In economic theory, graffiti cleanup, is analyzed as an externality, an abnormality to the efficient production of goods and services by the market. What does externality mean? Well, for most products the person who buys them, gets all the benefit. e.g. If I buy pizza, me, not the neighbors, get the benefit of enjoying pizza. And if the benefit of me eating pizza is more than the cost, bingo. The famous invisible hand operates and the right amount of pizza and goods are produced.
But with a good with externalities, such as cleaning graffiti, much of the benefits go to the neighbors, rather than solely to me. And the rational economist concludes that I will care just about my cost compared to my own benefit in cleaning graffiti, the market will not produce enough graffiti cleaning. That is because the benefits the neighbors get is external to my own choice if it is worth it to spend the time to try to get the graffiti.
And, even if the neighbors come to want a neighborhood with less graffiti, they are likely to act as free riders. They will come to count on me getting the graffiti cleaned, and being a free rider.