Social Network Analysis as a Toolkit for the Science of Social Work

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S O C I A L N E T W O R K A N A L Y S I S

Social Network Analysis as a Toolkit

for the Science of Social Work

Eric Rice University of Southern California

Amanda Yoshioka-Maxwell University of Southern California

A B S T R A C T The science of social work can be augmented by active engagement in social network analysis. We provide an overview of both egocentric analysis (also referred to as personal network analysis) and sociometric analysis (or whole network analysis), and discuss ways of incorporating these tools into social work research. Social network analysis is particularly useful in identifying mechanisms of social change; however, the science of social work is incomplete unless under-standing is linked to the processes that promote positive change. We draw on 4 articles published in conjunction with this article to demonstrate how mechanisms for social change can be modeled, and to illustrate the ease with which implica-tions for social work practice and direcimplica-tions for future intervention efforts emerge from such analyses.

K E Y W O R D S : science of social work, social network analysis, sociomentric, ego-centric, social change

doi: 10.1086/682723

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he science of social work can be greatly enhanced by active engagement with social network analysis. Spurred by John Brekke (2012), a discourse has emerged during the past several years regarding the potential for social work to emerge as a science. From the perspective of a social network researcher, Brekke’s most compelling commentary on the emerging science of social work in-cluded the tenet that social work as a science is deeply invested in human change. The power of social network analysis as a tool in the service of this agenda origi-nates from the proclivity of social network analysis to identify mechanisms of so-cial change. All four of the articles that serve as companions to this article focus on the ways in which relationships between social actors mediate well-being (three published in this issue [Barman-Adhikari, Rice, & Winetrobe, 2015; Henwood, Ste-fanic, & Petering, 2015; and Kriegel, Hsu, & Wenzel, 2015] and one published in a previous issue of JSSWR [Bunger, Doogan, & Cao, 2014]). For example, Henwood and colleagues (p. 385, this issue) found that homeless persons who exited Housing

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First programs reported their relationships with the program staff remained distant over time, and they reported higher numbers of peer relationships characterized by both conﬂict and support.

However, understanding phenomena is not enough (Brekke, 2012); rather the science of social work is incomplete unless understanding is linked to the pro-cesses that promote positive change. Again, social network analysis can prove an invaluable tool. For example, in Henwood et al. (2015), the authors’ analysis of the social network of homeless adults in two housing programs with very dif-ferent approaches quickly led to recommendations for change strategies:“Because recovery is inherently a social process, providers should discuss with consumers the type of relationships they have and might want to develop. Providers and consumers could focus on engagement with individuals already in a consumer’s network and the quality of their consumer–provider relationships” (p. 400). In fact, delineating mechanisms for intervention and social change becomes remark-ably straightforward in the context of social network studies when this tool is placed in the hands of social work scientists. In addition to Henwood et al., this collection of articles includes explicit analyses of the mechanisms of social change and recommendations for change strategies to promote well-being.

Brekke (2012) was also careful to point out that a science of social work occurs at many different levels of analysis, including individuals, families, organizations, communities, and even societies. Here too, social network analysis is an ideally suited tool for this intellectual agenda because this tool has long been indifferent to the level of analysis to which it is applied. Indeed, Henwood and colleagues (2015) and Kriegel and colleagues (p. 407, this issue) investigated networks sur-rounding individuals, whereas Barman-Adhikari and colleagues (p. 433, this issue) explored a community-level network, and Bunger and colleagues (2014) examined network links among organizations.

Core Ideas in Social Network Analysis

The intention of this essay is not to provide a history of social network analysis; for that we highly recommend Freeman’s (2004) The Development of Social Network Analysis: A Study in the Sociology of Science. However, some historical context is war-ranted. The earliest roots of social network analysis can be traced to social psy-chology at the turn of the 20th century, but particularly what Jacob Moreno and Helen Jennings referred to as sociometry in the 1930s (e.g., Moreno & Jennings, 1938). However, contemporary social network analysis received a huge burst of creative energy in the 1970s with the work of Harrison White and his students, including Mark Granovetter, Ron Burt, Ron Brieger, Peter Bearman, Kathleen M. Carley, Philip Bonocich, and Barry Wellman, among others. These innovators re-vived the tradition of sociometry and infused it with a newfound mathematical and theoretical rigor. Along with others in sociology, including Freeman, they

