For the depth buffer


primarily:
glEnable(GL_DEPTH_TEST);


In addition, with turning on glut:
glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGBA | GLUT_DEPTH); //need this for lighting/fill


But generally when clearing the color buffer you want to:
 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);


Remember, items will be clipped by near and far planes set by your perspective.
Consider updating your reshape to:

  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();

  gluPerspective(45, graph.winwidth/graph.winheight, 1.0, 10); //10 is the far plane, 1 the near
  glViewport(0,0,w,h);

  glMatrixMode(GL_MODELVIEW);
  glLoadIdentity();
  gluLookat(eyex,eyey,eyez,atx,aty,atz,upx,upy,upz);

  graph.winheight = h;
  graph.winwidth = w;