In my own words, Light Bulb Circuits

When current increases, brightness increases. Greater resistance (with more bulbs added in a series) reduces current flow, which reduces brightness equally. In a parallel circuit bulbs are always equally bright unless one branch has more bulbs, which means that branch has more resistance, which means the bulbs in that branch are not as bright as a single bulb in another branch would be. Am I correct? Do I have it?! ...if not, help, please...anyone :)