In this paper, we propose a clustering method based on the infinite betweenness centrality for temporal networks specified by 1-dimensional periodic graphs. While the temporal networks have a wide range of applications such as opportunistic communication, there are not many clustering algorithms specifically proposed for them. We give a pseudo polynomial-time algorithm for temporal networks, of which the transit value is always positive and the least common divisor of all transit values is bounded. Our experimental results show that the centrality of networks with 125 nodes and 455 edges can be efficiently computed in 3.2 seconds. Not only the clustering results using the infinite betweenness centrality for this kind of networks are better, but also the nodes with biggest influence are more precisely detected when the betweenness centrality is computed over the periodic graph.
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