Complex Network Metrics: Can Deep Learning Keep up With Tailor-Made Reference Algorithms?

Complex network metrics are used for ranking the importance of nodes in many different applications, e.g., spreader identification and percolation analysis. Examples for such node metrics include the degree centrality and betweenness centrality. The computation of some of these metrics is computationally expensive, e.g. the computation of betweenness takes $O(N^{3})$ of computation steps in the worst case, where $N$ is the number of nodes. In this study, we investigate the ability of deep learning via graph embedding to predict node centrality metrics in complex networks. Our study reveals that deep learning can identify vital nodes well for several of these metrics. Compared to exact computation with prohibitive costs, deep learning can get significant speedups, which scale up well with the size of the network. Further investigation on betweenness centrality reveals that the accuracy of deep learning is not as good as some tailor-made, tuned approximation algorithms. However, deep learning offers a nice trade-off between runtime and quality with its linear computational complexity regarding the network size, which makes it scalable on large networks and especially for these metrics with expensive computational costs. Our work is the first to explore the ability of deep learning on a wide range of networks metrics, and will hopefully induce future work on improved graph embeddings, tuned for specific network metrics.

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