Tactical Social Network Analysis: Using Affiliation Networks to Aid Serial Homicide Investigation

Abstract

Integrating crime pattern theory with tenets of social network theory, we argue that linking people who frequent the same places reveals intersecting behavioral patterns illustrative of case connectivity. Using the Green River serial murder investigation as a case study, we demonstrate that structural statistics may be useful in focusing investigative efforts. Significant shifts in the centrality of suspects emerge when we track the evolution of this case at 6-month increments, suggesting that the initial working case hypothesis misled investigators. Continued exploration into the utility of social network analysis (SNA) for tactical purposes will help advance applied criminology.

Keywords

social network analysis betweenness centrality crime pattern theory serial murder criminal investigations affiliation networks

Overview

The cases you dread the most are homicides in outdoor settings where there are no witnesses, little physical evidence, and no indication of a relationship between the killer and the victim. They are stranger-to-stranger crimes. . . . I was dealing with a case that would be much bigger, more complicated, and far more demanding than any I have seen before (p. 28).

The key similarity was the victims, not the killer’s signature (p. 44).

—David Reichert, Sheriff, King County (2004) (Lead Detective GRK case, 1983-1990)

The Green River Killer (GRK) was a serial offender, operating primarily in King County, Washington. Named after the recovery location of his first victims, this case exemplifies individual- and institutional-level mechanisms that can impede law enforcement efforts and lead to investigatory failure (Rossmo, 2009). A confounding factor in this series was the volume of leads: Information overload frequently occurs in major cases, particularly when media coverage is extensive. Consequently, a growing body of work seeks to develop data mining strategies for use in major investigations to avert investigatory failure and mitigate information overload by prioritizing leads (e.g., Calderoni, 2015; Rossmo, 2000). Underpinning many of these efforts is the idea proposed by crime pattern theory that the linkage between people and places is important.

Crime pattern theory (P. J. Brantingham & Brantingham, 2008) argues that routinized travel between central activity anchors (i.e., home, work, school, and recreation) generates spatial awareness. Spatial awareness refers to the knowledge of areas traveled that falls within a visual range of locations where people engage in different activities.¹ Popular places, such as gyms, schools, or bars, are locations at which the behavioral patterns of different individuals overlap, and as such, these locations shape the formation of crime patterns. Crimes occur at the intersection of the routine travel and activity of offenders and victims, because offenders can only commit crimes at or near the locations that they know about that also contain targets. This theoretical framework supports the development of profiling strategies that tap into offender behavioral patterns—we learn something about the offender’s activity patterns when spatial clusters emerge in a crime series, and Rossmo (2000) argues that investigators can prioritize suspects based on these spatial tendencies.

Building on the foundation set by spatial profiling strategies, we assert that social network analysis (SNA) offers complementary theory and empirical methods for linking people based on shared activities, and this may yield another mechanism for rethinking the relevance of suspects.² Our argument rests on the tenet that routine behavior is constrained by social factors (P. J. Brantingham & Brantingham, 1984, 2008). People, both offenders and victims, frequent places known to them through a personal network formed through social interactions that are facilitated by different mechanisms, that is, work, school, family, place of residence, and hobbies. For example, an offender will likely select a bar to visit if he or she knows that associates frequent the same location. Two complementary reasons anchor the offender to the bar—familiarity associated with spatial awareness and the social embeddedness that comes about from human interaction. As will be discussed in more depth later in this article, the concept of social embeddedness refers to the structuring force of a social network that curbs and enables behavior. To reveal the potential interconnectivity among people, even when we have no direct observations of their interactions, it is possible to map the degree to which people share commonalities in their social behavior and estimate the likelihood of contact.

Recasting the socio-spatial information generated from a major investigation involves deriving a social network from person-to-place linkage. Connecting each individual named in the GRK case to others based on shared activity nodes (places frequented) has the potential to illuminate the hidden social structure of the case. The challenge associated with using methods and analytics common to the field of SNA to study crime is that the techniques assume that complete network information is available. Missing information about people or their connections may significantly bias estimates. The GRK case provides an opportunity to explore this issue.

Examining the network at 6-month intervals, we assess whether new information gathered during the course of the investigation substantively altered the social structure of the case. This dynamic analysis revealed three implications: First, we find support for the theoretical argument that the intersection of offender and victim awareness space is critical to understanding crime occurrences. Two findings support this conclusion: (a) overlapping information about victim, suspect, and witness awareness space generated a network that exposed clusters of people with common activity patterns; and (b) the offender, one witness (considered a suspect), and two victims linked clusters representing different social circles.

Second, in regard to investigatory policy, this study suggests that SNA methods may be useful when evaluating the progress of an investigation. We base this implication on two findings: (a) an observed shift in the social position of two prime suspects may indicate that the initial working hypothesis misled the investigation, and (b) two structurally important victims held the network together, signaling the existence of two central “seed” cases in the series.

Third, criminological applications of SNA might be feasible, despite the possibility of missing information, once there is a sufficiently large cross-section of data. Two findings support this statement. We found that the networks stopped evolving 18 months into the investigation, which may indicate the attainment of an information threshold, after which new information did not materially alter the network. In addition, while the individual metrics for different suspects continued to fluctuate throughout the study period, the relative importance of key individuals remained stable, suggesting that ranked scores may offer a robust mechanism for identifying central actors.

