Finding All Connected Components of an Undirected Graph

Question

I have a list of objects (undirected edges) like below:

pairs = [

 pair:[\"a2\", \"a5\"],
 pair:[\"a3\", \"a6\"],
 pair:[\"a4\", \"a5\"],
 pair:[\"a7\", \"a         


        

Answer 1

You want to do Graph Traversal

In your specific example, you have no # of nodes, and it may even be difficult to traverse the graph so first we'll get a "graph"

// It will return an object like Vertices{node: EdgesTo{node,node}, node:...}
function toGraph(arr) {
    var graph = {}; // this will hold the node "IDs"
    for (var i = 0; i < arr.length; i++) {
        // "create node" if the it's not added in the graph yet
        graph[arr[i][0]] = graph[arr[i][0]] || {};
        graph[arr[i][1]] = graph[arr[i][1]] || {};
        // add bidirectional "edges" to the "vertices"
        // Yes, we set the value to null, but what's important is to add the key.
        graph[arr[i][0]][arr[i][1]] = null;
        graph[arr[i][1]][arr[i][0]] = null;
    }
    return graph;
}

Then it is very easy to traverse the graph using any method that you choose (DFS, BFS)

I will make an example using DFS:

// to be called after getting the result from toGraph(arr)
function getSubGraphs(graph) {
    var subGraphs = []; // array of connected vertices
    var visited = {};
    for (var i in graph) { // for every node...
        var subGraph = dfs(graph, i, visited); // ... we call dfs
        if (subGraph != null) // if vertex is not added yet in another graph
        subGraphs.push(subGraph);
    }
    return subGraphs;
}

// it will return an array of all connected nodes in a subgraph
function dfs(graph, node, visited) {
    if (visited[node]) return null; // node is already visited, get out of here.
    var subGraph = [];
    visited[node] = true;
    subGraph.push(node);
    for (var i in graph[node]) {
        var result = dfs(graph, i, visited);
        if (result == null) continue;
        subGraph = subGraph.concat(result);
    }
    return subGraph;
}

And you would end up calling it like getSubGraphs(toGraph(myArray)); and do whatever you need with that.

Fiddle Here