content_image/332647.jpg content_image/332645.jpg
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distributions of the actual network especially for the lower degree values. For each network, the mean in-degree is equal to the mean out-degree. As expected, this decreases with m$_{th}$ because the number of nodes and therefore, the number of links decrease with m$_{th}$ . For a Poisson distribution, it is expected that 〈 k 〉 ≈ log N , which is what we observe in Fig. 3 for the shuffled catalog. For the actual catalog however, the number of links are less than that of a random network and we get 〈 k 〉 ≈ 0 . 91 log N . The value 0 . 91 is higher than that reported for California in [10] and this means that larger number of links are possible for the nodes in the Japanese seismic network. 

## B. Distance distributions 

We use the great circle distance for computing the distance l$_{ij}$ between two event lo- cations. This is calculated using the Haversine formula [12]: if ( φ$_{i}$, λ$_{i}$ ) and ( φ$_{j}$, λ$_{j}$ ) are the (latitude, longitude) values for the two event locations and, Δ φ = φ$_{j}$ − φ$_{i}$ and Δ λ = λ$_{i}$ − λ$_{j}$ , then 

<img src='content_image/332645.jpg'>

