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Fig. 2 | Applied Network Science

Fig. 2

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

Fig. 2

A local breach affect in a real-time traffic application. When a global graph property is breached, the fastest path changes correspondingly. The fastest path is emphasized by the solid blue line. a At t=0 the global attribute, i.e. the fastest path is T=29 min and the local thresholds are T1=9 min,T2=11 min,T3=9 min. b At (t=3 min) a local breach occurs and the edge EH reduces its weight from 6 min to 2 min changing the local threshold T2 from 11 min to 10 min (denoted by the green path). This local breach did not affect the global graph T, since the total path time from A to L trough E (A-C-D-E-H-I-L) 31 min is still slower than the original path time 29 min. c A local breach leading to a global graph breach and a path change. At t=9 min the edge H-I reduces its weight from 8 min to 3 min, changing the local threshold T3 from 9 min to 7 min. This breach broke the global T since the total path time is now faster, (26 min is faster than 29 min) and global path is updated from (A-C-D-F-G-I-L) to (A-C-D-E-H-I-L) noted by the dashed blue line

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