title: Graph theory in public transportation
body: <p><img src="https://i.stack.imgur.com/qoz8g.png" alt="enter image description here"></p>
  
  <p>Hi,</p>
  
  <p>I am now developing public transportation guide software. In Europe an US Google Map provides this but in Turkey it does not.  I have database which contains all stations’ latitudes and longitudes, and other bus- line, station information. In my plan, firstly I will use graph theory (stations are vertexes; edge weights are distances among stations) and connect stations which are on the same bus-line; then find routes. After that I will demonstrate route on Google Map. I have accomplished the first step, connecting stations. However, after that I found a mistake in my plan which is shown in the figure. 
  Person wants to go near A to K, the program should say</p>
  
  <ol>
  <li>Walk to station A</li>
  <li>Got on bus 8 at station A</li>
  <li>Got off bus 8 at station E</li>
  <li>Walk to station H</li>
  <li>Got on bus 970 at station H</li>
  <li>Got off bus 970 at station K</li>
  </ol>
  
  <p>But, there is no connection between station E and H. So, graph algorithm cannot find a route from A to K. I should define a walk path between E and H. However this is only small demonstration of the city there are over 6500 station in the city. How can I solve this problem?
  I have an idea that add connections between stations with in 1km range; but I think that it is inefficient.
  Thanks.</p>