Transport network criticality metrics: a comparative analysis and a guideline for selection

Figures & data

Table 1. List of criticality metrics used in this study.

No	Metric name	Description	Technical requirements			Conceptual dimensions represented (see Section 3)			Relevant references
			Origin-Destination (OD) matrix	Transport network assignment	Others	Functionality	Ethical	Aggregation
1	Change in weighted total travel cost	Increase in total travel cost (distance and traffic flow) among all origin-destination pairs due to disruptions on an element	Calculated with socio-economic factors	All-or-nothing or user equilibrium assignment	Complemented with an interdiction method	Travel cost	Utilitarian	Network-wide	(Balijepalli & Oppong, 2014; Dehghani, Flintsch, & McNeil, 2014; Du, Kishi, Aiura, & Nakatsuji, 2014; Gauthier, Furno, & El Faouzi, 2018)
2	Change in expected user exposure	The average impact of disruptions experienced by all users in the transport system	Calculated with socio-economic factors	All-or-nothing or user equilibrium assignment	Complemented with an interdiction method	Travel cost	Utilitarian	Network-wide	(Jenelius, 2009; Jenelius & Mattsson, 2015)
3	Change in worst-case user exposure	The maximum impact of disruptions among all users in the transport system	Calculated with socio-economic factors	All-or-nothing or user equilibrium assignment	Complemented with an interdiction method	Travel cost	Utilitarian	Network-wide	(Jenelius & Mattsson, 2015)
4	Change in unweighted total travel cost	Increase in total travel cost (only distance) among all origin-destination pairs due to disruptions on an element	Calculated without socio-economic factors	All-or-nothing assignment	Complemented with an interdiction method	Travel cost	Egalitarian	Network-wide	(Wang, Chan, & Li, 2014)
5	Change in region-based unweighted total travel cost	Increase in total travel distance among all origin-destination pairs within a certain sub-area where the element is located due to disruptions on an element	Calculated without socio-economic factors	All-or-nothing assignment	Complemented with an interdiction method	Travel cost	Egalitarian	Local	(Jenelius & Mattsson, 2015; Wang et al., 2014)
6	Change in weighted accessibility	Decrease in weighted (by transport demand/flow) accessibility due to disruptions of an element. The weight is determined by the socioeconomic activities	Calculated with socio-economic factors	All-or-nothing or user equilibrium assignment	Complemented with an interdiction method	Accessibility	Utilitarian	Network-wide	(Chen, Yang, Kongsomsaksakul, & Lee, 2007; Luathep et al., 2011; Wang et al., 2014)
7	Change in unweighted daily accessibility	Decrease in unweighted, topological-based accessibility due to disruptions of an element	Calculated without socio-economic factors	All-or-nothing assignment	Complemented with an interdiction method	Accessibility	Egalitarian	Network-wide	(Luathep et al., 2011; Wang et al., 2014)
8	Traffic flow	Empirical traffic flow of the transport network	Not required	Not required	Empirical traffic flow	Travel cost	Utilitarian	Local	(Zhou, Fang, Thill, Li, & Li, 2015)
9	Traffic density	Traffic volume over capacity. Normally used as an approximation of congestion	Not required	Not required	Empirical traffic flow and road capacity (e.g. number of lanes)	Travel cost	Utilitarian	Local	(Scott et al., 2006; Zhou et al., 2015)
10	Weighted betweenness centrality	The traffic flow among the economic centroids. The traffic flow is determined by the socioeconomic profiles	Calculated with socio-economic factors	All-or-nothing or user equilibrium assignment	-	Travel cost	Utilitarian	Local	(Aydin, Duzgun, Wenzel, & Heinimann, 2018; Demirel, Kompil, & Nemry, 2015; Kermanshah & Derrible, 2016; Wang & Cullinane, 2014)
11	Exposure to disaster	Overlay of natural disaster maps with the transport network. This is often used for disaster preparedness studies	Not required	Not required	Overlays maps of natural disasters	Connectivity	Utilitarian	Local	(Kermanshah & Derrible, 2016; Koks et al., 2019; Sohn, 2006)
12	Nearby alternative elements	Number of other elements that are located within an x kilometre distance from an element.	Not required	Not required	GIS analysis	Connectivity	Egalitarian	Local	(Snelder, van Zuylen, & Immers, 2012)
13	Unweighted betweenness centrality	Betweenness centrality calculated based on the shortest paths among the economic centroids	Calculated without socio-economic factors	All-or-nothing assignment	-	Travel cost	Egalitarian	Local	(Aydin, Casali, Sebnem Duzgun, & Heinimann, 2019; Demirel et al., 2015; Kermanshah & Derrible, 2016; Wang & Cullinane, 2014)
14	Change in network average efficiency	Decrease in network efficiency due to disruptions of an element	Calculated without socio-economic factors	All-or-nothing assignment	Complemented with an interdiction method	Travel cost	Egalitarian	Network-wide	(Dehghani et al., 2014; Issacharoff, Lämmer, Rosato, & Helbing, 2008; Nagurney & Qiang, 2008)
15	OD k-connectivity	Decrease in the number of distinct shortest paths among all origin-destination pair due to a disruption of an element	Calculated without socio-economic factors	All-or-nothing assignment	The assignment has to be complemented with a network distinct path algorithm	Connectivity	Egalitarian	Network-wide	(Mishra, Welch, & Jha, 2012; Shier, 1979)
16	Minimum link cut centrality	The frequency of a link’s appearance in the cut sets of all pairs of economic centroids	Not required	Not required	Uses cut set algorithms from network theory	Connectivity	Egalitarian	Network-wide	(Snelder et al., 2012)
17	Unsatisfied demand	Amount of transport activity that cannot take place due to disruptions of an element	Calculated with socio-economic factors	All-or-nothing or user equilibrium assignment	Complemented with an interdiction method	Connectivity	Utilitarian	Network-wide	(Baroud, Barker, Ramirez-Marquez, & Rocco, 2014; Qiang & Nagurney, 2012)

