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In this article, I build on Grannis' (1998) analysis and examine the entire metropolitan regions of the three most populous U.S. Primary Metropolitan Statistical Areas (PMSAs). I find that t-communities, communities defined by their internal access via pedestrian streets, powerfully account for the racial patterning of households in all three metropolitan areas. Racial variation occurs between t-communities not within them, even when both distances between block groups or, in the case of households with children, racial variation between elementary schools is accounted for. While Grannis (1998) examined how similar t-communities connected by pedestrian streets were to each other, this study examines how internally homogeneous t-communities themselves are. Further, this study's analysis of households with children finds that they have settled in such a way as to assure a racially homogeneous t-community more than a racially homogeneous school. By analyzing the entire metropolitan areas of PMSAs in different regions, this study also discovered very large t-communities, hundreds of times larger than a typical t-community, in which pedestrian streets no longer have an important influence.Using the pedestrian street network, Grannis (1998) defined "t-communities" 1 as areas that are both connected internally by pedestrian streets and circumscribed by nonpedestrian streets, and then demonstrated that pedestrian street networks are one of the primary tools racial populations use to organize themselves in the urban cores of Los Angeles and San Francisco. While innovative and informative, Grannis' (1998) analysis was incomplete in several ways.First, Grannis (1998) did not actually examine if t-communities were racially homogeneous. Grannis (1998) examined connected components of t-communities, what Grannis (2001) has elsewhere termed "islands," but not t-communities themselves. While Grannis (1998) showed that t-communities connected by pedestrian-oriented streets were similar to each other, it did not show that t-communities themselves were internally homogeneous. Second, while Grannis (1998) attempted to account for the effects of spatial proximity, it did not account for the importance of schools in the relocation decisions of households with children. Parents may choose to live in a neighborhood because of the public school they gain access

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In a groundbreaking article, Moody and White (2003) introduced the concept of structural cohesion, simultaneously characterizing emergent communities and their internally embedded layers by the number of node-independent paths interconnecting individuals. Like many studies, however, they "corrected" the directionality discovered in some of their data. While often done for important purposes, doing so potentially confounds structural cohesion with unrelated concepts. Some relations, especially those relating to the dynamic aspects of social life, are inherently directed, in whole or in part, and it may prove worthwhile to respect this directionality. In this article, I recast structural cohesion in terms of directed social relations and identify four distinct ways of measuring it. In two example data sets-hiring relations among graduate programs and trust relations among neighborhood residents-I show that only strong embeddedness, a type of structural cohesion emerging from directed relations, proves to be a powerful, robust, independent explanatory factor. I further show that if the directionality in the data in these examples had been "corrected," the importance of structural cohesion would have been dramatically undervalued.