C H A P T E R F O U R Reconceptualizing Stage 1 Neighbor Networks LAYERS OF COMPLEX NETWORK STRUCTURES I have argued that there are at least four distinct stages of neighborly relations in which individuals may be involved. Each stage is embedded in or superposed on the previous stage. An individual’s stage 4 neighbor network is a subset of her stage 3 neighbor network, which is a subset of her stage 2 neighbor network, which is a subset of her stage 1 neighbor network. These individual neighbor networks evolve into neighborhood community networks through a process of concatenation. Residents have relations with their neighbors who interact with other neighbors, and so on. These neighborly relations concatenate and consolidate neighbor to neighbor to neighbor. The idea of concatenation gets at an important point: It emphasizes the fact that any network is a product of relation built upon relation built upon relation. How the relations fit together matters. There are several important corollaries of this fact. First, the resultant network is as far-reaching as its most extensive ramification. Relations concatenate to form a network typically larger, both in the number of interpersonal relations and in the size of the area it extends to, than any individual’s relations. Thus, relatively micro-level relations result in a macro-level structure. Second, the resultant network is as fragile as its weakest link. Anything that can cause a relation not to form, no matter how trivial, delimits the network. In contrast to the first corollary, micro-level fragilities can inhibit a macro-level structure. Third, the characteristics of the resultant network are not readily predictable from the characteristics of the local networks that concatenate to form it. Only as sets of individual networks concatenate do the characteristics of this aggregated network emerge. 37 CHAPTER FOURE FIGURE 4.1. Stage 4 neighbor network A hypothetical stage 4 neighbor network. Dots represent households. A line connects two dots if the represented households influence each other, if they share norms and values and are developing working trust. Therefore, the four distinct stages of neighborly relations concatenate into four distinct stages of neighborhood community networks: a network of concatenated geographic availability, a network of passive contacts, a network of actualized neighborly relations, and an influence network, with its inherent potential for social capital and collective efficacy. I now explore how they relate to each other. Networks of influence concatenate from stage 4 relations in which residents exchange norms and values and expectations and develop trust with their neighbors, whether or not they have developed an intimate, affective relationship. It is these stage 4 neighbor networks that potentially generate a sense of community, social capital, and collective efficacy. These stage 4 neighbor networks do not exist among all residents of a city. They are often quite delimited. Figure 4.1 shows a hypothetical 38 R E C O N C E P T UA L I Z I N G S TAG E 1 N E I G H B O R NETWORKS FIGURE 4.2. Stage 4 neighbor network induced within stage 3 neighbor network Dots represent households. A line connects two dots if the represented households have initiated contact. The stage 4 neighbor network is an edge-induced, rather than node-induced, subgraph of stage 3 neighbor network. stage 4 neighborhood community network among a tiny neighborhood of 20 households. In this illustration, the dots represent households, and a line connecting them indicates that they influence each other, that they have shared norms and values and are developing working trust. Three distinct influence clusters are apparent. The source of the constraint illustrated in figure 4.1 is the delimited stage 3 neighbor networks, which form the necessary substrate for the stage 3 neighbor networks. Stage 4 neighbor networks cannot extend anywhere stage 3 neighbor networks have not already extended. Figure 4.2 shows a hypothetical stage 3 neighbor network that might have led to the stage 4 neighbor network in figure 4.1. Stage 3 actualized neighbor interaction networks themselves emerge from the substrate of concatenated stage 2 passive contacts and thus stage 2 neighbor networks delimit stage 3 networks of actualized neigh39 CHAPTER FOURE FIGURE 4.3. Stage 3 neighbor network induced within stage 2 neighbor network Dots represent households. A line connects two dots if the represented households are functionally available to each other, if they unintentionally encounter each other and thus share passive contacts. The stage 3 neighbor network is an edge-induced, rather than node-induced, subgraph of Stage 2 neighbor network. borly relations. While individuals’ choices, their failures or refusals to actualize potential neighbors, may make actual neighbor networks smaller than potential neighbor networks, they can be no larger. Figure 4.3 shows a hypothetical stage 2 neighbor network that might have produced the hypothetical stage 3 neighbor network in figure 4.2. Finally, because a passive contact cannot exist unless residents are geographically available to each other, the network of passive contacts cannot transcend the network of geographic availability; it is logically impossible. While individuals’ lifestyles and habits may prevent them from having passive contacts with those who are geographically available to them, their behavior cannot cause them to have passive contacts with those who are unavailable. Figure 4.4 shows a hypothetical stage 40 R E C O N C E P T UA L I Z I N G S TAG E 1 N E I G H B O R NETWORKS FIGURE 4.4. Stage 2 neighbor network induced within stage 1 neighbor network Dots represent households. A line connects two dots if the represented households are geographically available to each other. The stage 2 neighbor network is an edge-induced, rather than node-induced, subgraph of Stage 1 neighbor network. 