Adjacency Matrix In Java

Question

I'm so confused by graphs and adjacency matrices. I'm doing an assignment for a class where I have a text file of nodes and a text file of edges and I have to read each of them and make them a graph onto which I can then perform operations such as determining if the graph is connected, finding a minimal spanning tree, traversals and finding paths. I've never worked with graphs before though, and I'm really confused by the whole thing, and I was wondering if someone could help explain some of this to me.

Firstly, do I build a graph on its own (with node and edges classes perhaps?) and then construct an adjacency matrix from that? Or is the adjacency matrix itself the graph?

And then I'm confused on how to implement the adjacent matrix into the program. The nodes are names things like "ND5" and "NR7" and so I would have to set and read the edges of [ND5][NR7] but I'm not sure how to set up a 2d array like that with strings for the outside and numbers on the inside.

I've been searching all over the internet and read through the whole chapter on graphs in my textbook, and I'm really not understanding just the first basic steps of getting this graph set up. I'd really appreciate the help. Thanks.

Answer 1

Firstly, do I build a graph on its own (with node and edges classes perhaps?) and then construct an adjacency matrix from that? Or is the adjacency matrix itself the graph?

There is no way anyone can answer that question for sure without actually reading the instructions for your assignment. However, unless the assignment specifically mentions Node and Edge classes or something, my guess is that you're just supposed to use the adjacency matrix to represent your graph.

And then I'm confused on how to implement the adjacent matrix into the program. The nodes are names things like "ND5" and "NR7" and so I would have to set and read the edges of [ND5][NR7] but I'm not sure how to set up a 2d array like that with strings for the outside and numbers on the inside.

I can totally understand your confusion here. What you actually want to do is create a bijection (a one-to-one relationship) between your node names and the indices of your matrix. For example, if you have n nodes in your graph, then you need an n×n matrix (i.e. new boolean[n][n]), and each of your nodes would correspond to a single integer in the range 0 until n (not inclusive of n).

I'm not sure what data structures you've covered in your class so far, but the easiest way to do this would probably be to use a Map<String, Integer>, which would let you look up a name like "ND5" and get back an integer (the index).

Another nice alternative might be to use an array. You could put all your node names into an array, sort it with Arrays.sort, and then once it's sorted you can use Arrays.binarySearch to find the index of a particular node name in that array. I think this solution is actually better than using a Map because it lets you do the lookups both ways. You use Arrays.binarySearch to do name-to-index lookups, and you just index into the array to do an index-to-name lookup.

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Example: Let's say we have this graph:

Given that graph, here's some sample code of how you could do this: (warning! it's untested)

import java.util.Arrays;

// Add all your node names to an array
String[] nameLookup = new String[4];
nameLookup[0] = "A";
nameLookup[1] = "B";
nameLookup[2] = "C";
nameLookup[3] = "D";

// Our array is already properly sorted,
// but yours might not be, so you should sort it.
// (if it's not sorted then binarySearch won't work)
Arrays.sort(nameLookup);

// I'm assuming your edges are unweighted, so I use boolean.
// If you have weighted edges you should use int or double.
// true => connected, false => not connected
// (entries in boolean arrays default to false)
boolean[][] matrix = new boolean[4];
for (int i=0; i<matrix.length; i++) matrix[i] = new boolean[4];

// I don't want to call Arrays.binarySearch every time I want an index,
// so I'm going to cache the indices here in some named variables.
int nodeA = Arrays.binarySearch(nameLookup, "A");
int nodeB = Arrays.binarySearch(nameLookup, "B");
int nodeC = Arrays.binarySearch(nameLookup, "C");
int nodeD = Arrays.binarySearch(nameLookup, "D");

// I'm assuming your edges are undirected.
// If the edges are directed then the entries needn't be semmetric.
// A is connected to B
matrix[nodeA][nodeB] = true;
matrix[nodeB][nodeA] = true;
// A is connected to D
matrix[nodeA][nodeD] = true;
matrix[nodeD][nodeA] = true;
// B is connected to D
matrix[nodeB][nodeD] = true;
matrix[nodeD][nodeB] = true;
// C is connected to D
matrix[nodeC][nodeD] = true;
matrix[nodeD][nodeC] = true;

// Check if node X is connected to node Y
int nodeX = Arrays.binarySearch(nameLookup, stringNameOfX);
int nodeY = Arrays.binarySearch(nameLookup, stringNameOfY);

if (matrix[nodeX][nodeY]) { /* They're connected */ }

// Print all of node Z's neighbors' names
int nodeZ = Arrays.binarySearch(nameLookup, stringNameOfZ);
for (int i=0; i<matrix.length; i++) {
  if (matrix[nodeZ][i]) {
    System.out.println(nameLookup[nodeZ] + " is connected to " + nameLookup[i]);
  }
}