Before discussing these implications in detail, it is necessary to examine the impetus for this study—the challenges that facilitate investigatory failure. Then, we show how criminological research can benefit from drawing upon crime pattern theory and two constructs from social network theory (social space and betweenness). Next, we explain how to monitor the organizational momentum of an investigation with SNA. Finally, after describing the methods and presenting our results, we deliberate on what benefits tactical SNA may offer to applied criminology.

Challenges to Investigating Serial Crime

Wendy Lee Coffield was a 16-year-old runaway, placed with a foster family in Tacoma, Washington. Habitually working as a prostitute, she solicited business from clients along Seattle’s Airport Tract known as the Strip—a motel district associated with street prostitution. July 8, 1982 was the last day anyone saw Wendy alive. One week later, two boys riding their bicycles near the Green River discovered her body floating near the shoreline. This case marked the starting point of an investigation that lasted for nearly two decades. Although suspected of being responsible for killing many more women, authorities concluded the investigation when they charged the perpetrator, Gary Leon Ridgway, with 49 murders in September 2001—about 20 years after identifying the first victim.

Almost from the onset, the Green River case captured significant public interest. Media interest combined with an aggressive investigative approach generated thousands of leads. At 18 months into the investigation, a multiagency task force significantly extended the resources assigned to this case. Yet, when it disbanded 5 years later at a cost of approximately US$20 million, the killer remained unidentified (Rossmo, 2000; citing Montgomery, 1993). This apparent stalemate in the investigation raises questions about why a team of highly trained investigators was unable to conclude the case, even when the suspect list included the perpetrator.

Clearly, the logistic issues associated with data management, compounding with each new victim, contributed to investigatory failure. Media attention generates vast quantities of information, not all of which are actually associated with the case. Simply put, there are too many leads. Another analytic challenge is to correctly identify and include victims who are relevant to the series: Evolving offender behavior may hamper efforts to link cases when the modus operandi does not contain enough of a signature to suggest that the same offender, or group, is responsible. Data issues, however, are not the only factors working against investigators.

Based on an examination of botched investigations, D. Kim Rossmo posits a theory of investigatory failure, suggesting that cognitive biases, probability errors, and organizational traps can even derail investigations that are well resourced (2009). At the individual level, cognitive biases—such as tunnel vision, reliance on intuition, and the absence of evidence or weighting evidence to support hypotheses—are common problems. Probability errors based on coincidences, similar fact-based evidence, and conjunction fallacy³ may also mislead investigators. In addition, organizational traps, such as inertia, can be problematic; once inertia sets in, the direction of the investigation does not change. Even with additional information, or the emergence of a secondary suspect, group egoism may cause delay in exploring the new evidence if it does not support their initial hypothesis. Investigators are “trapped” by their perspectives. While the subject of Rossmo’s (2009) inquiry was major cases, these kinds of issues threaten to impede cases of any size. In response to Rossmo’s call for finding ways to monitor case development, we suggest that integrating crime pattern theory with tenets of social network theory supports the use of SNA methods to “check” the progress of an investigation as case information accumulates.

Theoretical Integration

Crime Pattern Theory

From its theoretical inception, Paul and Patricia Brantingham (1984, 2008) argued that the key to unlocking crime patterns is to understand the spatial and social organization of crime. At the macro-level, crime patterns accrue from the summation of individual behavior. Routinized behavior generates activity space; this includes the locations wherein people engage in different activities (e.g., attend classes, work, buy groceries, or drink alcohol) and the pathways they use to travel between locations. Over time, a larger awareness space develops which includes knowledge of areas within a visual range of locations frequented and paths used. Popular places, such as a mall or movie theater, are locations where the routinized travel and activity patterns of many different individuals overlap. Sometimes, when offender and victim activity patterns intersect, crime occurs. Locations common to many offenders and victims may develop into high-crime places if they are located within a criminogenic backcloth—where the backcloth refers to the social, economic, and geographic context that influences area residents and workers, as well as city growth and development within the region (P. L. Brantingham & Brantingham, 1993, 1995).

At the individual level, the Brantinghams (2008) asserted that decisions about what to do and where to go occur within the framework of a social structure—where each family member, friend, and acquaintance has varying influence on the decisions of others in the network:

An individual’s daily and weekly activity pattern and primary activity nodes are shaped or modified by a network of friends. This network changes over time, as do primary activity nodes like school or work, and with change comes modifications in activity and awareness spaces. (p. 85)

Moreover, when people have one common activity anchor, they are likely to develop more shared places. Thus, routine activity establishes spatio-temporal movement patterns, through which offenders become familiar with places, routinize decision making into crime templates, and ultimately, discover their targets. It is the behavioral overlap between people that is the key to understanding violent stranger-on-stranger crime—but for the intersection, the offender would not encounter the victim.⁴

To better understand crime occurrence (1984, 2008), the Brantinghams suggest that we draw upon graph theory, stating that while spatial techniques, such as crime-trip analysis and gravity modeling, offer a window into thinking about geographic patterns, actual movement can be better understood by applying graph theory (1984). Graph-theoretical measures provide the “areal link between the sociological and geographical imagination” (Brantingham & Brantingham, 1984, p. 243) that integrate concepts of spatial and social structure—a point demonstrated by scholars exploring how activity space can be modeled with networks to reveal ecological communities (e.g., Bichler, Malm, & Enriquez, 2014; Browning & Soller, 2014; Hipp, Faris, & Boessen, 2012).⁵

Social Structure

SNA is a field of study, grounded in graph theory, which is devoted to understanding the mechanisms of social structure and how the interdependence among actors both constrains and enables their behavior (for a comprehensive introduction into the field, see Wasserman and Faust, 1994, or Knoke and Yang, 2008).⁶ The primary influence on social behavior is one’s relations with others, but these influences do not always come from direct contact. Arguing that social influences move through a network in a contagion process, Christakis and Fowler (2009) provide convincing evidence that indirect relations (the friend of a friend) can have significant effects on perceptions and attitudes, behaviors, and opportunities. Moreover, network structures are dynamic—interactions and reactions by individuals facilitate the formation and termination of social ties, thereby, altering the structure of relations (Snijders, Van De Bunt, & Steglich, 2010).

