County Topology

This graph shows the topology of U.S. counties. Each node in the graph represents a county, positioned at the county centroid, while each link represents two neighboring counties sharing a border. (This graph is only approximate, as it is based on simplified geometry.)

<!DOCTYPE html>
<svg width="960" height="600"></svg>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/topojson.v2.min.js"></script>
<script>

var svg = d3.select("svg"),
    width = +svg.attr("width"),
    height = +svg.attr("height");

var path = d3.geoPath();

d3.json("https://d3js.org/us-10m.v1.json", function(error, us) {
  if (error) throw error;

var features = topojson.feature(us, us.objects.counties).features,
      neighbors = topojson.neighbors(us.objects.counties.geometries);

features.forEach(function(feature, i) {
    feature.centroid = path.centroid(feature);
    if (feature.centroid.some(isNaN)) feature.centroid = null; // off the map
    feature.neighbors = feature.centroid ? neighbors[i]
        .filter(function(j) { return j < i && features[j].centroid; })
        .map(function(j) { return features[j]; }) : [];
  });

svg.append("path")
      .attr("fill", "#ddd")
      .attr("d", path(topojson.feature(us, us.objects.nation)));

svg.append("path")
      .attr("fill", "none")
      .attr("stroke", "#fff")
      .attr("stroke-linejoin", "round")
      .attr("d", path(topojson.mesh(us, us.objects.counties, function(a, b) { return a !== b; })));

svg.append("path")
      .attr("fill", "none")
      .attr("stroke", "#000")
      .attr("stroke-linejoin", "round")
      .attr("d", d3.merge(features.map(edges))
          .map(function(edge) { return "M" + edge[0] + "L" + edge[1]; })
          .join(""));

function edges(feature) {
    return feature.neighbors.map(function(neighbor) {
      return [feature.centroid, neighbor.centroid];
    });
  }
});

</script>

https://d3js.org/d3.v4.min.js

https://d3js.org/topojson.v2.min.js