It can't be distilled to a simple graph, but it's impossible to ignore.
In a recent post, "Single Moms Can't be Scapegoated for the Crime Rate Anymore," Philip Cohen tries to correct what he sees as an injustice in the way the United States' crime rate is discussed. He writes that many pundits believed the crime wave of the late 1980s and early '90s was caused by an increasing number of single mother families. However, as he shows in his charts, crime rates began declining in the early 1990s, even while the percentage of single-parent families continued to rise. In his mind, that means that family breakdown cannot explain the crime wave and "single mothers deserve an apology" from said pundits.
But by ignoring a host of policy and cultural shifts during that time, Cohen fails to prove his conclusion. When crime was rising in the '80s and early '90s, legislators, police, and criminal justice experts naturally began to think about ways to counter it. They tried a number of approaches: increasing the number and presence of police on city streets and "broken windows" and "hot spot" policing (intensive and assertive police presence in specific areas where crimes have been committed.) In his recent book The City That Became Safe, criminologist Franklin Zimring, using the sort of careful regressions missing from Cohen's analysis, concludes that improved policing is the only plausible explanation for New York City's record drop in crime during these years. It's entirely possible that smart policing compensated for the initial causes of rising crime whatever they were, including massive family breakdown. It's also worth noting that Washington D.C., the city which is the subject of Cohen's analysis, has by far the largest per capita police force of any large city in the U.S. It also has one of the highest percentage of single-parent homes.
The other well-known, and highly controversial, change in crime fighting was mass incarceration. Criminologists don't agree about whether crowded prisons can account for the crime drop of the 1990s and early 2000s, or if they can, by how much. Zimring himself is a skeptic, but others have argued that it can explain about 25 percent of the decline. Regardless, there is no disagreement that the majority, and perhaps the large majority, of inmates grew up in fatherless homes. It's difficult to get up-to-date data since the Bureau of Justice doesn't reliably track the family background of inmates. (They also put intact and step families in the same "two parent" category, though at least one study has found the later to be predictive of juvenile incarceration.) The 1987 "Survey of Youth in Custody" found that 70% did not grow up with both parents. Another 1994 study of Wisconsin juveniles was even more stark: only 13% grew up with their married parents. Here's the conclusion of Cynthia Harper and Sara McLanahan, the doyenne of researchers about single parenthood: "[C]ontrolling for income and all other factors, youths in father-absent families (mother only, mother-stepfather, and relatives/other) still had significantly higher odds of incarceration than those from mother-father families."