Applying these ideas to crime and delinquency, scholars assert that the network is both a source of opportunity for crime and a mechanism of social control (e.g., Carrington, 2011). It is through interactions with others, however fleeting, that one acquires resources and learns about new prospects, becomes embroiled in situations that may lead to victimization, finds others who could be potential cooffenders, and encounters people who can prevent them from being involved in crime, as either a victim or an offender.⁷ In addition, individual social behavior exhibits spatial and temporal properties that change as circumstances—in this case, structural relations—evolve. Two additional SNA constructs are particularly useful for the present study—social space and betweenness.

Social space

It is widely theorized by SNA scholars that people participating in common activities, will over time develop the potential to form social relations.⁸ When groups of people are coinvolved in many different events or activities, it is suggested that they are spending time in the same social space. Being located in the same space (attending classes together, frequenting the same coffee shop, and working at the same institution) provides an opportunity to meet and to form relations (Freeman, 1980).⁹ As relations influence attitudes, access to opportunities, and ultimately behavior, the routinization of activities may lead to the formation of a social circle, particularly when the set of joint activities revolve around the same foci. Feld (1981) writes that interpersonal ties and social clusters are likely to emerge among people who participate in different activities that share the same focus—where a focus is an entity (physical, social, legal) around which multiple joint activities occur. While not talking about criminogenic settings, a red light district is a plausible focus of street life around which different activities develop. This coincident activity provides the basis for the development of the social fabric of a community (Foster & Seidman, 1984).

Observing that people are traveling in the same or overlapping social circles is difficult as social circles are latent constructs (Kadushin, 1966). Arguably, latent social structure may become visible by projecting a bipartite graph. Bipartite graphs, more commonly referred to as affiliation networks, connect people to their activities. Projecting the graph (multiplying the incidence matrix by its transpose) reveals how people could be connected through their participation in common activities. Projected connectivity does not mean that people know each other. Instead, overlapping activity suggests the possibility of interaction; it is only when the number of common connections grows that the probability of direct association increases (Wasserman & Faust, 1994).

This method of deriving potential connectivity has many applications. For instance, projected affiliation networks are used to study organization interlock, where business leaders interlock organizations by sitting on the boards of other companies, being involved with charities, and the like. Research shows that corporate interlock influences organizational leadership (e.g., Janicik & Larrick, 2005), business survival (e.g., Uzzi, 1996), innovation (e.g., Hargadon & Sutton, 1997), research and development (e.g., Allen, James, & Gamlen, 2007), and civic involvement (e.g., Galaskiewicz, 1997). Criminologists also find that projected affiliation networks are useful in exposing the interlock between Securities and Exchange Commission (SEC) violators and other fortune 500 CEOs (e.g., Bichler, Schoepfer, & Bush, 2015), identifying working relations among officers through call-for-service coattendance (e.g., Young & Ready, 2015), and studying gang structure (e.g., Grund & Densley, 2015). More aligned to the present study, by linking people to meetings and projecting a person-to-person network, Calderoni (2015) shows how shifting position within a network may identify emerging leaders within mafia-style criminal enterprise groups. Although newly adapted to criminal justice applications, projected affiliation networks stand to contribute much to criminology.

Betweenness

Another network concept of interest to the present study is that of betweenness. In some respects, betweenness may counteract the constraint imposed on individuals by social embeddedness.¹⁰ Thus, to understand betweenness, we first need to consider embeddedness.

Social embeddedness exists because people live within a system of social relations, often involving intersecting and overlapping networks (e.g., kinship network, friendship networks, and work-related associations). To illustrate, consider someone who works with a relative. In this example, the pair of individuals (a dyad) has multiple connections, or bonds, with each other, and as such, the dyad will appear in two different networks: a kinship network and an employment network. Granovetter (1985) states that individuals

. . . do not behave or decide as atoms outside of a social context, nor do they adhere slavishly to a script written for them by the particular intersection of social categories that they happen to occupy. Their attempts at purposive action are instead embedded in concrete, ongoing systems of social relations. (p. 487)

Providing resources and meaning, social relations enrich life. Relations also foster social control by limiting and constraining behavior. In cohesive networks, behavioral aberrations are easy to identify and share with the group, thereby triggering social pressures to conform. Moreover, the stronger the tie is between people, the more likely their social worlds will overlap; as such, some networks tend toward greater cohesion over time (Granovetter, 1973). For instance, if Mary has two close friends, John and Chris, it is highly likely that John and Chris will eventually interact with each other directly. This growing interconnectivity further constrains an individual by limiting the amount of new information they may receive: Mary will receive news about Chris directly, and through John, circuitously. The benefit of this structure is that it makes the group highly cohesive; however, there is a significant disadvantage.

