How to measure the shortest route to the shopping center entrance?

Hi, everybody!

I have some feature classes in my geodatabase, including: 1 neighbourhood point \ each shopping center entrance points \ road network.


I am confused how to measure the shortest road distance from neighbourhood point to each shopping center in arcgis? (you know, maybe different entrances have different results, but I just want find the shortest one by road network.)

if I wanna use python, what should I write ?

regards