Research into word meaning and similarity structure typically focus on highly related entities like CATS and MICE. However,most items in the world are only weakly related. Does our representation of the world encode any information about these weak relationships? Using a three-alternative forced-choice similarity task, we investigate to what extent people agree on the relationships underlying words that are only weakly related. These experiments show systematic preferences about which items are perceived as most similar. A similarity measure based on semantic network graphs gives a good account for human ratings of weak similarity.