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Fig. 3 | Applied Network Science

Fig. 3

From: Managing large distributed dynamic graphs for smart city network applications

Fig. 3

A local breach affect in a real-time smart city OSN application. The graph reviews real- time influential rock-stars events, distributed to three graph datasets (geographic regions) denoted by D1,D2 and D3. The graphs edges are friendships among events participators, and we focus on the numeric attribute of average number of participators of each event, as well as the users average number of inner-community friendships (the vertices degrees). a We define entry-level conditions of 1000 followers per user, and at least 2 inner-community friendships. The global threshold T is defined by the average of 1300 followers per user and an average of 2.5 inner-community friendships. The change in the graph after time goes by as can be seen in (b,c). b describes D at t=1 min. A change occurred in this time space (0−1), and Bob un-friended Chuck, changing the local average degree in D1 from 2.5 to 2 which broke the local threshold of 2.5. This change did not break T since the total average degree is still bigger than 2.5 (it changed from 3.5 to 3.33), thus the global community-defining conditions remained valid. c describes D at t=2 min. Several changes occurred in this time space (1-2), and the number of followers of the rock stars in D3 was reduces by 4900, changing the local average of followers from 1943.8 to 1127.2. This change broke T since the total average of followers is less than 1300 (1297.8), thus the community broke its defining conditions

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