# DelayFlow Centrality

#### Definition

DelayFlow that incorporates travel time delay and commuter flow volume.

DelayFlow centrality are more similar with degree centrality and betweenness centrality with correlation scores above 0.5. Time delay is incurred for commuters to find alternative means to reach destinations when a node is down. To determine the extent of delay caused to the people affected, we compute t

[CHENG, Y.-Y. 2013]

DelayFlow centrality are more similar with degree centrality and betweenness centrality with correlation scores above 0.5. Time delay is incurred for commuters to find alternative means to reach destinations when a node is down. To determine the extent of delay caused to the people affected, we compute t

_{exp}(i,j), the expected time taken to travel from node i to node j, and t_{alt}(i,j), the time taken to travel from node i to node j using an alternative means of transportation (e.g. bus). The time delay factor l_{ij}is then defined to be t_{alt}(i,j)/t_{exp}(i,j). We assume that t_{exp}and t_{alt}are static throughout the day. The time delay factor l_{ij}is asymmetric as both t_{exp}(i,j) and t_{alt}(i,j) are asymmetric. The larger the l_{ij}value (>1), the greater the time delay. Let h_{ij}denote the number of commuters from node i to node j per hour, and h_{jk}(i) denote the number of commuters from node j to node k through node i per hour. where is the total commuter flow of the transportation network and[CHENG, Y.-Y. 2013]

#### Software

#### References

- CHENG, Y.-Y., LEE, R. K.-W., LIM, E.-P. & ZHU, F. DelayFlow centrality for identifying critical nodes in transportation networks. Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 2013. ACM, 1462-1463.