For this social group to thrive in a dynamic environment, someone must have ties that give them access to new information. Granovetter (1973, 1983) argued that pockets of strongly connected people link to other groups of people through weak ties. As illustrated in Figure 1, Mary could have an association to Ted, an acquaintance from work. As ties to people from different social groups are more likely to provide access to new information, Mary will hear about things not already circulating among her friends from Ted that will help her to better navigate the dynamic social environment within which she lives. A thin line represents her weaker bond to Ted relative to the strong associations she has with people from her close social group. Thus, positioning between different social groups maximizes one’s exposure to novel information, and sometimes, this situation offers great benefits.¹¹

Figure 1.

Illustration of social embedding and betweenness.

The interpretation of betweenness changes slightly when applied to a projected affiliation network. In a projected network, individuals connected by many common activities will appear to cluster in a group where most people are connected to each other. The potential that the cluster constitutes a social circle will depend on the number of shared activities. What is more interesting is that an individual who shares some common activities with different social groupings will have ties to different clusters, and thus, has the potential to bridge different social groups. Finding people situated between different social groups might be informative to understanding serial crime cases.

Present Study

Drawing from the prior discussion of crime pattern theory and social network theory, we argue that to understand crime patterns, particularly for serial cases, we need to model the connectivity among people (victims and suspects) and the places they frequent, for it is within this intersection that we find where the offender and victim crossed paths. As activity patterns are influenced by social networks, we must consider the degree to which people frequent the same places, for this could be indicative of a shared social circle. For instance, if John (suspect) and Jane (victim) were seen at the same motel, they have a common affiliation. If they were also seen at the same bar and the same prostitution stroll, there is a higher likelihood that they may operate within the same social circle as their activity spaces overlap considerably. Where this pattern becomes useful to a serial homicide investigation is if John also exhibits overlap with other victims, whereas other potential suspects do not.

While some victims in stranger-on-stranger crime are from the same social space, it is likely that many occupy different social worlds, particularly if different hunting grounds are used.¹² Clusters of people sharing social space will emerge when we link witnesses, friends, and associates to the places they frequent, but finding individuals positioned between different clusters will be even more informative. We propose that the person, or people, connecting (bridging) social groups tie crimes of the series together. While central individuals may be key witnesses or victims, it is more likely in stranger-on-stranger crimes that these individuals are the prime suspects, particularly if the network does not contain any other central actors. Who else but the suspect in a crime series would link the victims from different social space?

Mapping the social structure of a serial murder investigation, this study uses the central positioning of suspects to determine whether new information gathered through the course of the investigation substantively altered the network. Our aim is to explore whether the shifting position of individuals could act as a litmus test to forestall investigatory failure. We argue that by identifying which actors shift in structural position during the investigation, it may be possible to reduce the damaging effects of tunnel vision, emphasis of specific evidence, and intuition. SNA analytics can calibrate an individual’s connectivity, social distance, and influence within the network, relative to all others. Thus, SNA is useful because even if someone is a suspect in only one crime in the series, indirect connections may link them to almost every other victim. Targeting these individuals for greater scrutiny may eliminate information gaps, showing that direct connections actually exist. Moreover, SNA techniques are not scale dependent: They can handle small networks linking three people to networks comprised of thousands of actors, making them useful when data overload threatens the progress of an investigation. Additionally, network statistics are able to identify structurally important people from visually impermeable graphs, offering a significant improvement over linkage analysis.

Method

Data Sources

A journalistic account of the GRK case published by Smith and Guillen (1991) provided most of the initial information about the individuals and places relevant to this series. By supplementing official information with interviews of the victims’ families, law enforcement agents, and witnesses, Smith and Guillen constructed a detailed synopsis of the GRK investigation as it unfolded that integrated multiple perspectives.¹³ Published after most of the homicides occurred but before the case was solved, this is the most comprehensive, publicly available source that is unbiased by the final case outcome. The second source was a book written by Sheriff David Reichert (2004), the leading detective throughout the GRK investigation. His book provided firsthand accounts about the investigation, confirming connections suggested by Smith and Guillen. Extracting information from Reichert also ensured that critical investigatory details, unknown to the public, but pertinent to each phase of the inquiry, were included.

Cross-validating names and specific locations against details provided in the court transcripts (plea agreements and amendments) accruing from Ridgway’s trial (e.g., State of Washington vs. Gary Leon Ridgway), and a case anthology produced by Guillen and Smith (2003) and posted online by The Seattle Times, helped ensure that the information was accurate. Triangulating between these sources improved the validity and reliability of the data generation process, reducing the likelihood that critical individuals or ties among them were missing from the analysis. While not all suspects and witnesses were included—estimates suggest that the investigation connected thousands of individuals to this case—the sources used here are likely to represent the materially important parties involved in the case and their connections within the network.

Data Collection

To be included in the network, several pieces of information were necessary. First, each person must be named or have a unique description and an identifiable role or connection to the case (e.g., apple picker who found a body or associate of a victim). This list included victims, suspects, witnesses, body finders, and other persons of interest. In addition, we required a date on which the individual became involved in the case (in the event of multiple connections to the case, we recorded each dated association as a separate case link). Finally, we required a geographic reference. Spatial precision was not consistent: The investigation linked some individuals with an area of interest (e.g., the Airport District) and others to an exact location (e.g., the Moonrise Motel).