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devel-oped the tools that became the foundation of modern social network analysis. These techniques were pushed further in the 1980s and 1990s at the University of California, Irvine, where researchers refined, codified, and made the techniques publicly available. Most of the techniques developed by this new generation of network analysts were captured in the classic text Social Network Analysis: Methods and Applications by Wasserman and Faust (1994), and were translated into computer algorithms by Borgatti, Everett, and Freeman (2002) in UCINET. During the same period, as the expanding use of the Internet created explicit awareness of networks, computer scientists and physicists began to engage in network analysis with new-found enthusiasm (e.g., Watts, 1999). Over the past decade, appliedfields, such medicine and public health, have become increasingly concerned with social net-works. Although certainly not thefirst researchers to apply social network analysis to health, Christakis and Fowler (2007, 2008) published a series of articles in the New England Journal of Medicine, which brought social networks to a mainstream au-dience of physicians and behavioral health scientists. However, until the past few years, with some rare exceptions (e.g., Fraser & Hawkins, 1984), few social work researchers have availed themselves of these methods. And yet, several published articles have pointed out the important role of social work and social workers in personal and social support networks (Biegel, 1984; Maguire, 1981; Whittaker & Garbarino, 1983;), in addition to the general focus of the role of environment in examining human development and behavior within thefield of social work (Bronfenbrenner 1977). Therefore, it is our hope that this collection of articles on social network analysis will inspire more social work researchers and practitioners to use these methods in the pursuit of social work science.

Social network analysis emphasizes the importance of structure as a way of characterizing the social environment. These patterns of relationships between in-dividuals inﬂuence outcomes among members just as outcomes among members are inﬂuenced by their position within the larger network structure (Borgatti, Mehra, Brass, & Labianca, 2009; Krause, Croft, & James, 2007). This method broadly depicts individuals as embedded in connections between network members. The analysis seeks to understand the patterns in these connections (Scott, 1988), and social network data can be imagined as a social relational system composed of so-cial actors and their interactions (Wasserman & Faust, 1994). One of the key un-dertakings of this method in the social sciences is the use of graph-theoretic prop-erties that characterize structures, positions, and dyadic dimensions to explore the overall shape and interconnections of the network (Borgatti et al., 2009).

As previously mentioned, social network analysis can occur at many concep-tual levels of analysis, and thus, the network actors (also called nodes) can be in-dividuals, families, communities, organizations, or even nation states. Likewise, the interactions connecting actors can take a huge array of forms, including friend-ships, sexual partnerfriend-ships, marriages that join families, business relations, patient

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referrals, advice networks, and supply chains. Regardless of these conceptual issues, theﬁrst decision in any social network analysis is whether to study a focal actor and the relations that surround that person (i.e., egocentric analysis; also known as per-sonal network analysis) or to consider a population of actors and their intercon-nected relations (i.e., sociometric analysis, or whole network analysis).

Egocentric Analysis

Egocentric data enables exploration of the diversity of network ties that surround an individual; for example, neighborhood-based peers, school-based peers, and family members. This type of data focuses on the individual being studied (typi-cally called the Ego) and the alters, who are other individuals to whom the Ego is tied (Butts, 2008). Figure 1 depicts egocentric data visually. Alex is the Ego whereas the alters are shown as Brian, Carrie, David, Brother, Mom, and the case worker, Although this type of analysis does not include a global examination of the net-work of ties that extend beyond the focal Ego, egocentric data analysis can be adapted into survey data collection with relative ease. Furthermore, egocentric analysis highlights the effect that these small networks can have on behavior, which in turn, underscores the importance for practitioners and researchers to examine an individual’s local network to more fully understand the level of risk

Figure 1. An example of an egocentric network. In this network, the Ego, or focal actor, is depicted by the node for Alex at the center point of the network. The alters, or individuals with relations to the Ego, are shown with nodes for Brian, Carrie, David, Mom, Brother, and Case Worker. The lines indicate interactions or a relationship between the connected nodes. All alters are connected to the Ego, but alters are not necessarily connected to one another. Take note that alters with relations to Alex may be con-nected with one another, forming triads and other subgroups.

