Combining System Dynamics, Social Networks, and Geographic
Information Systems
Peter S. Hovmand, Ph.D.
Assistant Professor
George Warren Brown School of Social Work
Washington University in St. Louis
Campus box 1196
One Brookings Drive
St. Louis, MO 63130, USA
Phone: 314 935 7968
Fax: 314 935 8511
phovmand@ wustl.edu
Ronald Pitner, Ph.D.
Assistant Professor
George Warren Brown School of Social Work
Washington University in St. Louis
Campus box 1196
One Brookings Drive
St. Louis, MO 63130, USA
Phone: 314 935 9636
Fax: 314 935 8511
rpitner@ wustl.edu
System dynamics has always held the potential to synthesize and advance
theories in social science. Increasingly, social scientists and policy makers are
recognizing the importance of complexity and turning to methods like geographic
information systems, social network analysis, agent based modeling, chaos
theory, and system dynamics. All of these approaches draw some underlying
modeling mathematical framework. The approach discussed here brings system
dynamics, social network analysis, and geographic information systems together
in a novel way to understand a specific problem that will have scientific relevance
to community psychologists, urban planners, social workers, geographers,
political scientists, and public administration. Moreover, showing how the
various mathematical frameworks connect within a concrete example will help
realize the potential of system dynamics to advance theories and interventions of
contemporary social problems.
Keywords: methodology, social networks, geographic information systems, urban
modeling
Perceptions of safety 2
1. Introduction
What is the relationship between environment and perceptions of safety? Previous
research has characterized unsafe and violence-prone areas as possessing social and physical
incivilities (Perkins et al. 1993). Social incivilities are signs in the neighborhood of public
drunkenness, noisy neighbors, prostitution, drug trafficking, gang-related activity, homelessness,
and loitering. Physical incivilities refer to visual indicators of disorder and can range from
vandalism, graffiti, and yard debris to unkempt, dilapidated, and abandoned houses and buildings
(Perkins et al. 1993). Research has shown that incivilities invoke perceptions of crime and
disorder among residents and potential offenders (Perkins, Meeks, and Taylor 1992; Taylor
1999; Taylor and Gottfredson 1986; Taylor, Gottfredson, and Brower 1984). In turn, residents
withdraw leaving spaces undefined. Undefined spaces are characterized by the fact that no one
feels that it is their responsibility to monitor or maintain them. As a consequence, potential
offenders commit crime and violent acts that add to existing incivilities, forming the causal
feedback loop depicted in Figure 1 where an increase in Physical and social incivilities leads to
increases in Perceptions of crime and disorder, leading to more Crime and violence that feed
back and increase Physical and social incivilities. The positive feedback loop depicted in Figure
1 has been popularized as the “broken window” theory. Although several studies discuss the
importance of understanding the physical environment in relation to crime, many do not directly
show how such changes lead to a stable reduction in neighborhood crime.
Establishing formal and informal social control over undefined spaces has been a critical
component of reducing crime, incivilities, and increasing perceptions of safety. However, our
“perceptions” of physical spaces do not necessarily correspond to maps of such spaces. Thus, we
argue that perceptions of spaces are mental representations with systematic biases that change
Perceptions of safety 3
dynamically with the social network and perceptions of crime. In order to develop a better
understanding of the dynamic relationship between environment and perceptions of safety, we
need to employ a combination of methods like system dynamics computer modeling, social
network analysis, and geographic information systems to represent and study the complex
interactions of multiple nonlinear feedback loops.
Figure 1. Feedback relationship between incivilities,
perception, and crime and violence
+
ee. and
Physical and violence
social incivilities J
\. Perceptions of crime
and disorder
Kubrin and Weitzer (2003) have called for new studies in social disorganization theory
that model spatial dynamics, including methods that develop dynamic models, attend to
reciprocal or feedback effects, and address context effects on individual level outcomes. This
paper addresses this call by developing and illustrating a method for modeling the spatial and
social structures underlying the dynamics of crime and violence and perceptions of safety.
Theoretically developing such models and then testing them empirically will up avenues of
research in social geography, geographic information sciences, community and environmental
psychology, environmental criminology, and system dynamics.
