Good data structure for storing graph-like map

Hi,

I'm creating a strategy-based kingdom expansion game, where you start with one city and try to expand as far as possible from there. All the cities fit on a hexagon-grid and are connected by the edges of the hexagons.

Here's a diagram to illustrate what I'm trying to achieve: 

Each city must be connected to another city by road, which means that all the cities are connected. At this point, I began to realize that this map is very similar to a graph, with the cities being nodes, and the roads being edges …