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Generating Complete Graphs
license: gpl-3.0

Click the label to generate the next complete graph.

Complete graphs are a family of simple graph that have n vertices and an edge set containing all possible links (C(n, 2)). For n >= 1, the complete graph on n vertices is denoted Kn.

The code that generates the graphs could be improved. I was lazy and generated the edge set with the Cartesian product (resulting in a lot of useless parallel edges). If only JavaScript had something like Python's itertools...

The D3 code running this example is based on Mike Bostock's "Modifying a Force Layout II". I had no idea how to "update" a force graph, so this example was a lifesaver.

<!DOCTYPE html>
<svg width="960" height="500"></svg>
<script src="https://d3js.org/d3.v4.min.js"></script>
<script>
// GRAPH GENERATION
var graph = {};
// Generates a complete graph kn
function generateCompleteGraph(n) {
// Number of vertices = n
graph.vCount = n;
// Number of edges (from Handshake Lemma)
graph.eCount = (1/2) * n * (n - 1);
// Generate vertices
graph.nodes = [];
for (var i = 0; i < n; i++) {
graph.nodes.push({"id": i})
}
// Generate edges
graph.links = [];
// Using Cartesian Product due to laziness
// it works, but generates a lot of useless "parallel edges".
// A better solution would be to generate C(n, 2) combinations.
for (var u = 0; u < n; u++) {
for (var v = 0; v < n; v++) {
if (u != v) {
graph.links.push({"target": u, "source": v})
}
}
}
}
// Start with kn = 1
generateCompleteGraph(1);
// VIEW
// Based on Bostock's "Modifying a Force Layout II": https://bl.ocks.org/mbostock/0adcc447925ffae87975a3a81628a196
var svg = d3.select("svg"),
width = +svg.attr("width"),
height = +svg.attr("height"),
color = d3.scaleOrdinal(d3.schemeCategory10);
// Label
var text = svg.append("text")
.style("cursor", "pointer")
.attr("x", 50)
.attr("y", height-40)
.attr("font-family", "sans-serif")
.attr("font-size", "35px")
.text("Kn = " + graph.vCount)
var simulation = d3.forceSimulation(graph.nodes)
.force("charge", d3.forceManyBody().strength(-50))
.force("link", d3.forceLink(graph.links).distance(200))
.force("x", d3.forceX())
.force("y", d3.forceY())
//.alphaTarget(1)
.on("tick", ticked);
var g = svg.append("g").attr("transform", "translate(" + width / 2 + "," + height / 2 + ")"),
link = g.append("g").attr("stroke", "#000").attr("stroke-width", 1.5).selectAll(".link"),
node = g.append("g").attr("stroke", "#fff").attr("stroke-width", 1.5).selectAll(".node");
restart();
function restart() {
// Update text label
d3.select("text").text("Kn = " + graph.vCount);
// Apply the general update pattern to the nodes.
node = node.data(graph.nodes, function(d) { return d.id;});
node.exit().transition()
.attr("r", 0)
.remove();
node = node.enter().append("circle")
.attr("fill", function(d) { return color(d.id); })
.call(function(node) { node.transition().attr("r", 8); })
.merge(node);
// Apply the general update pattern to the links.
link = link.data(graph.links, function(d) { return d.source.id + "-" + d.target.id; });
// Keep the exiting links connected to the moving remaining nodes.
link.exit().transition()
.attr("stroke-opacity", 0)
.attrTween("x1", function(d) { return function() { return d.source.x; }; })
.attrTween("x2", function(d) { return function() { return d.target.x; }; })
.attrTween("y1", function(d) { return function() { return d.source.y; }; })
.attrTween("y2", function(d) { return function() { return d.target.y; }; })
.remove();
link = link.enter().append("line")
.call(function(link) { link.transition().attr("stroke-opacity", 1); })
.merge(link);
// Make nodes draggable
d3.selectAll("circle")
.call(d3.drag()
.on("start", dragstarted)
.on("drag", dragged)
.on("end", dragended));
// Update and restart the simulation.
simulation.nodes(graph.nodes);
simulation.force("link").links(graph.links);
simulation.alpha(1).restart();
}
function ticked() {
node.attr("cx", function(d) { return d.x; })
.attr("cy", function(d) { return d.y; })
link.attr("x1", function(d) { return d.source.x; })
.attr("y1", function(d) { return d.source.y; })
.attr("x2", function(d) { return d.target.x; })
.attr("y2", function(d) { return d.target.y; });
}
function dragstarted(d) {
if (!d3.event.active) simulation.alphaTarget(0.3).restart();
d.fx = d.x;
d.fy = d.y;
}
function dragged(d) {
d.fx = d3.event.x;
d.fy = d3.event.y;
}
function dragended(d) {
if (!d3.event.active) simulation.alphaTarget(0);
d.fx = null;
d.fy = null;
}
// When text label is clicked, increment (kn -> k(n+1))
d3.select("text").on("click", incrementGraph);
function incrementGraph() {
// Generate new graph
generateCompleteGraph(graph.vCount+1);
// Update view
restart();
}
</script>
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