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and protective factors affecting the individual. For example, much of our prior work on homeless youth has used an egocentric approach, and demonstrated that these youth’s connections to family and housed peers were associated with lower levels of both HIV-risk taking (Rice, Monro, Barman-Adhikari, & Young, 2010) and substance-use behaviors (Rice, Milburn, & Monro, 2011). In contrast, these ego-centric analyses also showed that homeless youth who primarily connected with other homeless youth were associated with increased reports of risk taking (Rice et al., 2011; Rice et al., 2010).

In egocentric studies, participants are asked to nominate alters to whom they are tied, the attributes of those individuals (e.g., race, gender, age, substance-use history), and the nature of the ties to each alter (e.g., provides support, endorses particular behaviors). Then, the participant is asked questions exploring if and how the alters are tied to one another. Questions to collect data on the Ego’s local network structure are easily administered via survey instruments (Butts, 2003, 2008). Once these local networks are constructed, the researcher can better un-derstand the roles that each member serves in the network, helping to explain access to information, the ﬂow of information, availability of support, and the myriad inﬂuences on the person’s behaviors—all of which are potential targets for intervention efforts.

Much of the methodological rigor behind egocentric analysis has focused on issues related to data collection. A paramount concern among social network re-searchers stems from the use of surveys, and whether, in the context of a survey, individuals are able to accurately remember all relevant alters in their network (e.g., Brewer & Webster, 2000; Marin, 2004). Some research has shown that when people were asked to recall their network contacts in the context of survey re-search, respondents often forget a substantial number of contacts (Brewer et al., 2000). Marin (2004) found that the connections most likely to be recalled were affective strong ties and relations of longer duration. Moreover, she found struc-tural bias in participants’ responses insofar as the Ego persons were more likely to recall those relations that had a greater number of shared ties in the network. Although in most cases, recall error tends to be biased away from strong ties, the evidence is somewhat mixed on this point (e.g., Brewer et al., 2000; Hammer, 1984; Sudman, 1988). Based on extensive review of this problem, Brewer (2000, 2002) has suggested and tested several viable solutions, including nonspeciﬁc prompting, reading backlists, semantic cues, multiple elicitation questions, and reinterviewing.

Another area of key importance to egocentric analysis involves issues of net-work composition and measuring what portions of the Ego’s netnet-work are com-posed of different types of alters. What is important to consider in the context of egocentric social network analysis is how to characterize the composition of the network. For example, a single alter attribute can be operationalized in an

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egocentric analysis in at least three ways: (a) the number of alters possessing the attribute, (b) the proportion of alters possessing the attribute, or (c) the presence or absence of alters with the attribute. The choice is not trivial; the approach to network characterization affects how mechanisms of social change are under-stood. In the context of social support, what might be most important is the number of people an individual can rely on in times of need; having one source of support is good, but having two or three is even better. However, in the context of social inﬂuence, the proportion of network alters who engage in a behavior might be more relevant. The presence of four alters who smoke cigarettes might not matter as much for large networks as small networks, because the critical issue is the proportion of those alters in the reference group. Are these four smokers in a network of eight individuals or 20 individuals? A youth is far more likely to feel pressured if 50% of a network smokes rather than 20%. Last, in some instances, the presence of at least one person whoﬁlls a crucial role affects well-being. Stud-ies of high-risk adolescents have often found that having at least one caring adult helps to foster resilience (Keating, Tomishima, Foster, & Alessandri, 2002; Zimmer-man, Bingenheimer, & Notaro, 2002).

Because we recognize the gap in papers and texts that didactically explore egocentric methods, we have provided some sample SAS code (see Appendix) that can be used to create variables from egocentric data, which can be incorporated into statistical models. We hope this appendix is helpful to egocentric novices who are looking for a concrete starting point. The code provides an example of how to create variables that capture the proportion of alters with a given attri-bute, the number of alters with a given attriattri-bute, and the presence or absence of a type of alter.

The article by Kriegel and colleagues (2015) provides an example of how ego-centric analyses can motivate social work science. These authors used egoego-centric network analysis to assess the ways in which the networks of homeless women mediate the relationships between the women’s incarceration experiences and their behavioral health outcomes. Kriegel and colleagues found that women with incarceration histories reported connections with more network alters who also had incarceration histories and more alters who engaged in risky sex behaviors, both of which were subsequently associated with increased reports of substance use and sexual risk-taking behaviors. These mediating mechanisms provide clear directions for social change. Kriegel and colleagues suggested,“Attention paid to network composition could include developing community integration interven-tions geared toward providing clients with access to prosocial individuals as alter-natives to networks of higher risk individuals” (p. 426).

