def paintEvent(self, event):
        paint = QtGui.QPainter()
        paint.begin(self.ui.frame_graphic) #Если просто self, то рисуется за фреймом. а если оставить так то получаю QPainter::drawPoints: Painter not active
        paint.setPen(QtCore.Qt.red)
        size = self.size()
        for i in range(1000):
            x = random.randint(1, size.width()-1)
            y = random.randint(1, size.height()-1)
            paint.drawPoint(x, y)
        paint.end()

import sys, random, math
from PyQt4 import QtGui, QtCore
from graph import *
class GraphWindow(QtGui.QMainWindow):
    def __init__(self, parent=None):
        QtGui.QWidget.__init__(self, parent)
        self.ui = Ui_MainWindow()
        self.ui.setupUi(self)
    
    def paintEvent(self, paint):
        paint = QtGui.QPainter(self)
        paint.begin(self)
        paint.setPen(QtCore.Qt.red)
        size = self.size()
        for i in range(1000):
            x = random.randint(1, size.width()-1)
            y = random.randint(1, size.height()-1)
            paint.drawPoint(x, y)
        paint.end()
if __name__ == '__main__':
    app = QtGui.QApplication(sys.argv)
    main = GraphWindow()
    main.show()
    sys.exit(app.exec_())