To compensate for the lack of uniformity associated with the spatial data and extend activity space to include a larger awareness space, it was necessary to create a standardized unit of geography for each location that was larger than a single address. Using the latitude and longitude for each place of interest, we aggregated points to 2010 Census Blocks for King County.¹⁴ The places that were more broadly described (e.g., SEATAC Airport or the Strip) were assigned to census block associated with the centroid of the area described. Notably, the court transcripts and supplemental case files posted by The Seattle Times were instrumental in this process.

Sample Description

Of the 99 people identified, missing information (e.g., lack of a precise geographic reference or an inability to pinpoint when they became associated with the case) reduced the sample size to 88 people (88.9% of the individuals identified). As reported in Table 1, while victims accounted for the majority of people identified, other individuals (e.g., body finders, witnesses) comprised almost 30% of the sample.

Table 1.

Description of People and Places Included in the Study.

Study units Descriptive categories	% (N)
People	(88)
Victims	56.8
Investigatory involvement (e.g., witnesses, body finders)	29.6
Suspects	8.0
Family and associates	5.7
Places	(58)
Body disposal sites	37.9
Last seen locations	44.8
Material to investigation or combination	17.2

Looking at the data capture process geographically, there were 237 data points. Locations outnumber people because individuals could be associated with multiple locations throughout the investigation. Most of this information was usable: 79.7% of the data points mapped. On average, each person was linked to two locations (SD = 1.2; minimum = 1 and maximum = 7). Aggregating locations by census block resulted in 58 unique study places. As reported in Table 1, most areas were either body disposal sites or last seen locations.

Network Generation

Linking each person to the case locations they were associated with produced a bipartite graph. We converted the graph to a person-to-person network by linking people to each other if they were associated with the same place (in this case, a census block). Conversion occurred by multiplying the two-mode incidence matrix for the network (e.g., people connected to places) by its transpose.¹⁵

Reconfiguring the master network into six observations (networks) provided an opportunity to determine whether the accumulation of case information changed the central positioning of suspects.¹⁶ The first observation pertains to the first 6 months of the investigation. As the investigation progressed, each new network included data from the prior observation plus information collected during the subsequent 6 months. With little research in this area, we used 6-month intervals in accordance with Calderoni’s (2015) dynamic analysis of the social structure of an organized crime network as revealed throughout the course of an investigation. As noted in Table 2, within 2 years of the discovery of the first victim, the network contains 75% of the people and 86% of the places associated with the crime series.

Table 2.

Cumulative Distribution of the Addition of People and Places Through Phases of the Investigation.

Investigatory phase	People			Places
Investigatory phase	People added	Cumulative frequency	Cumulative percentage	Places added	Cumulative frequency	Cumulative percentage
Phase 1: 07/82-12/82	24	24	27.3	21	21	36.2
Phase 2: 01/83-06/83	15	39	44.3	11	32	55.2
Phase 3: 07/83-12/83	20	59	67.0	12	44	75.9
Phase 4: 01/84-06/84	7	66	75.0	6	50	86.2
Phase 5: 07/84-12/84	10	76	86.4	5	55	94.8
Phase 6: 01/85-12/03	12	88	100.0	3	58	100.0
Aggregate: 07/82-12/03	—	88	—	—	58	—

Network Statistics

This study reports standard network descriptive statistics, betweenness centrality scores, and Jaccard coefficients.¹⁷ First, for comparative purposes we must provide several descriptive statistics, including the number of actors and ties in each network, along with its density. The number of actors and ties is simply a description of the sample size. Density reports the overall cohesion of the network. To calculate density, we divide the number of ties observed in a network by the possible ties that would exist if all actors were interconnected. In a hypothetical network where every actor is connected to every other actor, the density score would be 1, indicating that 100% of possible ties are present. Networks with low density are sparse networks, where actors have little connectivity.

Freeman’s betweenness centrality identifies how centrally positioned a person is in the network: It calculates for any given person, the proportion of times they sit along the shortest paths among all others in the network (Borgatti, Everett, & Johnson, 2013). The general formula to calculate the betweenness score for actor j is

b_{j} = \sum_{i < k} \frac{g_{i j k}}{g_{i j k}},

where g_ijk is the number of geodesic paths (shortest paths) connecting actors i and k through actor j, and g_ik is the total number of geodesic paths connecting i and k. The standardized version of this equation was used to enable comparisons across different networks: Standardization simply divides betweenness by (g − 1) (g − 2) / 2, where g is the number of actors in the network (Knoke & Yang, 2008).

Sitting between pairs of other people, this position of “middleman” connects others who do not have a direct link to each other. Within the context of how we constructed these networks, a person with a high betweenness centrality score shares common behavioral patterns with different clusters of other individuals named in the case. When suspects emerge with high betweenness centrality, it means that their behavioral routines have possible commonalities with different clusters of victims, and we can use this information to prioritize investigative leads.

The Jaccard coefficient compares the structure of two networks by calculating the percentage of the network that remains the same between successive periods. Given that our networks denote intervals in an investigation, the Jaccard coefficient will help us determine whether the network changed with an additional 6 months of police work. Generally, values between 30% and 60% indicate that the network is evolving at a steady pace; when coefficients exceed 60%, there is little change in the network; and anything below 30% (or 20% if a more conservative threshold is desirable), indicates that the network changed rapidly, becoming a new configuration (Snijders et al., 2010). As used in this study, we interpret scores less than 30% to indicate rapid progress in the investigation and values of 30% to 60% to suggest that the investigation is progressing at a steady rate. If the Jaccard values exceed 60%, the network is not changing enough, suggesting that the new information uncovered with an additional 6 months of police work did not materially change the course of the investigation.