Perceptions of safety 4
2. Background and theoretical considerations
In 2000, approximately 22.0% of St. Louis city residents fell below the poverty line,
compared to 11.3% nationally (National Council of Churches 2002). In that same year, St. Louis
ranked third in the nation for violent crimes (Federal Bureau of Investigation 2001). It is
important to state that there is nothing inherently negative about residents that live in poor areas.
Rather, there is something about the physical design of these areas that contribute to a perception
of danger and disorder, which leads to increase criminal activity among youth. These design
features include communities that have large numbers of abandoned and dilapidated buildings,
debris in streets, graffiti, drug-related activity, loitering, and overall neighborhood
disorganization (Astor, Meyer, and Behre 1999; Pitner, Lloyd, and Bell under review; Reiss and
Roth 1993; Astor, Meyer, and Pitner 1999, 2001; Meyer and Astor 2002; Perkins et al. 1993;
Sampson and Lauritsen 1994; Taylor and Gottfredson 1986).
In contrast to theories organized around the demographic explanations for crime, social
disorganization theory emphasizes the effects of places (Kubrin and Weitzer 2003). Social
disorganization theory posits that “weak social networks decrease neighborhood's capacity to
control the behavior of people in public, and hence increase the likelihood of crime” (Kubrin and
Weitzer 2003, p. 374). Studies from environmental psychology, urban planning, social work,
education, public health, and environmental criminology suggest that physical cues serve as
markers for unsafe and violence prone areas (Brantingham and Brantingham 1981; Skogan 1976;
Eck and Weisburd 1995; Newman and Franck 1980; Perkins et al. 1990; Perkins, Meeks, and
Taylor 1992; Taylor 1994, 1997; White 1990; Taylor and Gottfredson 1986). Many of these
unsafe and violence-prone areas have similar characteristics that have been defined as social and
physical incivilities (Perkins et al. 1993).
Perceptions of safety 5
2.1. Undefined public spaces
Areas that have high levels of social and physical incivilities may be thought of as
undefined public spaces (Cisnemos 1995; Newman 1973, 1995; Newman and Franck 1980). The
term ‘undefined’ refers to areas where no one feels that it is their responsibility to monitor or
maintain. As a consequence to this lack of care, the level of incivilities in these areas increase,
which leads to heightened perceptions of lawlessness and crime. Politicians and police
departments often refer to this concept as the “broken window” theory, which posits that a
sequence of events typically take place in undefined public spaces:
Evidence of decay (accumulated trash, broken windows, deteriorating building exteriors) remains
in the neighborhood for a reasonably long period of time. People who live and work in the area
feel more vulnerable and begin to withdraw. They become less willing to intervene to maintain
public order or to address physical signs of deterioration. Sensing this... offenders become bolder
and intensify their harassment and vandalism. Residents become yet more fearful and withdraw
further from community involvement and upkeep. This atmosphere then attracts offenders from
outside the area, who sense that it has become a vulnerable and less risky site for crime (Wilson
and Kelling 1982, p. ?).
Several studies have documented the relation between undefined spaces and residents’
perceptions of danger (Day 1994; Goldstein 1994; Greenberg, Rohe, and Williams 1982;
Newman and Franck 1980; Perkins, Meeks, and Taylor 1992). More recent community-based
interventions focus on the dynamics of individuals participating in defining and defending their
public space (Donnelly and Kimble 1997).
2.2. Territoriality, defensible spaces, and social control
Proshansky, Ittelson, and Rivlin (1970) defined territoriality as “achieving and exerting
control over a particular segment of space” (p. 180). The notion of social control is central to
social disorganization theory, yet most studies have only looked at informal social controls, and
there is a need to include examination of formal controls such as enforcement of legal and
regulatory codes (Kubrin and Weitzer 2003). Formal social controls have direct effects on crime
Perceptions of safety 6
and disorder, as well as the potential to influence residents’ informal practices (Kubrin and
Weitzer 2003). The relationship between formal controls and their effects on neighborhoods
capacity to engage in informal control is inherently nonlinear. For example, both too little and
too much policing can weaken neighborhood capacity to exert informal control (Kubrin and
Weitzer 2003).
