Connecting each rigid body clone to adjacent other clones

I have this code which spawns a sphereprefab at each of the vertices of a mesh. Im trying to have each sphere connected to the adjacent ones with spring joints to simulate soft body physics.

Im not sure how to go about connecting each clone to the adjacent clones inside a script.

I was thinking about some sort of proximity system where each sphere detects other rigid bodies in X radius and connects itself to each of them in a script. But Im not sure how to do this/It doesnt seem like the most efficient way.

Thank you

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class gen : MonoBehaviour {
    public Mesh mesh;
    public GameObject SpherePrefab;
    private static int sphereCount = 0;
    private static GameObject SphereContainer;
    // Use this for initialization
    private void Start () {
        SphereContainer = new GameObject("Sphere container");
        Vector3[] verts = mesh.vertices;

        for(int i = 0;  i < verts.Length; i++)
            GameObject sphere = Instantiate(SpherePrefab, verts[i] + transform.position, Quaternion.identity) as GameObject ;
   = "Sphere " + sphereCount;
            sphere.transform.parent = SphereContainer.transform;


    // Update is called once per frame
    void Update () {