1 neighbor network that might lead to the hypothetical stage 2 neighbor network in figure 4.3. What is important to note in this stage 1 figure is that, while certainly not all stage 1 relations translate into stage 2, 3, and 4 relations, only existing stage 1 relations do. Stage 4, stage 3, and stage 2 neighborly relations cannot exist where stage 1 neighborly relations do not already exist. For example, it is impossible for stage 4, or stage 3, or stage 2 neighborly relations to exist between the community on the right and the community on the left because no stage 1 relations exist between them. To study efficacious neighborhood communities emerging from neighbor networks, therefore, we need a definition of a neighborhood community whose importance is derived from the potential for influ41 CHAPTER FOURE ence networks to emerge from within a community, from the potential for neighbor networks to concatenate within it, from the consolidation of stage 2 passive contacts it allows. A neighborhood equivalent that maps the maximal extent of the overlapping circles of passive contacts among residents likewise maps the maximal extent of potential neighbor networks and thus the maximal extent of actual neighbor networks, and thus ultimately maps the largest potentially efficacious neighborhood community. T-COMMUNITIES AND ISLANDS It is imperative, therefore, that we properly identify these stage 1 relations, this geographic availability foundational to the emergence of passive contacts, neighborly interactions, trust, and the realization of shared norms and values among neighbors. In chapter 3, I defined this geographic availability in terms of shared walking arenas that that mediate, guide, and constrain passive contacts, or unintentional encounters. To the extent that this is accurate, then the concatenated network of overlapping passive contacts can be no larger than the concatenated network of walking arenas; conversely, the network of potential neighborly relations, based on concatenated passive contacts, is a subset of the concatenation of these walking arenas. I have argued that tertiary face blocks effectively proxy walking arenas in urban areas. In this study, therefore, the maximal concatenation of contiguous tertiary face blocks, of walking arenas, represents the maximal consolidation of individual residents’ potential contact with each other. Use of this neighborhood equivalent signifies internal access. All residents within it have a potential for neighborly relations using walking arenas. While it is unlikely that all, or even any, residents would traverse the entirety of this neighborhood equivalent, its internal contiguity allows residents to interact with their neighbors down the street, who interact with other neighbors farther down the street, and so on throughout the network. 42 R E C O N C E P T UA L I Z I N G S TAG E 1 N E I G H B O R NETWORKS Such a neighborhood equivalent also signifies constraint. To the extent to which passive contacts depend upon walking arenas, the neighborhood so specified defines the limit to the concatenation of neighbor relations. Finally, because passive contacts are necessary for the development of higher-stage neighbor networks, the concatenated network of tertiary face blocks serves as an effective surrogate for networks of potential neighbors, for networks of actualized neighbors, and for influence networks from which emerge the neighborhood effects that researchers concern themselves with. How do I define the maximal concatenation of tertiary face blocks? Face blocks do not actually touch each other; they are separated by intersections. While the distinction between tertiary and nontertiary face blocks is determinative, the distinction between tertiary and nontertiary intersections is not entirely so.1 It may be the case that nontertiary intersections only inhibit, rather than entirely disrupt, the development of passive contacts. Therefore, I will define two types of neighborhood equivalents, one connecting tertiary face blocks using only tertiary intersections and the other connecting tertiary face blocks using all intersections. Definition. A t-community2 is a maximal contiguous network of tertiary face blocks and tertiary intersections. Figure 4.5 illustrates t-communities. In the figure, lines represent streets. Bold lines represent nontertiary streets, and nonbold lines represent tertiary streets. Thus, all crossings of nonbold and nonbold lines are tertiary intersections and all crossings of bold and nonbold lines are nontertiary intersections. Four distinct t-communities exist in the figure, labeled 1, 2, 3, and 4. They are easily identifiable by considering the maximal contiguous set of nonbold lines. Boundaries and internal access are not logical inverses of each other. While the bounded area A is coterminous with t-community 1, the bounded area B is coterminous with three distinct t-communities, 2, 3, and 4. This is quite common. It is tempting to combine t-communities 2, 3, and 4, which are bounded by the same set of nontertiary streets into a single neighborhood equivalent. In fact, this melding is exactly what many neighborhood equivalents would do, despite the impossibil43 CHAPTER FOURE FIGURE 4.5. T-communities ity of overlapping circles of tertiary street-based passive contacts connecting their residents. Clearly, however, no access is available among residents of t-communities 2, 3, and 4 via tertiary streets. If we were to relax the definition of the concatenated network of walking arenas that circumscribe the overlapping networks of passive contacts and thus the higher stages of potential neighborly