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Generating Graphs by Creating Associative and Random Links Between Existing Nodes

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Abstract

The study and analysis of real-world social, communication, information and citation networks for understanding their structure and identifying interesting patterns have cultivated the need for designing generative models for such networks. A generative model generates an artificial but a realistic-looking network with the same characteristics as that of a real network under study. In this paper, we propose a new generative model for generating realistic networks. Our proposed model is a blend of three key ideas namely preferential attachment, associativity of social links and randomness in real networks. We present a framework that first tests these ideas separately and then blends them into a mixed model based on the idea that a real-world graph could be formed by a mixture of these concepts. Our model can be used for generating static as well as time evolving graphs and this feature distinguishes it from previous approaches. We compare our model with previous methods for generating graphs and show that it outperforms in several aspects. We compare our graphs with real-world graphs across many metrics such as degree, clustering coefficient and path length distributions, assortativity, eigenvector centrality and modularity. In addition, we give both qualitative and quantitative results for clarity.

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Acknowledgements

This work was supported by the Technology Innovation Program (20006489, “Development of the embedded robot equipment control system equipped with an AI vision module for industrial environment”) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea), and by Korea Institute of Science and Technology (KIST) under the project “HERO Part 1: Development of core technology of ambient intelligence for proactive service in digital in-home care”.

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  1. Imaging Media Research Center, Korea Institute of Science and Technology, Seoul, Republic of Korea

    Muhammad Irfan Yousuf & Suhyun Kim

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  1. Muhammad Irfan Yousuf
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  2. Suhyun Kim
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Correspondence to Suhyun Kim.

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Communicated by Irene Giardina.

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A Generating Time Evolving Graphs

A Generating Time Evolving Graphs

We calculate the cosine distance between the original and generated graphs at \(t = \{1,2, \ldots , 10\}\) and present the results in Fig. 13. We see that, on average, the Mixed Model is more consistent and generates graphs with less variation in eigenvector centrality score over time. For the assortativity coefficient metric, we calculate the point distance between the original and generated graphs and present the results in Fig. 14. In some datasets, e.g., EnronEmail and Digg, Mixed Model generates smaller distances while in some datasets, e.g., Skitter and YouTube, Chung–Lu performs better than other models. Forest Fire outperforms in LinuxEmail whereas Barabasi–Albert outperforms in the Brightkite dataset.

Fig. 13
figure 13

Cosine distance of eigenvector centrality of 10 snapshots of the original and generated graphs

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Fig. 14
figure 14

Point distance of assortativity coefficient of 10 snapshots of the original and generated graphs

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Yousuf, M.I., Kim, S. Generating Graphs by Creating Associative and Random Links Between Existing Nodes. J Stat Phys 179, 1–32 (2020). https://doi.org/10.1007/s10955-020-02517-z

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