Informal social control can be achieved when residents construct real physical barriers
(e.g., fences or security bars), or when they create symbolic ones (e.g., flowers gardens, plants,
shrubs, and yard decorations) (Perkins et al. 1993). These territorial markers carry nonverbal
messages of ownership and care. Thus, they serve to deter crime by creating a sense of
community among residents, which makes them more vigilant of potential criminal activity in
their neighborhoods. Although research is mixed on whether defensible space actually leads to
less neighborhood crime, there is a general consensus that higher levels of defensible space are
associated with lower levels of fear and higher informal social control (Clarke 1995; Clarke and
Homel 1997).
Numerous U.S. federal government-funded studies have examined the association
between design of residential settings and criminal activity (Donnelly and Kimble 1997; Kohn,
Franck, and Fox 1975; Newman and Franck 1980; Taylor, Gottfredson, and Brower 1984).
These projects have, at best, yielded conflicting findings (Bursik and Grasmick 1993;
Rosenbaum 1988; Taylor and Gottfredson 1986). Indeed, the role that environmental design
plays in crime prevention is a complex one (see Taylor (2002) for a detail discussion of this
issue). And, although several studies discuss the importance of understanding the physical
environment in relation to crime, many do not directly show how such changes lead to a stable
reduction in neighborhood crime.
Perceptions of safety Z
2.3. Neighborhoods, blocks, and models of spatial environments
Many studies on the influence of spatial environments on residents’ perceptions of crime
have typically expected a correlation between crime and perceptions at the neighborhood level,
with boundaries of administrative units (e.g., census blocks or zip codes) as proxies for
neighborhood boundaries. A repeated concem about weak or conflicting neighborhood effects
has been the possible low correspondence between definitions of neighborhood boundaries
between researchers and residents (Coulton et al. 2001). For example, Coulton et al. found that
residents’ definitions of urban neighborhood boundaries differed from census block tracts and
from each other, even for residents living on the same street block. One strategy has been to use
residents’ definitions of neighborhood boundaries in the tradition of environmental psychology
and urban sociology (Lee 1970). A second strategy has been to work with smaller units of
analysis such as street blocks, sacrificing a correspondence with demographic data from
administrative units for more salient boundary definitions. A third approach has been to ignore
neighborhood and block effects in favor of physical distances between locations of crime events
and residents’ locations.
The problem that each of these strategies tries to resolve is how to reconcile physical
models of spatial environments with cognitive models of spatial environments. We frequently
regard space as defined by physical barriers such as buildings, streets, hallways, and entrances
that restrict motion along with visual and auditory stimuli (Stea 1970). Hence, there is a tendency
to think of cognitive models of spatial environments as cognitive maps with spatial relationships
similar to geographic maps with landmarks, travel routes, and preserved metric information
(Barkowsky 2002; Tversky 1993).
Perceptions of safety 8
However, our cognitive models of spatial environments are more like “cognitive
collages” and “spatial mental models”, depending on an individual’s familiarity with his or her
environment (Tversky 1993). When individuals do not know the details of their environment,
they are much more likely to draw on different forms of information that are unlikely to be
organized into single coherent maplike representation (Tversky 1993). Instead, individual’s
internal representations are more cognitive collages, i.e., “overlays of multimedia from different
points of view” (Tversky 1993, p. 15). In situations where environments are simple or well-
learned, people tend to develop more accurate intemal representations of spatial layouts or
spatial mental models.
Both cognitive collages and cognitive spatial models of spatial environments have been
found to be systematically biased by language and perspective (Majid et al. 2004; Tversky 1993).
Moreover, environments perceived by residents as dangerous and associated with fear are not
necessarily an accurate perception of actual crime (Matei, Ball-Rokeach, and Qiu 2001;
Rasmussen, Aber, and Bhana 2004). For example, individuals that are more strongly connected
to media and interpersonal communication networks are more likely to also be more fearful
(Majid et al. 2004). Hence, residents’ cognitive spatial models of their neighborhood
environments are likely to change with their perception of crime and coping strategies
(Rasmussen, Aber, and Bhana 2004), as they engage or withdraw from their neighborhood
environments, and move in and out of social networks.
