duck

    if (Physics.Raycast(camera.ScreenPointToRay(Input.mousePosition), out hit))
    {

        MeshCollider meshCollider = hit.collider as MeshCollider;
        if (meshCollider == null || meshCollider.sharedMesh == null)
        {
                return;
        }

        Mesh mesh = meshCollider.sharedMesh;
        int[] triangles = mesh.triangles;

        int v0 = triangles[hit.triangleIndex * 3 + 0];
        int v1 = triangles[hit.triangleIndex * 3 + 1];
        int v2 = triangles[hit.triangleIndex * 3 + 2];

        List<int> newTriangles = new List<int>();

        for (int i = 0; i < triangles.Length/3; ++i)
        {
            c0 = triangles[i*3 + 0];
            c1 = triangles[i*3 + 1];
            c2 = triangles[i*3 + 2];

            int count = 0;
            if (c0 == v0 || c0 == v1 || c0 == v2) { count++; }
            if (c1 == v0 || c1 == v1 || c1 == v2) { count++; }
            if (c2 == v0 || c2 == v1 || c2 == v2) { count++; }

            if (count == 2)
            {
                // it's a neighbouring triangle!
            }
        }
    }