To generate a map like this without using a matrix, I recommend starting with a center tile and then populating the map outwards by using a modified breadth first search algorithm. First of all, we'll need something a little better than a list of adjacent tiles. You could simply have four variables, one for each direction that stores the next tile, as such:
private Tabellone up = null;
private Tabellone down = null;
private Tabellone left = null;
private Tabellone right = null;
Say we start with the center-most tile. All you have to do now is figure out how many of the directions are null, and create a new Tablellone object for each direction, making sure to set each of the variables in this current object and to set the appropriate opposite variable in the object created.
Tabellone adj = new Tabellone();
up = adj;
adj.setDown(this);
Once you've filled out all of the directions on this tile, you then choose one of the other tiles you've created and perform the same operation. This is where the breadth-first search algorithm comes in. You can use a queue to go through each tile you've created and fill out the directions. To make the algorithm stop, simply set a limit on the number of tiles you want to create and use a counter to keep track of how many have been created.
int count = 0;
ArrayList<Tabellone> queue = new ArrayList<Tabellone>()
queue.add(/*center tile*/);
while (count < 100) { //if we want 100 tiles
//take out the center tile from the beginning of the array list, create a tile for each direction and add those tiles to the array list, then increment count by 1.
}
Note: This algorithm as it stands will create a diamond shaped map, if you want a square, you'd need to have a variable for each diagonal direction as well.
Of course, if this seems a little more complicated than you'd like, I'd recommend a coordinate system.