2.4. Social networks
Few studies have incorporated both social networks and geographic networks in their
analysis, despite the potential advantages of doing so (Faust et al. 1999). Social network analysis
offers a theoretical framework of the structure of social phenomena that is linked with structural
Perceptions of safety 9
theories of action (Scott 2000). Measures of network relations provide a basis for studying
system structure and processes in terms of patterns of interferences (Streeter and Gillespie 1992).
It is arguably the complex interactions between fast and slow dynamics of a systems components
within networks that generates many of the dynamics of real-world networks (Reggiani,
Nijkamp, and Sabella 2001). Hence, the combination of systems theory and network theory
offers “a valid and powerful contribution to the research into analytical approaches oriented
toward modeling the complexity of space-time systems” (Reggiani, Nijkamp, and Sabella 2001,
p. 387).
2.5. System dynamics (SD)
System dynamics (Forrester 1999, 1971; Richardson and Pugh 1986) is a method for
studying the relationship between dynamic behavior and structure in terms of feedback loop
mechanisms that has been applied to a variety of physical and social system problems. System
dynamics has also been applied to urban problems (Alfeld 1995; Sancar and Allenstein 1989;
Mass 1974; Schroeder, Sweeney, and Alfeld 1975; Levine, Hovmand, and Lounsbury 1998;
Forrester 1969), with a call for more research on urban poverty and violence (Alfeld 1995).
A conceptual model of perceptions of safety is shown in Figure 2. This conceptual model
includes the main relationships discussed in the previous sections, and provides the general
functional form for a theory of perception of safety:
dP
— =£(E,S
" ,(E,S)
ds
— =f,(P
dt 2(P)
dT
— =f,(S
dt (8)
Perceptions of safety 10
Figure 2.
Perceptions off
safety
Events of 2
Violence and
crime B1
Social
structure
Territoriality
ii weet
Such conceptual models might be satisfactory for studying the plausibility of a general
theory, and could be operationalized by modeling the relationships between the macro variables.
For example, on could have a single scalar variable representing social structure and
operationalize the variable using any one of the many summary statistics for social networks.
Likewise, one might talk about average territoriality or average perception of safety over a group
of blocks. While this would allow one to test whether or not the feedback structure in Figure 2
could account for the dynamic behavior pattems, such a strategy would not allow one to test the
strong underlying assumptions behind the summary statistics. To do this, one will need to
disaggregate the major stock variables, and this entails combining geographic information
systems or spatial information, social networks, and system dynamics while preserving the
essential features of each.
It is worthwhile to note that each of these approaches has a different but complementary
way of representing some facet of complex relationships in a social environment (see Table 1).
Geographic information systems (GIS) are excellent for presenting and analyzing the spatial
relationships and identifying spatial patterns in attributes. Social networks analysis is an
Perceptions of safety 11
excellent way to represent social structure, and the strength of system dynamics is the explicit
modeling of causal feedback relationships to explain dynamic phenomena.
Table 1. Comparison of geographic information systems,
social network analysis, and system dynamics
Spatial Social Dynamics/temporal
relationships structure dimension
Geographic
information systems v ? ?
(GIS)
Social network
analysis ? v ?
(SNA)
System dynamics
(SD) ? ? v
‘¥’ =solid application of method, ‘?’ = difficult or questionable application of method
3. Method
Three different approaches have been considered for embedding spatial phenomena
within system dynamics models: as attributes at locations in space, as nodes in graph networks,
and as cells (Sancar and Allenstein 1989). The basic approach taken here is to model spatial
phenomena as attributes within geographic network models (Haggatt 1967), and define social
networks in terms of these graphs.
Geographic spaces are typically depicted as planar maps with attributes assigned to
points. Spatial patterns are identified by analyzing the relationship between attributes and their
spatial location. These relationships can be abstracted in the form of a graph where the nodes
represent areas and the edges represent adjacency relationships. For example, Figure 3a shows
the crossroads that define the blocks of a City of St. Louis neighborhood while Figure 3b shows
the corresponding graph. Each node in the graph corresponds to a block, and each edge
Perceptions of safety 12
corresponds to a pair of adjacent blocks. So, for example, block 4 corresponds to node 4. And
since blocks 3 and 5 are both adjacent to block 4, there are corresponding edges between nodes 3
and 4, as well as 4 and 5.
