and has no arbitrariness in its selection. Also, any event identified as a recurrence of a main event does not loose its status if the period of the catalog is enlarged later, as this will only result in the list of recurrences getting longer if the added events satisfy the condition of coming closer to the main event in the intervening period. The network is constructed by considering every event in the catalog as a node and each recurrence is represented by a directed edge between the pair of events, directed according to the time ordering of the earthquakes. The two variables associated with each edge are – l$_{ij}$ , the distance between the epicentres of the two events and t$_{ij}$ , the time interval between the them. Each node has an out-degree equal to its number of outward edges (the number of its recurrences) and an in-degree equal to the number of events it is counted to be a recurrence of. The first event in the catalog will not have any incoming edges to it and the last event in the catalog will have no outgoing edges from it. Note that the recurrences defined here do not necessarily relate to the conventional methods of defining aftershocks and thus the largest magnitude event in the network need not have the most number of recurrences. The overall structure of the network represented by the outgoing links and the incoming links describes the clustering of seismicity in the region studied. 

## III. THE CATALOG 

The catalog studied here is the Japan University Network Earthquake Catalog [11] cover- ing the rectangular region (126 . 433 $^{◦}$E–148 . 0 $^{◦}$E) longitude and (25 . 730 $^{◦}$N–47 . 831 $^{◦}$N) latitude, for the period between January, 1986–December, 1998. The catalog has a threshold magni- tude of m$_{JMA}$ =2 . 0. However, we have limited our study to events with magnitude ≥ 2 . 5. 

The total number of such events are 114804. In order to verify the dependance of the net- work properties on magnitude threshold and on the number of events, subsets with higher magnitude thresholds viz 3 . 0 , 3 . 5 , 4 . 0 and 4 . 5 which contain 53525, 20067, 6268 and 2038 events respectively and a subcatalog with m$_{th}$ = 3.0 for a shorter period from 1986 –1992 with 22975 events, were generated from the main catalog. The b value = − 0 . 87 was obtained from a plot of log N ( m ) vs m , where N ( m ) is the cumulative number of earthquakes of mag- nitudes ≥ m , and the linear fit was good in the range 2 . 5 ≤ m ≤ 7. In order to distinguish the causal features of seismicity, networks were constructed from the shuffled catalog, where we have adopted an identical shuffling procedure as in [10]. Subsets and sub catalogs of 