Results

Network Characteristics

Table 3 provides descriptive statistics for networks at each interval of the investigation and illustrates what each network looks like. Note that line thickness indicates the number of shared places between pairs of people (diamonds depict suspects, and circles indicate another case status). As the investigation progressed, networks increased in size, with the addition of actors and ties: the greatest increase being between Time₂ and Time₃. Density decreases over time with the exception of the final phase. Despite these notable changes in the observed networks, it is possible that the new information did not aid the investigation, particularly if the new data pertains to peripheral players. A more detailed inspection of network stability is required.

Table 3.

Description of Valued Actor-to-Actor Networks by Interval.

Interval	Network visualization^a	Descriptive statistics
T₁		24 actors
07/82-12/82 (first 6 months of the investigation)		102 ties
07/82-12/82 (first 6 months of the investigation)		19% density
T₂		39 actors
07/82-06/83 (12 months)		220 ties
07/82-06/83 (12 months)		15% density
T₃		59 actors
07/82-12/83 (18 months)		424 ties
07/82-12/83 (18 months)		13% density
T₄		66 actors
07/82-06/84 (24 months)		556 ties
07/82-06/84 (24 months)		14% density
T₅		76 actors
07/82-12/84 (30 months)		686 ties
07/82-12/84 (30 months)		12% density
T₆		88 actors
07/82-12/03 (entire investigatory period)		1,304 ties
07/82-12/03 (entire investigatory period)		18% density

Black diamond shapes indicate suspects, gray circles are victims, and white circles represent other people material to the investigation, such as witnesses, family members, and friends. Dashed lines indicate new ties found during the additional 6 months of the investigation. Thicker lines depict greater connectivity—more places in common.

Network Stability

Figure 2 illustrates that developments in the investigation up to 18 months contributed substantively to identifying people material to the case. The new information gathered across these successive phases (T₁ → T₂ and T₂ → T₃) was materially changing the structure of the network. However, after 18 months (T₃ → T₄), the network stabilized as indicated by the Jaccard coefficient of .763 (76.3% similarity). This means that with the exception of the catchall final time period (30 months to December 2003), investigatory efforts after 18 months generated little change in the overall structure of the actor-to-actor network.

Figure 2.

The Jaccard coefficients measuring network stability between successive periods.

Network stability does not mean that individuals are in fixed positions. It simply means that the new information being generated (additional connections among actors or the introduction of new people to the case) was not substantively altering the overall structure of the network relative to what was already known, signifying that the case was not advancing as quickly as it had. Notably, information gathered during periods of stability may still contribute insight into the relative position of specific people: New information may change actor-level centrality scores.

Prominence of Actors

As illustrated in Table 3, betweenness centrality—represented by the size of the symbols representing nodes—varies over time.¹⁸ The highest scoring individual at the beginning of the investigation was Melvyn Foster (represented by the rectangle containing a large diamond in the first row of Table 3): He clearly links clusters of people. By the third period, however, the focus on this suspect falls into question as Gary Leon Ridgway (depicted in the second rectangle) becomes more noticeable. Yet, as case information accumulates, the standing of both suspects declines. Notably, two victims figure prominently by the second interval—Debra Bonner (larger circle) and Terry Milligan (smaller but prominent circle). Their central positioning tells us that their behavioral circles overlapped with unique clusters of other victims, suspects, and witnesses, suggesting that Debra and Terry are seed cases in the series. Overall, four people (4.5% of actors) are positioned at the intersection of different clusters of actors throughout the observation period.

Table 4 draws our attention to the actual scores represented by the symbols. To test the robustness of these findings, the normed betweenness centrality scores for key suspects are compared, first using all case information, and then, with Melvyn Foster’s early “suspect” connections ignored. Norming the values allows for meaningful comparison across networks of different size. During the first time frame, Foster emerges as the most central figure; however, his position within the network declines. By the third observation (18 months into the investigation), Ridgway catapults to the most prominent position in this network: His centrality increased by a factor of 14.9. Moreover, at this point, Ridgway’s centrality is about 2.4 times that of Foster. In addition, while Ridgway’s score declines, even at the end, he is central enough to warrant attention. In the second bank of results, we see that if the GRK Task Force refrained from concentrating on Foster, without question, Ridgway would be the most central suspect until December 1984. The takeaway from this analysis is that even though normed scores fluctuated, the relative importance of key individuals remained fairly stable.

Table 4.

Normed Betweenness Centrality Scores for Suspects.

Suspects	T₁07/82-12/82 (6 months)	T₂07/82-06/83 (12 months)	T₃07/82-12/83 (18 months)	T₄07/82-06/84 (24 months)	T₅07/82-12/84 (30 months)	T₆07/82-12/03 (entire period)
All major suspects included
Gary Leon Ridgway (PS)	—	0.17	2.54	1.53	1.21	1.16
Bobby Woods	—	0.17	0.20	0.26	0.27	0.30
James M. Tindal	—	—	—	1.19	0.87	0.74
Dan Smith	0.06	0.02	0.03	0.03	0.03	0.03
Melvyn Foster (PS)	1.54	0.64	1.08	1.45	1.35	1.31
Ignoring Melvyn Foster as an initial suspect
Gary Leon Ridgway (PS)	—	0.05	0.73	0.39	0.24	0.18
Bobby Woods	—	0.05	0.05	0.06	0.06	0.04
James M. Tindal		—	—	0.32	0.15	0.12
Dan Smith	—	—	—	—	—	0.01
Melvyn Foster (PS)	—	—	—	—	—	0.27
People in network	24	39	59	66	76	88

Note. Betweenness centrality scores calculated on the binary network. Primary suspects noted with “PS.”

