WASHINGTON  — It’s still possible in Boston for a mail carrier, an accountant, and a Harvard-trained psychiatrist — basically, the crowd from Cheers — to live as neighbors.

That finding by the real estate brokerage Redfin makes the capital of Massachusetts a rarity at a time when neighborhoods in most U.S. cities are increasingly isolated from each other by income and home values.

Redfin analyzed home sales over the past 24 months in 20 major U.S. cities, breaking down the data by neighborhood. Many of the cities reflect home values that have outpaced wages over the past 15 years and contributed to a widening wealth gap among neighborhoods that mirrors a national trend.

San Francisco, for example, enjoys the benefits of tech fortunes, but its homes are largely unaffordable for the police officers, firefighters, and teachers. And while housing in Baltimore seems affordable, low and unstable incomes there have depressed home-ownership rates. Ribbons of highways have ferried the middle class out of cities such as Detroit, leaving behind concentrations of poverty.

Redfin said its analysis is a first step in examining changes over time in neighborhoods and in economic mobility.

“Our argument is the shape of the American city is the shape of American life,” said Glenn Kelman, chief executive officer of Redfin. “When the only time you meet someone wealthy is when you’re handing them a croissant, the likelihood that your kids are going to attend a good school and know how to pursue a career go down.”

To assess affordability, Redfin compared sales prices to median incomes. Other cities with above-average levels of economic diversity include Denver, Seattle, and Washington, which have benefited from an influx of educated workers and technology companies.

But high-tech can widen the wealth gap. Almost all of San Francisco — the hub for the most prominent software and computer firms — consists of homes worth more than what a middle-income family can afford. While other cities, such as Baltimore and Philadelphia, contain small clusters of wealthy neighborhoods along with large swaths of relatively low-priced homes, many residents lack the stable income and savings to buy.

In some cases, the data suggest that better-off residents work in a city but live in the suburbs, so that only a small share of the city itself is economically diverse. A mix of high-end and affordable housing exists, for example, in less than 10 percent of San Antonio, Memphis, Jacksonville, Detroit, Indianapolis, and Columbus.

Home values began to climb faster than incomes in late 1999. Housing prices used to hew closely to gains in average hourly earnings. But a gap developed between the two during the housing boom, narrowed slightly during the Great Recession, then widened again once the economy began to recover about six years ago.

The separation of neighborhoods by income has prevented children from progressing economically, according to research published last year by economists at Harvard University and the University of California, Berkeley. Boston ranked fourth in upward mobility. Jacksonville, Detroit, Indianapolis, and Columbus each ranked toward the bottom.

First Published November 22, 2015, 5:00 a.m.