Figure 3. Correspondence between (a) a map of neighborhood blocks, and
(b) a graph of their spatial relationships
Spatial information about each block is treated as an attribute of a node, while
relationships between blocks (adjacency, distances, etc.) are described in the form of a square
matrix. For example, in a model with n blocks, information about crime or degree or
territoriality is represented as a vector of length n (or equivalently a 1-by-n matrix) where each
element corresponds to a block. In a similar fashion, information about relationships can be
represented as an n-by-n matrix where each element quantifies the relationship between two
blocks or nodes in the graph. So one might have a 40-by-40 matrix describing the adjacency of
one block to another with 1’s indicating that the blocks are adjacent and 0’s otherwise. In
general, one can consider several types of relationships simultaneously (e.g., geographically
Perceptions of safety 13
adjacent blocks, social relationships between blocks, effects of noise such as sirens and gunshots
on other blocks) by including multiple square matrices, one for each type of relationship.
By representing areas as nodes and relationships as edges, one can include both spatial
and social network variables within a common graph framework. Since graphs can be
represented as matrices, a system dynamics model relating spatial and social network dynamics
can be written as expressions involving various matrix operations. The extent that one can then
explore the form of a dynamic model involving spatial relationships and social networks is
therefore only limited by the ways that one can combine the various vectors and matrices. To do
this and illustrate the process, several basic formulations will be described and applied in a
simple model of perception of safety.
3.1. Networks as graphs
The neighborhood graph in Figure 3b is represented as an n-by-n matrix G where each
element e,,€G defines an attribute of the relationship between node i and j (e.g., distance
between blocks, strength of the social connections between the blocks, amount of interaction).
In some cases, the nature of the relationship is symmetric so e, , =e,,. For other types of graphs,
it will be useful to represent asymmetric relationships such as relative differences between two
entities, and e,, will not necessarily be the same as e,,. The main point to note is that there is
quite a bit of flexibility in what types of relationships can be represented in the form of a graph.
For a more detailed discussion on representing social relationships as graphs, see Wasserman and
Faust (1994).
Since these graphs will be dynamic and the value of the elements changing over time are
functions of other variables, it is necessary to draw a distinction between weak connections and
Perceptions of safety 14
non-existent connections. For example, if the edges in the graph are taken to represent the
strength of the relationship between neighboring blocks, then one will need to be able to
distinguish between the weak relationships and the relationship that can’t logically occur (e.g.,
because two blocks are not neighbors in the geographic sense). In this case, one might can adopt
the convention that a) >0 indicates a neighbor relationship, however weak, while Qj =0
indicates no possibility of a relationship.
3.2. Adjacency of two nodes
In order to calculate the effects between neighbors, it is frequently useful to have an
indicator matrix of a graph representing the existence of a connection. For example, if one wants
to represent the effects of sound transmitted to adjacent blocks, then one doesn’t necessarily
want to know how strong the relationship is, but just that there is a particular type of relationship
between two nodes. To do this, it’s useful to have an n-by-n indicator matrix of the graph G,
a,, GA (G) where:
lt ife, >0
=| us fe eG.
ai i" otherwise
3.3. Connectedness of two nodes
It is also useful to know whether or not two nodes are connected by a path. This can be
done with an n-by-n indicator matrix of the graph G , Gj €C(G), where entries are 1 if the
nodes are connected via a path, and 0 otherwise. The easiest way to calculate C(G) is to take
the inner or dot product of G , n—1 times. That is, for Gj €C(G):
otherwise
n- times
C, +h fC.) >0 here c’,, G-G-..G.