Discussion

Criminological Implications

Integrating criminology and social network theory stands to significantly enhance our understanding of crime because social network theory can be used to model the mechanisms through which people learn how to, where to, and with whom they can offend, as well as how victims come into contact with offenders (e.g., Carrington, 2011). Extending a theoretical argument put forth by the Brantinghams (P. J. Brantingham & Brantingham, 1984, 2008; P. L. Brantingham & Brantingham, 2015), we assert that social networks strongly influence the choices people make about the activities they engage in, and as many social activities require convergence at set locations, networks shape spatial behavior. Drawing upon SNA theory, we also assert that as individuals positioned between social groups are the sources of new information and experiences (Granovetter, 1973, 1983), they are critical to understanding behavior, as well as changes in behavior or new experiences, including victimization. Individuals associated with different subgroups of people have unique positions because their overlapping behavioral patterns make them more central to the entire network. In effect, they hold the network together. Combined, these tenets are particularly useful in understanding the occurrence of stranger-on-stranger crime.

As discussed at length earlier in this article, linking people to the events and places they frequent provides a method of capturing overlapping activity—the key to understanding crime occurrence according to crime pattern theory. Projecting affiliation networks reveals the potential connectivity among people based on shared experiences (Wasserman & Faust, 1994). Individuals with high connectivity are likely to share the most behavioral patterns with different social groups (overlapping activity and awareness space)—in a stranger-on-stranger crime series, this should be the offender.

As projected networks enable the simultaneous modeling of spatial and social connectivity, this will advance tests of crime pattern theory. By adopting a network method, we move from relying on models that assume independence among subjects (e.g., linear, regression-centered approach), or those capturing only spatial dependence (e.g., gravity models), to methods aimed at simultaneously capturing social and spatial dependence among actors. Not only does this fit better with many criminological theories, but it also expands the range of explanatory variables at our disposal—all structural statistics are potential independent variables.

Given the theoretical congruence between SNA and criminology (Carrington, 2011), it is not surprisingly that a growing number of criminologists are reexamining what we think we know about crime and deviance using a network perspective. This theoretical integration stands to trigger significant change in the discipline, leading some to predict the coming of a networked criminology (Papachristos, 2011). Although still in a nascent stage of development, criminologists are already demonstrating how network research enhances our understanding of organized crime and terrorist operations (e.g., Campana, 2011; Everton & Cunningham, 2014; Malm & Bichler, 2013), gang conflict and violent activity (e.g., Papachristos, 2009; Tita & Radil, 2011), online crime networks (e.g., Décary-Hétu, Morselli, & Leman-Langlois, 2011; Joffres & Bouchard, 2015), and illicit market activity (e.g., Morselli & Petit, 2007). More apropos to the present study, scholars have recently begun to consider the merits of using SNA as an investigative tool (e.g., Calderoni, 2015, Sierra-Arevalo & Papachristos, 2015; Van der Hulst, 2009) and to model activity space (Bichler et al., 2014; Hipp et al., 2012).¹⁹ Considering our findings in light of what Rossmo (2009) said about investigatory failure, we advocate that network analytics may be used to “check” the progress of an investigation as case information accumulates.

Criminal Justice Implications

As expressed by David Reichert, lead investigator on the GRK case, stranger-on-stranger homicide is difficult to investigate. Prioritizing the investigation of suspects based on their position within the network may forestall the premature dismissal of individuals when a working hypothesis forms. New leads should alter the network as an investigation progresses: Social structure is dynamic, and the introduction of new people (and places) should significantly change the configuration of the network until we achieve information saturation or we reach a population limit. Once all affiliated individuals have been uncovered and all associations among them known, the network ceases to evolve. Thus, by monitoring how the structure of the network changes throughout the course of an investigation with the Jaccard coefficient, analysts can ascertain when investigatory efforts reach a saturation threshold. Network stability may signal that there are no players left to uncover (meaning that the perpetrator is in the network), or that the direction of the investigation needs to change drastically—the investigation reached a dead end.

Our results revealed that within 18 months of the start of the GRK investigation, the person most central to the network was Gary Leon Ridgway, the perpetrator of the murders. Interestingly, at this point in the investigation, the task force had focused on Melvyn Foster. As the investigation reached a saturation threshold, the scores move toward equalization but continued to draw attention to both suspects. The findings are somewhat robust considering that if the task force refrained from identifying Foster as the prime suspect so early in the investigation, Ridgway would remain the most central suspect throughout the first 2.5 years of the crime series. It is hard to know in hindsight if these results would sway the organizational momentum that led investigators to focus on Foster to the exclusion of Ridgway. With this said, it is reasonable to suggest that if these network metrics had been available at the time, it might have prevented the working hypothesis from solidifying so early on in the investigation by encouraging members of the GRK Task Force to pay greater attention to Gary Leon Ridgway.