Sociometric Studies

Sociometric data, sometimes called whole network data, are a collection of nodes (actors in the network, e.g., individuals, families, or organizations that are the

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smallest unit of analysis) and ties (also called edges) in a particular population at a given point in time. Figure 2 depicts typical sociometric data, indicating how these data capture both direct and indirect ties in a population of actors. This particularﬁgure comes from our recent study of homeless youth and depicts the prior month’s conversation contacts among a group of youth sampled at one particular drop-in agency over a one-month period. However, sociometric ties can focus on a variety of social relationships, such as friendship ties, sexual contacts, persons with whom an individual uses drugs, or collaborative networks among social service agencies. Sociometric data goes beyond simple dyadic relationships, and provides an understanding of how a population of nodes is connected in a larger web of interconnected direct and indirect ties that exist in any community. For instance, sociometric network data can be used to assess the extent to which youth engage in risky sexual behavior (Rice, Barman-Adhikari, Milburn, & Monro, 2012). By examining the sexual connections among a given population of adoles-cents, it is possible to understand which youth are at greater risk than others, based on not only their direct connections to risk-taking alters but also their position in a larger network space and how that position might engender oppor-tunities for risk and resilience. These analyses can reveal how a network is orga-nized and structured, and network variables can be used in regression analyses to provide information on the effect of these network properties on engagement in certain behaviors (Rice, et al., 2012; Valente, Gallaher, & Mouttapa, 2004).

Figure 2. An example of a sociometric network from our recent study of homeless youth. The graphic depicts the prior month’s contacts among a group of homeless youth sampled at one drop-in agency over a 1-month period. As typical of sociometric data, these data capture both direct and indirect ties in a population of actors. This graphic illustrates that for this network, a larger core exists, with a num-ber of dyads and triads existing in more peripheral positions.

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Perhaps the two most commonly discussed sociometric properties of networks are network density and network centrality. Social scientists have long contended that networks with higher densities, specifically greater interconnectivity among group members, are more homogenous in terms of the network members’ behav-ior (e.g., Blau, 1964; Durkheim, 1893/1964). Density is typically calculated as a pro-portion with a value ranging from 0 to 1, which represents the actual number of direct ties as a function of the possible number of ties in a network of a given size. Centrality assesses the prominence of certain members in a network, and cen-trality is measured in various ways, including degree cencen-trality, betweenness, and Bonacich centrality. Degree centrality is a measure of the number of ties within a network to a particular node, or the number of edges adjacent to a node (Borgatti, 1995; Freeman, 1978; Otte & Rousseau, 2002). Degree centrality assesses the local popularity or prominence of a given node. By calculating the degree centrality of each node in a network, and then converting those values into variables, re-searchers can examine minimum, maximum, and average degree centrality for the net-work and determine if behavioral outcomes are associated with those measures. As a measure of centrality, betweenness is a count of the number of pairs of nodes between which a given node lies. As such, this measure of centrality as-sesses how effectively one node bridges the gaps between other nodes. Although these nodes might not be the most influential members of a group (Cook, Emer-son, Gillmore, & Yamagishi, 1983), and are often not the most popular members of a group, it is important to note that, as Burt (2005) suggested, the nodes that lie between other nodes are critical because they connect otherwise disconnected parts of a network. Bonacich centrality is a modified measure of degree centrality. Whereas degree centrality equates the number of connections to an individual’s level of power in a network, Bonacich centrality weighs those connections by considering the centrality of the connections to an individual’s connections, essen-tially providing an estimate of embeddedness of an individual within the larger network. Thus, Bonacich centrality accounts for not only the importance of con-nectivity but also the centrality of the people to whom an individual is connected (Hanneman & Riddle, 2005).

