Geoscience Reference
In-Depth Information
The physical network described above is transferred to graph in the most typical
way, stations to nodes/vertices and links to edges. As Barth
lemy [ 36 ] have shown,
there are many ways of representing public transport system as a network. For the aim
of this paper we have chosen the space-of-stops or so called L-space representation.
Each station is represented in graph by a node and an arc (oriented edge) between two
nodes indicates that these are consecutive stations of at least one route [ 24 ].
As the result from previous, neighbors are only those stations that can be reached
within single-station trip. As mentioned before, the graph we constructed is directed
and thus it better re
é
ects real conditions of selected public transportation network.
As weights we used the volume of public traf
fl
c between stations for given time.
As expected, there are two modes in the network corresponding with rush hours.
The
first mode, second and third interval sample, is the sharper one, as during
rst
interval there is only small amount of traf
c. Second mode can be detected between
12 and 18 h. The volume of traf
c is then slowly declining when approaching
midnight. Both nodes are visible on all statistics, but mostly on the
fl
ow.
Rides per arc summarize
fl
flow intensities in subsequent samples. Minimum of
11.1 rides is found in the
rst (+60 %)
and third sample (+168 %). First peak is reached over the morning commuting
times over 6
first sample. Network grows fast between
9 AM period when we observe 47.6 rides per arc. High level of
mobility is then preserved with slightly falling trend until afternoon (
-
2 %).
After 3 PM the network rises once again (+10 %) and reaches 24 h culmination at
49.4 rides per arc. Last sample is at the level 30.6 rides to which and beyond the
network dies relative slowly (
4 and
64 %) in compare to morning rises. Urban
heartbeat is regular but not symmetric. Visual representation in graph series in the
Fig. 2 supports this observation.
Second panel in the Table 1 summarizes few basic statistics for communities
identi
14,
28,
ed on described network [ 37 ]. If we compare statistics with previous we can
conclude, that with rising amount of traf
c, the network is more concentrated. It is
also visible from smaller amount of bigger communities in the rush hours. High
modularity levels in all samples suggest that the network under observation is
composed of surprisingly well de
ned structural elements. The individual parts of
topology are connected rather inside than between. Links between these play the
role of bridges. Only about 9 % of rides over 24 h cycle establish these bridges.
We further pay attention to the number of nodes per community as one of
possible evaluation criteria. Naturally, nodes have varying position in the network
captured by different centrality measures, including the basic degree distribution.
But still we may see from the Fig. 3 that we consistently observe about one large
community having above 100 departure points. Average number of nodes per
community varies between minimum of 24 in the
first sample and maximum of 40
in the evening peak sample. The average lies at 35 nodes, which describes a
standard network community in Bratislava daily cycle. Larger composition units
appear during morning peak 6
-
9 AM and afternoon/evening 12 AM
-
9 PM.
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