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An entropy-based social network community detecting method and its application to scientometrics

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Abstract

Community structure is one of the important properties of social networks in general and in particular the citation networks in the field of scientometrics. A majority of existing methods are not proper for detecting communities in a directed network, and thus hinders their applications in the citation networks. In this paper, we provide a novel method which not only overcomes the above mentioned disability, but also has a relative low algorithm time complexity which facilitates the application in large scale networks. We use the concept of Shannon entropy to measure a network’s information and then consider the process of detecting communities as a process of information loss. Based on this idea, we develop an optimal model to depict the process of detecting communities and further introduce the principle of dynamic programming to solve the model. A simulation test is also designed to examine the model’s accuracy in discovering the community structure and identifying the optimal community number. Finally, we apply our method in a citation network from the journal Scientometrics and then provide several insights on promising research topics through the detected communities by our method.

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Acknowledgments

This study was partly funded by China Scholarship Council (No. 201306120159) and National Natural Science Foundation of China (No. 71271070, No. 71201039, and No. 71172157).

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Authors and Affiliations

  1. School of Management, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Yongli Li, Guijie Zhang, Yuqiang Feng & Chong Wu

  2. Dipartimento di Economia Politica e Statistica, Università di Siena, 53100, Siena, Italy

    Yongli Li

Authors
  1. Yongli Li
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  4. Chong Wu
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Corresponding author

Correspondence to Guijie Zhang.

Appendices

Appendix 1

The following Table 3 shows the time complexity of the mentioned community detection methods in Introduction.

Table 3 Time complexity of these algorithms mentioned in Introduction
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Appendix 2

Here gives the analysis on time complexity of this paper’s method. Recall Table 1, the second step of Initialization needs the time complexity O(n 2), and the first step of Loop needs the time complexity O(n−1) which consists of refreshing the new community’s information with time complexity O(n−1) and finding the optimal merging communities with time complexity O(n−1). The second step of loop needs the time complexity O(n−2). Similarly, when the community number is n−m, namely the \( m{\text{th}} \) step of loop, it needs the time complexity O(n−m). Note that the above m changes from n−1 to 1. Accordingly, the whole time complexity can be obtained by adding the above mentioned all steps’ complexity. As a result, the whole algorithm’s time complexity is O(n 2).

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Li, Y., Zhang, G., Feng, Y. et al. An entropy-based social network community detecting method and its application to scientometrics. Scientometrics 102, 1003–1017 (2015). https://doi.org/10.1007/s11192-014-1377-5

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