Myriad resources are available to help researchers get started with conducting sociometric analysis, including several excellent textbooks. Our personal recom-mendations are Valente’s (2010) Social Networks and Health; Wasserman and Faust’s (1994) Social Network Analysis; Carrington, Scott, and Wasserman’s (2005) Models and Methods in Social Network Analysis; and Scott and Carrington’s (2011) The Sage Handbook of Social Network Analysis. Courses in sociometric social network analysis are taught in many sociology, communications, and public health departments across the nation. Moreover, many highly useful software packages for social net-work analysis are available online, including UCINET (Borgatti et al., 2002), Gephi (Bastian, Heymann, & Jacomy, 2009), Pajek (Batageli, 1998), JUNG (O’Madadhain,

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Fisher, Smyth, White & Boey, 2005), NetworkX (Hagberg, Shult, & Swart, 2008) and the R network suite (R Core Team, 2013). Notably, the free R network suite is constantly being augmented by cutting-edge social network modelers from a variety of disciplines. A comprehensive list of options can be found online (http:// www.gmw.rug.nl/∼huisman/sna/software.html).

The availability of these packages has heled advance social network analysis because sociometric data are often cumbersome to analyze. Moreover, sociomet-ric data can be expensive to collect, and researchers often face challenges such as establishing an effective definition of the boundary of a population. In some instances, defining a boundary is a primary obstacle whereas it is a trivial matter in others. For example, to understand the social relationships in a high school, the school becomes the boundary and data are collected from all students in that school, including the students connections to one another. Such clear-cut bound-aries are not always so readily apparent in the context of social work science. In our work with homeless youth, we often struggle with how to bound this inher-ently transitory, changing, and open system of relationships. Marsden (2005) out-lined three generic boundary specification strategies. First, the positional approach is based on delineating formal membership in some community or organization, and then sampling from that list. The positional approach is typically used in so-ciometric studies of adolescents in school settings, which feature classroom ros-ters or other formal membership lists. The second boundary strategy is label the relational approach, and is based onfirst defining the key social relation of interest and then sampling individuals who share that relation. Heckathorn’s (1997) respondent-driven sampling is an example of such a technique and a strategy that is frequently used tofind hidden populations. The third strategy is the event-based approach, which is featured in the article by Barman-Adhikari and colleagues (2015). In this approach, a shared social or physical event is used to define an arbitrary boundary for an unbounded group. In Barman-Adhikari et al.’s study, membership in a network of homeless youth was defined by attendance at a par-ticular homeless youth drop-in center more than once during the month of data collection. A primary disadvantage of artificially bounding an unbounded net-work emerges if researchers have the mistaken impression that these data capture all aspects of the network, which is impossible given the definition of the network as being unbounded; therefore, biases of the missing data must be wrestled with conceptually always and empirically when possible.

The article by Barman-Adhikari and colleagues (2015) demonstrates the utility of the event-based approach in social work science. The authors collected socio-metric data from a network of homeless youth to understand how embeddedness in street life can facilitate substance abuse. The beneﬁt of sociometric analysis is its capacity to inform social work interventions in terms of how network dynam-ics affect the well-being of individuals and communities. Barman-Adhikari and

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colleagues further explored the nature of network embeddedness by calculating the k-core to which a given node belongs. K-cores refer to a minimal subnetwork of actors within a network who are connected to a minimum of k other actors in that subnetwork. Every node in the network can be assigned a particular k-core score, and this score can be subsequently merged with an existing behavioral dataset to examine how such a position is related to behaviors. In this case, Barman-Adhikari and colleagues found that youth with the highest k-core scores had formed a subnetwork of individuals in which methamphetamine use was far more prevalent than in other regions of the network. Of key importance is the effective identiﬁcation of what structural features of the network reinforce risk taking and then accounting for those network structures in intervention design.

Random Graph Analysis

Exponential random graph models (ERGMs) are a set of statistical models used with sociometric network data to assess the factors associated with the presence or absence of a particular tie and whether that tie cannot be attributed to chance alone. ERGM is used to estimate the effect of covariates on ties while examin-ing the dependence of these ties based on the covariate(s) of interest ( Jamali & Abolhassani, 2006; Valente, Fujimoto, Chou, & Spruijt-Metz, 2009; Wasserman & Pattison, 1996). Although the use of ERGMs is limited to dyadic understanding of networks ties, models can be developed without violating the required assump-tion of independence among actors (because network data is inherently relaassump-tional; Cranmer & Desmarais, 2011). Essentially, ERGMs work by deriving exponential families of distributions for each network examined (Holland & Leinhardt, 1981) to determine, based on a set of covariates, whether actors in the network are dis-proportionately related to one another.

