We did an analysis on this network using Cytoscape and a spreadsheet program.
Network diamater of Istanbul bus lines appears to be 107. That is, taking all trips made on bus lines (you are allowed to hop in and out of the bus as many times as you like to make a shortest trip possible), the farthest two nodes are 107 steps away.
There are 5509 nodes or bus stops in our network. And there are 12052 bus lines connecting these bus stops. The average shortest path in Istanbul is approximately 24 steps. Each bus stop has an average of 2.8 neighbors. When we look at the average clustering coefficient we find 0.08 which indicates as very sparse network.
The longest shortest path is 107 steps. As we said most of the trips are around 24 steps.
We used Cytoscape to visualize this network. In this visualization we painted the bus stops in Europe in shades of blue and for the ones in Asian side in shades of red. Please click on the image to see it bigger.
We can see that a graph visualization algorithm (this time forced directed algorithm of cytoscape) can separate the two continents.
We made two versions of this network one was showing all the routes between two nodes and the other was consolidating all these nodes into one but keeping the number of routes as an attribute of the link.
Here is an image from the consolidated network of bus stops.
This time the edge thickness indicates number of different routes passing from that link. The colors are similar to the previous image, blue is Europe, red is Asia. The size of the nodes shows the betweenness centralities of these nodes. Betweenness centrality gives us how frequently you would pass from that particular node for your trips in Istanbul. As can be seen a very few of them are very big in size but the rest is very small.
See below for a list of the top ten most visited bus stops in Istanbul:
Same analysis can be made for the edges (or links) as well. Which of the links most visited?
It is not a surprise to see that the most visited links would be the ones on bridges crossing Bogazici. Since these are directional links the links between Beyaz Evler (Kadıköy) and Kavacık Köprüsü (Beykoz) appears twice in both directions. You would expect that there will be high number of routes crossing these high betweenness centrality links. But no actually their route numbers are very low. The first two for example have 2 routes each. Is this a trend? Let’s look at the plot of number of routes vs. betweenness centrality of bus stop links.
As can be seen there is no correlation. We don’t have yet data about the number of service on these routes. By services we mean number of times busses operate on a route in a given work day. When we have that information we can check the number of capacity on these high betweenness centrality links.
We can create the municipality network from the locations of the bus stops.
Size of the nodes show the population of each municipality. Colors indicate the centrality of each node. We can see that Beykoz and Eyüp being the most central municipalities.
When we look into the total number of routes in and between municipalities the first think we notice is that the biggest number of routes are within each municipality. Üsküdar, Ümraniye, Kadıköy, Pendik and Fatih are the first five in order. Üsküdar having 2847 routes linking itself to itself and Fatih has 2131. The highest number of routes linking two municipalities is from Beşiktaş to Şişli with 144 followed by Şişli to Beşiktaş with 142 links. Just to Remind that these are the number of different routes between municipalities not the total number of services.
When we look at the most central municipality it appears to be Eyüp, followed by Beykoz. The chart above shows all the municipalities and their populations. Some of the very highly populated municipalities like Bağcılar are not central and on the other hand for example Beşiktaş has approximately same centrality with Üsküdar but has significantly less population.
When we also compare the betweenness of links between these municipalities we can see the following result.
As can be seen from the below chart there is no correlation between edge betweenness and number of routes (not services) passing from these edges.