relations, it would not be by including long stretches of nontertiary streets that act as boundaries. The next logical relaxation would be to allow for the possibility that neighborly relations might cross nontertiary intersections. Therefore, I define my second neighborhood equivalent by relaxing the above definition to include nontertiary intersections. Definition. An island3 is a maximal contiguous network of tertiary face blocks and any intersections. Consider again figure 4.5. In this figure, there are four t-communities but three islands. T-communities 1 and 2 form part of the same island because they are the maximal contiguous set of tertiary face blocks and any intersections. Islands highlight the fact that residents of t-communities 2, 3, and 4 do not have access to each other, even if we allow them to cross nontertiary intersections. It is highly unlikely that overlapping circles of passive contacts will connect their residents. If any t-communities were to be grouped by traditional analyses, they would almost 44 R E C O N C E P T UA L I Z I N G S TAG E 1 N E I G H B O R NETWORKS certainly be t-communities 2, 3, and 4. In contrast, I argue that it is far more likely that overlapping circles of passive contacts, if they connect any two t-communities, will connect t-communities 1 and 2. Since islands are maximal networks of tertiary face blocks and any intersections, while t-communities are maximal networks of tertiary face blocks and tertiary intersections, t-communities are necessarily subsets (although not necessarily proper subsets) of islands. While I expect t-communities to have more pronounced effects, islands will measure the potency of nontertiary intersections. I offer one further illustration to help readers understand islands and t-communities. Imagine if all of the nontertiary face blocks (but not nontertiary intersections) were removed from a city. In a few cities, a gridlike pattern of tertiary streets would remain. In most, however, multiple independent networks of tertiary streets would now exist, effectively isolated from each other.4 These are what I am terming islands. Households in one island would not be able to reach other, often nearby, households in another island. Figure 4.6 illustrates this point. It maps an area in Los Angeles. Lines represent only tertiary streets. Arrows indicate streets that continue beyond the edge of the map. In the center of the map is a large set of tertiary streets, indicated by bold lines, which, while connected to each other, do not connect to any of the tertiary streets extending from the various edges of the map. This set of tertiary streets forms an island. Note that the map is drawn to scale. The distances separating the tertiary streets forming the central island and the tertiary streets near the edges are in most cases quite substantial, often measured in hundreds of feet. This analysis may seem counterintuitive to some readers, who would imagine that the network of tertiary streets would ultimately connect all households within a city, although perhaps at a great distance. This very idea was at the heart of human ecologists’5 arguments that physical distance was a crude index for functional distance. In the latter half of the twentieth century, however, many street systems have been designed (or redesigned) to create disconnected networks of tertiary streets. Urban renewal has transplanted these patterns into much older cities as well.6 Consequently, in most cities, the tertiary street system is not continuous, even if it once was. 45 CHAPTER FOURE FIGURE 4.6. Tertiary street island Lines represent Tertiary Streets. Streets that comprise Island are in bold. Arrows represent Streets which continue beyond the edge of the figure. Note: Map is drawn to scale. Now, if one imagines overlaying these islands with the grid of nontertiary streets they would be dissected into t-communities. T-communities are defined both by their internal connection via tertiary streets (as islands are) and by being bounded by nontertiary streets. MAIN POINTS IN REVIEW In this chapter, I turned my focus to the networks formed by the concatenation of neighboring relations. Some (perhaps all, perhaps none) stage 3 neighbor networks translate into stage 4 neighbor networks. Some (perhaps all, perhaps none) stage 2 neighbor networks translate into stage 3 neighbor networks. Some (perhaps all, perhaps none) stage 46 R E C O N C E P T UA L I Z I N G S TAG E 1 N E I G H B O R NETWORKS 1 neighbor networks translate into stage 2 neighbor networks. No neighbor networks, however, develop where there were not already stage 1 networks in place. This is why an accurate definition of stage 1 neighboring relations is so important. Most sociological studies of neighborhoods use administrative geography that implicitly defines two households as stage 1 neighbors if they are in the same administratively defined area. However, residents of these spatially defined analytic units may not be geographically available to each other. In contrast, I define two new neighborhood equivalents in terms of the concatenated network of walking arenas as represented by tertiary face blocks. These two neighborhood equivalents are distinguished by the intersections that connect face blocks within them. The first neighborhood equivalent, t-communities, includes only tertiary intersections, while the second, islands, includes all intersections. While I expect t-communities to have more pronounced effects on neighborhoods as social entities, I include islands to measure the potency of nontertiary intersections. Both of these new neighborhood equivalents are meant to focus on the potential for passive contacts, or unintentional encounters, between neighbors, and thus on the interactional aspect of neighborhoods. 47