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Like @Anko suggested, you should use a graph as data structure for your game map. If you use the this implementation of a graph in Java as a starting point you can represent your map as follows:

Graph<Zone> gameMap = new Graph<>();

Zone zone1 = new Zone("Zone1");
Zone zone2 = new Zone("Zone2");
Zone zone3 = new Zone("Zone3");
Zone zone4 = new Zone("Zone4");
Zone zone5 = new Zone("Zone5");
Zone zone6 = new Zone("Zone6");
Zone zone7 = new Zone("Zone7");
Zone zone8 = new Zone("Zone8");
Zone zone9 = new Zone("Zone9");
Zone zone10 = new Zone("Zone10");

gameMap.addEdge(zone1, zone2);
gameMap.addEdge(zone2, zone3);
gameMap.addEdge(zone2, zone4);

If you want to check if you can attack zone2 from zone1 you can just do

// can attack zone2 from zone1
gameMap.hasEdge(zone1, zone2);

Here you can find the complete implementation of the above example.