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which can be calculated though graph properties such
as centrality.
Traditional methods of finding centrality and node
importance are not relevant in weighted and directed
graphs (Opsahl et al., 2010). Recently, researchers
have developed many metrics to represent these prop-
erties for weighted graphs accurately. On road net-
works, not all links have the same functional capac-
ity and importance, and it is crucial to incorporate
this distinction within analyses. This paper shows
how essential links can be identified within complex
road networks using centrality principles on weighted
graphs. It also gives precedence to the structural prop-
erties of the network which has a significant impact on
the proposed centrality metric. Road transport metrics
like edge capacity and daily traffic value are consid-
ered as edge weights to analyze networks better on a
higher level.
The paper is organized as follows. Section 2 high-
lights some of the research done in this field. Sec-
tion 3 introduces several metrics used to quantify con-
nectivity within a network. Section 4 describes data
collection and processing methodology used to per-
form analyses. Section 5 shows the impact of destroy-
ing edges within a network using a synthesised graph
and a real world graph. We also propose a solution
to identify critical links in the network and demon-
strate its performance on real world graphs. Finally
we present conclusions of our work and future direc-
tion of our research.
2 RELATED WORK
(Gauthier et al., 2018) performed stress tests on links
to find out critical connections in networks. The au-
thors experimented with real-world scenarios, includ-
ing traffic flows. They compared results with topo-
logical methods, which have a more significant com-
putational overhead, showing that the criticality of
links depends on the metric being evaluated. This
method seems to be a viable option to determine crit-
ical links. While their research was limited to a small
net work, their results look promising. (Almotahari
and Yazici, 2020) introduced link criticality index for
ranking connections. They used network flows to
evaluate the criticality of a link using readily avail-
able sensor and traffic data. They were able to find
critical links in the network using only the top 20% of
the origin-destination pairs. This approach might not
fare well for all kinds of network structures. Network
topology dramatically affects the performance of this
algorithm. (Furno et al., 2018) proposed a framework
to identify vulnerable nodes in large scale road net-
works. Road networks are modelled as graphs and big
data techniques were used to improve performance.
Betweenness centrality metric is used to evaluate the
critical nodes. Resilience metrics - Vulnerability, ef-
ficient information exchange were used to evaluate
their procedure. City scale networks were represented
as undirected graphs independent of contextual traf-
fic data. (Li et al., 2020) proposes a “Traffic Flow
Betweenness index”(TFBI) to identify critical links
in a network. The index is determined by shortest
travel path, traffic flow, and origin-destination de-
mand. Critical links determined using TFBI are se-
lected and masked from the network to assess their
impact. Compared to the traditional methods, their
approach is computationally less intensive. However,
their method does not consider non-linear effects due
to degradation of connectivity in a sub-network af-
fecting the rest of the network. (Herrera et al., 2016)
analyzed the resilience of water distribution networks
using graph concepts. Their approach involved calcu-
lating redundant paths between nodes and generating
flow graphs to analyze edge operating capacity and
maximum flow through the system. This approach is
suitable for analyzing networks with a threshold for
edge capacity and can scale for large networks.
(Bhatia et al., 2015) studied the Indian railway
network, finding out critical links using percolation
theory. They selected the giant component (largest
connected part of the network) from the network to
perform their analysis and established a metric ”crit-
ical functionality” which is the ratio of nodes in gi-
ant component to that in the original network. Later
they experimented by removing individual nodes and
routes and observing the overall connectivity of the
network. (Singh et al., 2015) developed a service built
using PostGIS and pgRouting, which helps calculate
alternate shortest paths in the event of a natural disas-
ter or any similar incident that compromises an edge.
(Henning et al., 2017) developed a method to
identify critical networks within small city networks
using the centrality indices of edges. They propose a
function that depends on the centrality indices, which
classifies each edge as critical or non-critical. This pa-
per serves as an essential basis for our solution as we
are interested in analyzing the relation between node
and edge importance in large-scale networks.
(Opsahl et al., 2010) published a study in which
they have conducted extensive work to generalize
centrality measures for weighted graphs networks and
find the shortest paths among such networks. (Pas-
sos and Cardoso, 2020) followed up on the previously
mentioned paper and suggested improvements to the
metrics. They suggested that using logarithmic ratios
to calculate variable node centrality would minimize
Identification of Critical Links within Complex Road Networks using Centrality Principles on Weighted Graphs
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