Using iGraph to build a Distribution Model

I would like to analyze the distribution of the Customers from a Shop, if the Shop is closed or terminated. Consider the following sample data-set;

| ShopID | MonthlyCVisitCount |   Lat     |     Lng    |
--------------------------------------------------------
|  A1    |      15000         |  39.84349 |  116.33986 |
|  A2    |      24560         |  39.84441 |  116.33995 |  
|  A3    |      14789         |  39.84615 |  116.34012 |
|  A4    |      35479         |  39.84891 |  116.34039 | 

I would like to build a distribution model using NetworkX or iGraph based on the distance (i.e., lat, lng) and determine how the distribution (MonthlyCVisitCount) would spread if I supposedly close the shop A1.

Is it possible to obtain the shortest path from A1 to A2, A3, A4 and based on some business rules, I can analyze the distribution.

Edit 1:

Consider the modified dataset;

| PrimaryShopID | ToShopID |  Dist |
------------------------------------
|     A1        |    A2    | 0.125 |
|     A1        |    A3    | 0.354 |
|     A1        |    A4    | 0.950 |

The dataset above has distance between ShopID A1 to multiple shops, now that I have distance calculated and based on this distance I provide weights, say;

0 to 200 – 50%

201 to 500 – 20%

501 & above – 0%

Meaning that 30% of Customers I have lost.

How do I proceed with this scenario, I am mostly comfortable in working with R, any example or a pointer to the same problem will be helpful