"Gang activity really originated in this area because they [gang leaders] had the power to start it. But they also have the power to finish it and stop the negative cycle.
"It is real redemption when you can have people who were notorious for tearing down their community helping to build it up."
Following that meeting a committee of gang leaders now gathers weekly. Sometimes they argue, but they usually come back the following week, and the mayor hopes they will be able to travel to other trouble spots in the US to help diffuse violence.
Brown has a very personal motivation for wanting to turn Compton's gang violence around. In the Seventies, before she was born, her grandmother was murdered in a home invasion there. She saw the effect on her mother.
She is proud that what she has achieved so far was done not through heavy policing but conflict mitigation. The last several months had seen a reduction in violent activity of about 65 per cent, she said, and people jogging at night was a sign of her success.
Despite being on course for its safest year in decades, Compton still has its share, more than its share, of violence. Two weeks ago, Lontrell Lee Turner, 16, was gunned down as he was on his way home from church. There have been 26 homicides this year in a city of 100,000 people, resulting in a murder rate more than three times the overall average for Los Angeles.
But that is still a huge drop from the 100 murders a year during the city's most violent period 25 years ago. Last year, hundreds of guns were handed over when police offered to pay up to US$200 ($260) for each.
Armed with degrees in public policy and urban planning, Brown won last year's Compton election in a landslide. Her first budget was in surplus and debts are being paid off.
The residential property market has risen, up more than 10 per cent in the past year, as people have been priced out of other neighbourhoods. Properties are being snapped up by investors. Families are attracted to Compton's location. It is close to the airport, Long Beach port, the second busiest container port in the US, and near offices in the city.
Brown sees gangsta rap as a "snapshot of a decade period in this city's 126-year history." She added: "It was real because they rapped about the life they lived. But you really have to be proud of the process and the evolution."