The article by Bunger and colleagues (2014) provides an example of how such a seemingly esoteric modeling technique can be profoundly useful to social work science. Bunger and colleagues sought to understand how referral and staff-expertise networks evolved over a 2-year period in response to substantial new funding for a regional network of children’s mental health agencies. To do this, they used a longitudinal version of ERGM called stochastic actor-oriented modeling. This modeling strategy allowed the research team to assess exogenous effects (i.e., properties of the agencies, such as agency revenue) and endogenous network ef-fects (e.g., the existence of reciprocal ties at baseline) to examine which agencies were connected after 2 years. The models essentially generate coefficients for these endogenous and exogenous effects that can be interpreted in ways analo-gous to a regression coefficient. However, this extremely complex modeling strat-egy yields practical social work insights: “Agency directors can strategically use new funding as an opportunity to expand their network of partners. As evidenced in this study, an influx of funding for service expansion was accompanied by

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dramatic growth in partnerships” (Bunger et al., 2014, p. 531). Of key importance here is that the network model identiﬁed the mechanism primarily responsible for the growth of the agency partnerships.

Mixed-Method Network Analyses

Qualitative and quantitative methods can be merged in the context of social net-work inquiry to provide a rich understanding of social context and the mecha-nisms of change. This mixed-methods approach likely needs the least explanation because it involves using one or more of the techniques already discussed in con-junction with a qualitative analytic technique, such as semistructured interviews, focus groups, or ethnographic shadowing. The best such work tends to use quali-tative and quantiquali-tative social network data in conjunction to contextualize the social processes under investigation (e.g., Palinkas et al., 2011).

Henwood and colleagues provide an example of how social work science is aided by mixed-method network analysis. These researchers sought to understand how the social networks of homeless individuals entering Housing First programs and treatmentﬁrst programs might be differentially affected by these two struc-tural service interventions. They found that individuals in the Housing First in-tervention had a greater proportion of agency staff members in their networks, whereas those in the treatmentﬁrst program tended to have relationships with staff that grew more distant over time rather than closer. The role of these staff members in the participants’ transition from homelessness to being securely housed was expanded on in the qualitative analysis by one of the Housing First participants who described in moving detail how the case managers visited him in the hospital when he was sick, making him feel loved. As mentioned previously, Henwood and colleagues’ study has many insights about the value and role of consumer–provider relationships that will be of interest to practitioners.

In recent years, mixed-methods work has been used extensively in social net-work data collection (Palinkas et al., 2011; Rice et al., 2014). In such techniques, standard social network survey methods are augmented or replaced by coding qualitative interview data into social network data. This type of technique was used by Henwood and colleagues (2015) to generate their network dataset, wherein they coded egocentric network data gathered from the transcripts of semistruc-tured interviews they conducted with participants. They were able to do so because the interview protocol included a speciﬁc focus on social relationships, and the questions probed respondents for speciﬁc information about their social networks.

Conclusion

Although a brief overview such as this article can serve only as an introduction to the complexities of social network analysis, we hope that readers will be in-spired to join in this emerging use of social network analysis in the science of

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social work. These tools are ideally suited for researchers who are looking to explore avenues for social change, tailoring interventions to include a variety of network factors impacting behavioral health. The four social network articles introduced in this discussion provide four outstanding examples of the various ways that the techniques of social network analysis network can be used in the service of the science of social work and the generation of knowledge to beneﬁt human well-being.

Author Notes

Eric Rice is an associate professor in the School of Social Work at the University of Southern California. He is an expert in social network theory, social network analysis, and the application of social network methods to HIV prevention research.

Amanda Yoshioka-Maxwell is a doctoral student in the School of Social Work at the University of Southern California.

Correspondence regarding this article should be sent to Dr. Eric Rice, School of Social Work, University of Southern California, 1149 S. Hill St., Los Angeles, CA 90015 or via e-mail to [email protected]

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Submitted: May 13, 2015 Revision submitted: June 1, 2015 Accepted: June 1, 2015 Electronically published: July 9, 2015