban rail network identified by \(h\)-index has a feature that there is a correlation coefficient of no less than a certain value between the station and a certain number of stations. It indicates that the operation status of the station can represent the status of some stations in the urban rail network. However, \(h\)-index is not sensitive to both high cited papers and low cited papers, so it is not conducive to the objective evaluation of those scientists with low number of papers and high cited papers. Then [PERSON] [17] puts forward an evaluation \(g\)-index which can reflect the high frequency paper.  
**Definition 2**.: _Papers are listed in descending order of citation number. The cumulative citation number of \(g\) papers with the highest citation number is greater than or equal to \(g^{2}\), while the cumulative citation number of \(g+1\) papers is less than \(\left(g+1\right)^{2}\), which is the scientist's \(g\)-index [17]._  
For instance, suppose that the citation number of four articles of a scholar is [20; 18; 16; 10], and the corresponding \(g^{2}=\left\{1^{2},2^{2},3^{2},4^{2}\right\}\), because \(10<4^{2}\), then the scholar's \(g\)-index is \(3\). When \(g\)-index is used to evaluate the importance of urban rail network nodes, it can avoid the problem that \(h\)-index is not sensitive to the identification of nodes with high passenger flow correlation, and improve the accuracy of identification of important nodes in urban rail network.  
From a scientist's perspective, the \(h\)-index is known to be exponentially harder to increase: when one's \(h\)-index is 150, a 150 times cited paper does not qualify to increase the \(h\)-index any further. As such, when relating this back to urban rail network, every line should be equally busy for a node to be identified as busy. However, as the \(h\)-index in this paper considers the relationship between passenger flow and passenger flow of each station, it can be seen from Figure 1 that the passenger flow in the interval can reflect the correlation between the flows, and the passenger flow status of each station at each sampling time is different, that is to say, the \(h\)-index proposed in this paper further considers the relationship between passenger flow in the urban rail network.