Basic drawing, Vertex and Edge.

drawing/Edge.pde

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+class Edge {
+  Vertex v1,v2;
+  Edge(Vertex _v1, Vertex _v2){
+    v1=_v1;v2=_v2;
+    v1.E.add(this);
+    v2.E.add(this);
+  }
+  void draw(){
+    strokeWeight(2);
+    stroke(0,0,255);
+    line(v1.x,v1.y,v2.x,v2.y);
+  }
+}

drawing/Graph.pde

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+class Graph{
+  ArrayList<Vertex> V=new ArrayList();
+  ArrayList<Edge> E=new ArrayList();
+  boolean ValidNewEdge(Vertex v1,Vertex v2){
+    if(v1==v2)return false;
+    for(Edge i:v1.E){
+      if((i.v1==v1)&&(i.v2==v2))return false;
+      if((i.v2==v1)&&(i.v1==v2))return false;
+    }
+    return true;
+  }
+}

drawing/Vertex.pde

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+class Vertex{
+  int x,y;
+  boolean mouseover=false;
+  ArrayList<Edge> E=new ArrayList();
+  Vertex(int _x,int _y){
+    x=_x;y=_y;
+  }
+  Vertex(int _x,int _y,boolean _mo){
+    x=_x;y=_y;mouseover=_mo;
+    if(_mo)vertex_under_mouse=this;
+  }
+  void draw(){
+    noStroke();
+    if(mouseover){
+      fill(0,255,0);
+    }else{
+      fill(255,0,0);
+    }
+    ellipse(x,y,Vertex_Rad*2,Vertex_Rad*2);
+  }
+  void checkmouseover(){
+    if(sqrt((mouseX-x)*(mouseX-x)+(mouseY-y)*(mouseY-y))<=Vertex_Rad*2){
+      mouseover=true;
+      vertex_under_mouse=this;
+    }else{
+      mouseover=false;
+    }
+  }
+}

drawing/drawing.pde

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+final int DRAW_NORMAL=1;
+final int DRAW_DRAG=2;
+final int Vertex_Rad=8;
+Vertex drag_start;
+Vertex vertex_under_mouse;
+void setup() {
+  size(640, 360);
+  noStroke();
+}
+Graph G=new Graph();
+int draw_state=DRAW_NORMAL;
+
+void draw() {
+  background(255);
+  //Draw everything else
+  //Draw Vertices
+  for(Vertex i:G.V){
+    i.draw();
+  }
+  //Draw Edges
+  strokeWeight(2);
+  for(Edge i:G.E){
+    i.draw();
+  }
+  if(draw_state==DRAW_DRAG){
+    strokeWeight(2);
+    stroke(0,0,255);
+    line(drag_start.x,drag_start.y,mouseX,mouseY);
+    //println("DRAW_DRAG:",drag_start.x,",",drag_start.y,",",mouseX,",",mouseY);
+    //Draw the dragged line;
+  }
+}
+void mouseMoved(){
+  vertex_under_mouse=null;
+  for(Vertex i:G.V){
+    i.checkmouseover();
+  }
+}
+void mouseDragged(){
+  mouseMoved();
+  if(draw_state!=DRAW_DRAG){//start dragging
+    drag_start=vertex_under_mouse;
+    draw_state=DRAW_DRAG;
+  }
+
+}
+void mousePressed(){
+  if(vertex_under_mouse==null){
+    G.V.add(new Vertex(mouseX, mouseY,true));
+  }
+}
+
+void mouseReleased(){
+  if(draw_state==DRAW_DRAG){
+    draw_state=DRAW_NORMAL;
+    if(vertex_under_mouse!=null){
+      if(G.ValidNewEdge(drag_start,vertex_under_mouse)){
+        G.E.add(new Edge(drag_start,vertex_under_mouse));
+        println("Valid");
+      }else{
+        println("Invalid");
+      }
+    }
+  }
+}

drawing/sketch.properties

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+mode.id=processing.mode.java.JavaMode
+mode=Java