score:1

Modify how the links are drawn to include the width and height of the rects:

// Transition links to their new position.
link.transition()
  .duration(duration)
  .attr("d", function(d){
    var s = {
      x: d.source.x + 50,
      y: d.source.y + 100
    }, t = {
      x: d.target.x + 50,
      y: d.target.y
    }
    return diagonal({source: s, target: t});        
  });

Running code:

<!DOCTYPE html>
<html lang="en">
  <head>
    <meta charset="utf-8">
    <title>Tree Example</title>
    <style>
    .node {
      cursor: pointer;
    }
    .node circle {
      fill: #fff;
      stroke: steelblue;
      stroke-width: 3px;
    }
    .node text {
      font: 12px sans-serif;
    }
    .link {
      fill: none;
      stroke: #ccc;
      stroke-width: 2px;
    }
    </style>
  </head>

  <body>

<!-- load the d3.js library -->
<script src="http://d3js.org/d3.v3.min.js"></script>

<script>
var treeData = [
  {
    "name": "Top Level",
    "parent": "null",
    "children": [
      {
        "name": "Level 2: A",
        "parent": "Top Level",
        "children": [
          {
            "name": "Son of A",
            "parent": "Level 2: A"
          },
          {
            "name": "Daughter of A",
            "parent": "Level 2: A"
          }
        ]
      },
      {
        "name": "Level 2: B",
        "parent": "Top Level"
      }
    ]
  }
];
// ************** Generate the tree diagram  *****************
var margin = {top: 20, right: 120, bottom: 20, left: 120},
    width = 960 - margin.right - margin.left,
    height = 500 - margin.top - margin.bottom;

var i = 0,
    duration = 750,
    root;
var tree = d3.layout.tree()
    .size([height, width]);
var diagonal = d3.svg.diagonal()
    .projection(function(d) { return [d.y, d.x]; });
var svg = d3.select("body").append("svg")
    .attr("width", width + margin.right + margin.left)
    .attr("height", height + margin.top + margin.bottom)
  .append("g")
    .attr("transform", "translate(" + margin.left + "," + margin.top + ")");
root = treeData[0];
root.x0 = height / 2;
root.y0 = 0;

update(root);
d3.select(self.frameElement).style("height", "500px");
function update(source) {
  // Compute the new tree layout.
  var nodes = tree.nodes(root).reverse(),
      links = tree.links(nodes);
  // Normalize for fixed-depth.
  nodes.forEach(function(d) { d.y = d.depth * 180; });
  // Update the nodes…
  var node = svg.selectAll("g.node")
      .data(nodes, function(d) { return d.id || (d.id = ++i); });
  // Enter any new nodes at the parent's previous position.
  var nodeEnter = node.enter().append("g")
      .attr("class", "node")
      .attr("transform", function(d) { return "translate(" + source.y0 + "," + source.x0 + ")"; })
      .on("click", click);
  //nodeEnter.append("circle")
  nodeEnter.append("rect")
      //.attr("r", 1e-6)

  //.attr("rx",0)
    //.attr("ry",0)
    //.attr("x",100)
    //.attr("y",100)

    .attr("width",100)
    .attr("height",100)
    .attr("stroke","black")
    .attr("fill","white")


      .style("fill", function(d) { return d._children ? "lightsteelblue" : "#fff"; });
  nodeEnter.append("text")
      .attr("x", function(d) { return d.children || d._children ? -13 : 13; })
      .attr("dy", ".35em")
      .attr("text-anchor", function(d) { return d.children || d._children ? "end" : "start"; })
      .text(function(d) { return d.name; })
      .style("fill-opacity", 1e-6);
  // Transition nodes to their new position.
  var nodeUpdate = node.transition()
      .duration(duration)
      .attr("transform", function(d) { return "translate(" + d.y + "," + d.x + ")"; });
  nodeUpdate.select("circle")
  //nodeUpdate.select("rect")
      .attr("r", 10)
      .style("fill", function(d) { return d._children ? "lightsteelblue" : "#fff"; });
  nodeUpdate.select("text")
      .style("fill-opacity", 1);
  // Transition exiting nodes to the parent's new position.
  var nodeExit = node.exit().transition()
      .duration(duration)
      .attr("transform", function(d) { return "translate(" + source.y + "," + source.x + ")"; })
      .remove();
  nodeExit.select("circle")
  //nodeExit.select("rect")
      .attr("r", 1e-6);
  nodeExit.select("text")
      .style("fill-opacity", 1e-6);
  // Update the links…
  var link = svg.selectAll("path.link")
      .data(links, function(d) { return d.target.id; });
  // Enter any new links at the parent's previous position.
  link.enter().insert("path", "g")
      .attr("class", "link")
      .attr("d", function(d) {
        var o = {x: source.x0, y: source.y0};
      //var o = {x: (source.x0 + 100), y: (source.y0 + 100)};
        return diagonal({source: o, target: o});
      });
  // Transition links to their new position.
  link.transition()
      .duration(duration)
      .attr("d", function(d){
        var s = {
          x: d.source.x + 50,
          y: d.source.y + 100
        }, t = {
          x: d.target.x + 50,
          y: d.target.y
        }
        return diagonal({source: s, target: t});
        
      });
  // Transition exiting nodes to the parent's new position.
  link.exit().transition()
      .duration(duration)
      .attr("d", function(d) {
        var o = {x: source.x, y: source.y};
        return diagonal({source: o, target: o});
      })
      .remove();
  // Stash the old positions for transition.
  nodes.forEach(function(d) {
    d.x0 = d.x;
    d.y0 = d.y;
  });
}
// Toggle children on click.
function click(d) {
  if (d.children) {
    d._children = d.children;
    d.children = null;
  } else {
    d.children = d._children;
    d._children = null;
  }
  update(d);
}
</script>

  </body>
</html>


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