Table 2. Topological properties of the networks.

	Number of links	Number of nodes	Beta index	Average clustering coefficient	Mean betweenness centrality	Global efficiency
Bangladesh	1258	962	1.308	0.0411	0.0159	0.0673
Barisal	344	294	1.17	0.0164	0.0359	0.1089
Chittagong	922	733	1.258	0.0589	0.0283	0.0617
Dhaka	1173	969	1.211	0.0363	0.0205	0.0589
Khulna	489	424	1.153	0.0263	0.0432	0.0749
Rangpur	115	89	1.292	0.0187	0.1933	0.1109
Rajshahi	581	456	1.274	0.0522	0.0289	0.0863
Sylhet	165	138	1.196	0.0193	0.0621	0.1427

Figure 1. Illustration of the three-step empirical comparison: (a) listing of the 100 most critical links based on each metric for each network, (b) Spearman-rank correlations among the metrics in each network, (c) three robustness indicators summarising the eight networks.

Figure 2. (a) Average, (b) Range, and (c) Consistency indicators of the correlation coefficients between all metrics pairs across the eight networks. The numbers on the axes corresponds to the metrics in Table 1.

Figure 3. Grouping of empirical similarities among the metrics.

Figure 4. Distribution of absolute difference in metrics correlation coefficients among several pairs of networks.

Figure 5. A five-step guideline to select criticality metrics.

Table 3. Spearman-rank correlation coefficients of criticality metrics for the Barisal division.

		Connectivity – Egalitarian – Network-wide		Connectivity – Egalitarian – Local	Accessibility – Egalitarian – Network-wide
		#15	#16	#12	#7
Connectivity – Egalitarian – Network-wide	#15	1	0.28	−0.23	0.28
	#16	0.28	1	0.064	0.26
Connectivity – Egalitarian – Local	#12	−0.23	0.064	1	0.054
Accessibility – Egalitarian – Network-wide	#7	0.28	0.26	0.054	1

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