Perceptions of safety 15
3.4. Propagation of event information over a network
An event such as a crime or incivility happens at a particular location or in a specific area
represented by anode. A description of an event is therefore a vector E of length n. How event
information is passed throughout the neighborhood depends on the relationships between the
nodes as represented by G, and the nature and representation of information. The actual
information received about the event also has a spatial component. It is not just that one is aware
that a crime occurred, but that it occurred on a particular block. So the information received
about the event is another n-length vector O. To represent the propagation of event information,
we must then write an expression for O in terms of E. A simple model of event information
propagating over the social network G is a word-of-mouth mechanism where if one person
knows about the event (there was a robbery on a particular block), then everyone within that
social network knows about the event. Thus any two nodes that were connected would know the
same information. This can be written as an expression involving the connectedness indicator
matrix C(G) and transpose of E (denoted E'):
O =C(G)-E'.
3.5. Relative differences
Differences between various blocks play an important role in shaping expectations,
perceptions, and as drivers of behavior. If V is a n-length vector of node attributes, then the
relative differences between the nodes can be calculated as A, =1''V —(1'V)' where 1 is a n-
length vector containing only 1’s. However, A, represents the differences between all pairwise
combinations of nodes, whereas relative differences between two groups are usually constrained
by what can be observed between two nodes. An easy way to include the effects of such
Perceptions of safety 16
constraints is to take the entry-wise or Hadamard product (written as ) of the difference matrix
A, with either the adjacency or connectedness indicator matrix. For example, if perception of
safety is represented as a n-length vector, then the relative differences in perceptions of safety
between neighboring blocks can be expressed as:
(1"POS —(1'POS)')oA(G) .
It is generally easy to develop expressions that capture the explicit relationships between
spatial variables and social networks using graphs as the common topological representation.
The next section shows how these components can be combined in a system dynamics
simulation model of perception of safety.
4. Example
Figure 4 shows a system dynamics model of three state variables: perception of safety to
the social network structure of a neighborhood with n blocks, and territoriality. Perception of
safety is an n-length vector POS (Perception of safety in Figure 4), the social network structure
of the neighborhood is the n-by-n matrix S (Social network in Figure 4), and territoriality is an n-
length vector T (Territoriality in Figure 4). These variables are explicitly related through set of
differential equations that define 6 major feedback loops. They also specify a family of dynamic
hypotheses about the relationship between the causal feedback structure in Figure 4 and the
dynamic behavior patterns of perception of safety.
Perceptions of safety
17
Figure 4. Stock-and-flow representation of Perception of Safety (POS) Model
Time constant
change in POS
a
—_
Gap in
perceived
safety a
oS Perception
: of safety
aan sacenton of Minimum gap in
piraet : safety hss) perceived safety
irect
perception of -
crime rate
Adjancent
blocks in social
Network perception
of crime rate
network
ao
aa
J
Effect of perceived
gap in safety on
social network
= Bl
+
R1
1) ad Social
Path connected network
R2 blocks in social ,
network = + Change in
social network
Rate of i) he
crime and
violence Tenor Time constant
seme __| Merriorialty change in
Change in social network
territoriality
ey is
Time constant
change in
territoriality
4.1. Equations
Perceptions of safety do not change when perceptions match observations. So change in
perception of safety is considered a function of the difference between (a) current perceptions of
safety, and (b) observed events of crime and safety. Events can be observed directly (O ¢irec: ) OF
indirectly through social networks (0 ji40,,), and the total effect on perception of safety is the
sum of the two. The time that it takes to adjust perceptions of safety is represented by the time
constant TC , . The rate of change for perceptions of safety can then be is expressed as:
Perceptions of safety 18
APOS _ + dirt +0 reors) —POS
dt TC, ,
The social network changes as a function of the relative differences in perceptions of
safety between neighboring blocks. In this model, it is assumed that between two neighboring
blocks, the lowest relative perception of safety will determine the relationship. This can be
calculated by taking the minimum of the relative difference and its transpose. The time that it
takes to change the strength of ties in a social network is represented by the time constantTC,.
So the change in the neighborhood's social network is:
dS _Min(AA)°A(S) here A =1'POS-(1:POS)'.
at TC,
Change in territoriality is taken as a function of the difference between the total weakness
of the social ties with neighboring blocks and the current territoriality. The total weakness of the
social ties for a given block is essentially the reciprocal of the total strength of its social ties with
neighboring blocks, which can be expressed as($-1')*. The time that it takes for changes in
territoriality to respond to changes in the social network is represented by the time constant TC, .
