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Seismic activities show a space-time symmetry in some research. They have been recently studied using complex network theory. Earthquake network similarity is studied by us from seismic catalogs in the same region for a given period of time. In this paper, we first calculate the distance between feature vectors which represent the topological properties of different networks. A hierarchical clustering of earthquake networks in the same region is shown by using this method. It is found that similar networks are not the networks of adjacent years but those with decades time difference. To study the period of similar earthquake networks in the same region, we use wavelet analysis to obtain the possible periods at different time scales of the regions of the world, California and Japan. It is found that some of the possible periods are consistent with the results which have been already found by seismologists. The study of similar seismic activities from the perspective of the complex network will help seismologists to study the law of earthquake occurrence in a new way, which may provide possible research thinking for earthquake prediction. [ABSTRACT FROM AUTHOR]