Apparently, female murderers are more likely to kill men than male murderers. The ratio is 3:1 for men, and 4:1 for women.
A majority, but not an overwhelming majority, of violent crimes are committed by someone the victim already knows. The main exception is robbery (75% strangers).
For all crimes, men are more likely to be victimized by strangers than women. Eg., strangers commit 44% of total assaults, but only 33% of assaults on women.