Our findings also provide additional support for those arguing that despite data limitations, SNA metrics have utility in tactical analysis (e.g., Calderoni, 2015; Sparrow, 1991; Van der Hulst, 2009). Once a sufficient amount of evidence accumulates, the network stabilizes and betweenness centrality metrics cease to fluctuate radically. In the present study, we found that according to the Jaccard coefficient the information threshold occurred at 18 months. This finding suggests that using a sufficient time window may reduce the validity threats posed by the incompleteness of data. Notably, we presented a single-case study using publicly accessible data. Thus, we caution that it is premature to suggest that 6-month intervals should be the standard, or that all case-relevant people are identifiable within 18 months. We do not know how long our data collection periods should be and whether the time frame depends on the type of crime under investigation or the amount of resources applied to the case. It may be possible to examine network evolution on a monthly, or even weekly, basis using case data. These issues require additional research.

Limitations

There are two potential limitations to this study. First, some network analytics are particularly sensitive to missing data (Knoke & Yang, 2008). If people, or some of their relations, are missing from the observed network, structural statistics may misidentify the most central actors. While the misidentification of central actors may compromise tactical use of SNA if the objective is to disrupt a criminal network, that is, remove the most central drug suppliers in a trafficking network, we argue that the inherent sensitivity of some centrality measures can be advantageous when used for a different purpose. As case evidence builds, new information should alter network structure and cause different individuals to “pop out” as being central to the case. If continued investigatory efforts fail to uncover novel information, the social network would remain unchanged. This may signal to investigators that an organization trap may have set in, challenging the leadership to reassess the direction of their efforts. In this scenario, assessing the change in scores becomes a focal point of the analysis rather than determining the score per se. We used betweenness centrality; however, widespread use of this metric to monitor case development is still a long way off; replications must test the sensitivity of different centrality measures to identify the best indicator or set of indicators. Readers should be aware that centrality refers to a family of concepts, each with its own metric, and though dozens of measures exist, there are a small number that are regularly used—that is, beta centrality, closeness, degree centrality, eigenvector centrality, and k-step reach centrality (Borgatti et al., 2013).

The second pressing issue is that geographic aggregation necessitated the loss of spatial precision. This introduces standing arguments about the modifiable area unit problem that dogs the application of spatial analysis to crime problems. Originally, we collapsed activity at adjacent motels on a strip. The reason behind this research protocol was that at the block level, the bank of properties together generated a target-rich habitat used as a hunting ground (for an explanation of target-rich habitats, see Felson, 2006).²⁰ Because many of case-relevant sites in this series were remote, block-level aggregation did not work for all locations, forcing us to use census tracts. Critics may argue that aggregating at this level grouped places with no real proximity. The counterargument is that physical proximity does not necessarily guarantee social connectedness. For instance, prior research examining crime at budget motels in Chula Vista, California, found that differences in the management of adjacent motels generate significant variation in how crime problems manifest at the block level (Bichler, Schmerler, & Enriquez, 2013). For this reason, future research should explore different spatial units to see whether our findings are scale invariant. If so, the method is robust to spatial variation.

Conclusion

Major serial crime cases require analytic tools capable of sorting through a large volume of information to find common linkages among victims. It is by identifying the common linkages that investigators uncover the correct perpetrator(s) and ultimately terminate the series. In this study, we examined change in betweenness centrality scores across successive time slices to identify how the network position of specific people changed throughout the investigation. Theoretically, this is consistent with tenets of crime pattern theory (P. J. Brantingham & Brantingham, 2008). People with the greatest connectivity are likely to share common behavioral patterns with others (same activity space). If the network truly represents the cumulative activity space that is critical to the series, the offender should be the most central actor.

While this analytic technique will help test criminological theory, it also has criminal justice applications: It could help redirect focus on pivotal victims and suspects when investigatory circumstances threaten to derail a case (Rossmo, 2009). Examining the overall structure of the network, we find that it became stable early on (18 months into the investigation), even though the investigation continued to add more people and places, as well as ties among known individuals. This investigatory stagnation suggests that either all of the critical actors are already known (meaning that the suspect pool includes the offender), or a new direction is needed to move the case forward.

While this case study demonstrates the potential utility of tactical SNA, as with all research, replication will determine whether this method is useful in different contexts and with alternative data sources. Considering that only publicly available information was used, using all pertinent evidence generated during an investigation while it is in progress would provide a better test of the utility of projected affiliation networks and betweenness centrality.

Footnotes

Acknowledgements

The authors presented a version of this article at the International Symposium on Environmental Crime and Crime Analysis (ECCA), June 2014, Kerkrade, the Netherlands. They would like to thank Lisa Chavez and Pedro Martinez for their assistance with data collection, and D. Kim Rossmo for helpful comments.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

Author Biographies

Gisela Bichler, PhD, is professor of criminal justice at California State University, San Bernardino. Generally, her recent scholarship explores the interplay between the environment and offending behavior, with an emphasis on the influence of social networks. Recent publications include Journal of Research in Crime and Delinquency, Crime and Delinquency, Crime Patterns and Analysis, Global Crime, and the Security Journal.

Steven Lim, MS (GIS), is a research assistant in the Center for Criminal Justice Research and a deputy sheriff in San Bernardino County Sheriff’s Department. With a joint specialization in social network analysis and geographic information sciences, he studies how socio-spatial networks underpin crime problems.

Edgar Larin, BA, is a research assistant in the Center for Criminal Justice Research and a second lieutenant, U.S. Army. His academic area of specialization is crime and intelligence analysis.

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