Thus, changes in territoriality can be written as:
aT _1-8-1)7-T
dt TC, :
The rate of crime and violence on a block is an n-length vector E, which is taken to be
inversely related to the territoriality of that block. This can be expressed asE =1—T. The
directly observed events of crime and violence that happen on the block is simply O =E,
direct
while the indirectly observed events of crime and violence is a function of the connection matrix
and E, Oysyox =C(S):E.
Perceptions of safety 19
4.2. Simulation results
In this example, the model starts with all the blocks having the same perception of safety
but differing in the strengths of their network relationships. The results show how the
neighborhood social structure evolves over time in response to these initial conditions (see
Figure 5).
At the start of the simulation, all the blocks start out at the same level of perceived safety
(see Figure 6), but differences in the strength of neighborhood ties (Figure 7) lead to changes in
territoriality (Figure 8), which causes a corresponding increase in the rate of crime and violence
(Figure 9). Initially these differences are small, but they feed back into the perceptions of safety,
leading to more changes in the social network. The pattern continues until the ties have decayed
enough to isolate block 6 from the crime and violence of block 15, and stops when blocks 5 and
15 have little or no territoriality, high levels of crime and violence, low perceptions of safety, and
no social ties with other blocks in the neighborhood. Substantively, these results show us how
differences in social networks might lead to a pattern of declining territoriality, increasing crime
and violence, and decline in social structure.
5. Conclusion
More generally, the results also illustrate how explanations inspired by looking at the
correlation between spatial elements over time (Figure 5) can be verified or refuted by examining
the intervening variables (Figures 6 through 8). Moreover, one is able via the simulation to
conduct additional experiments to test explanations about the relationship between specific
aspects of behavior and the underlying feedback loops. This facilitates the development of more
rigorous and empirically verifiable hypotheses, better social theories of crime, violence, and
Perceptions of safety 20
perceptions of safety, and thus ultimately improves our chances of developing better and more
empirically based community interventions for crime and violence.
Figure 5. Changes in neighborhood social network, and crime and violence over time, where
dark edges represent stronger connections, and larger circles represent higher rates of crime and
violence. Dashed lines indicate weak relationships that could exist.
Perceptions of safety
Figure 6. Perception of safety for blocks 5, 6, and 15.
Perception of safety
2
-2
-10 15 40 65 90
Day
Perception of safety[b5] : Networks 5-1-8 baserun. —3——t—2—3-— 3-4
Perception of safety[b6] : Networks 5-1-8 baserun. ——2—2—2—2—2-—_
Perception of safety[b15] : Networks 5-1-8 baserun. ——3—3—3—3—_3—
Figure 7. Strength of neighborhood ties in social network between blocks 5, 6, and 15.
Social network
eee, |
-10 15 40 65 90
Social network{b5,b5] : Networks 5-1-8 baserun
Social network{b5,b6] : Networks 5-1-8 baserun
Social network{b5,b15] : Networks 5-1-8 beserun 3
Social network!b6,b5] : Networks 5-1-8 basenun #
Social network{b6,b6] : Networks 5-1-8 baserun
Social network{b6,b15] : Networks 5-1-8 beserun £ é
Social network{b15,b5] : Networks 5-1-8 beserun
Social network{b15,b6] : Networks 5-1-8 beserun s
Social network{b15,b15] : Networks 5-1-8 baserun
Perceptions of safety 22
Figure 8. Territoriality of blocks 5, 6, and 15.
Territoriality
ee ee ee
0.8
0
-10 15 40 65 90
Day
Temitoriality[b5] : Networks 5-1-8 baserun
Temitoriality[b6] : Networks 5-1-8 baserun
Temitoriality[b15] : Networks 5-1-8 bases ~—3—3—3— 33 3-3
Figure 9. Rate of crime and violence for blocks 5, 6, and 15.
Rate of crime and violence
0
-10 15 40 65 90
Day
Rate of crime and violence[b5] : Networks 5-1-8 baserun. —t>——2—2—3-—-
Rate of crime and violence[b6] : Networks 5-1-8 baserun. —-2—-2—2—2—
Rate of crime and violence[b15] : Networks 5-1-8 baserun. —-3—-3——3—3—
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