Social Network Theory and Analysis: A Complementary Lens for Inquiry

Transcription

1 Journal of Sport Management, 2008, 22, Human Kinetics, Inc. REsearch methodology Social Network Theory and Analysis: A Complementary Lens for Inquiry Catherine Quatman University of Toledo Packianathan Chelladurai The Ohio State University As an emerging research approach, social network theory and analysis has been embraced and effectively applied in disciplines that have overlapping interests with sport management researchers including such fields as organizational behavior and sport sociology. Although a number of sport management scholars have investigated network-related concepts, to date no sport management studies have fully utilized the analytical tools that social network theory and analysis have to offer. In conjunction with a discussion about the ontological, epistemological, and methodological perspectives associated with network analysis, this article uses several examples from the sport management and organizational behavior bodies of literature to illustrate a number of the advantageous techniques and insights social network theory and analysis can offer. These examples are meant to provide a general understanding of the utility and applicability of the social network theory and analysis and potentially inspire sport management researchers to adopt a social network lens in their future research endeavors. Social Network Analysis A Complementary Lens for Inquiry As the recipient of the 2004 Earle F. Zeigler Award, Dr. Wendy Frisby eloquently challenged scholars in the field of sport management to embrace critical social science as a lens of inquiry (Frisby, 2005). Conveying concern that research in the field of sport management tends to be overly focused on the same theories and paradigms, Frisby stressed the need for and value in utilizing diverse topics and approaches to enhance our understanding. Frisby has not been alone in her assertions. A number of sport management researchers, including several other previous Zeigler award winners, have raised Quatman is with the Dept. of Health and Human Services, University of Toledo, Toledo, OH Chelladurai is with the Dept. of Sport and Exercise Management, The Ohio State University, Columbus, OH

2 Social Network Theory and Analysis 339 similar issues (e.g., Chalip, 2006; Olafson, 1995; Pitts, 2001; Slack, 1998). In fact, the October 2005 special issue of the Journal of Sport Management was dedicated to critical reflection on the constrained idea space (i.e., content and diversity of knowledge circulating) in the field and expanding the horizons of sport management research through innovative approaches. In many regards, the intent and content of this special issue demonstrated an emerging recognition of a need for looking beyond the dominant mainstream frameworks and approaches. As such, it is important to also recognize that in order for sport management to continue to evolve as an academic discipline, the search for and integration of alternative methods should be an ongoing process. In essence, as Amis and Silk (2005) expressed, [T]here is a need for a variety of ways of seeing and interpreting in the pursuit of knowledge; the more one applies, the more dimensions and consequences of the field can be illuminated. It is in this sense that we embrace an expansion of knowledge, of ways of seeking and interpreting through engagement with alternative ontological, epistemological, ideological, political, and methodological approaches to the study of sport management (p. 361). In recent years, a rapidly developing research perspective called social network theory and analysis has emerged as a promising research approach in a variety of disciplines; many of which overlap with the interests of sport management scholars. For example, in 2006, Academy of Management Review released a special topic forum directed toward integrating network analytic approaches into the management discourses. Studies incorporating social network theory and analysis have also emerged in such fields as recreation and leisure studies (e.g., Stokowski, 1990), tourism (e.g., Saxena, 2005), and sport sociology (e.g., Nixon, 1993). Although some sport management scholars have utilized social networkrelated theories and concepts (e.g., Babiak, 2003; Cousens & Slack, 1996; Cousens & Slack, 2005; Sagas & Cunningham, 2005; Frisby, Thibault, & Kikulis, 2004; Thibault & Harvey, 1997), to date no studies in the field have implemented the unique methodological tools social network analysis has to offer. Thus, embracing the encouragement of Frisby (2005), Amis and Silk (2005), and others, the purpose of this article is to fundamentally introduce social network analysis as a new and promising research lens to the field of sport management. The article begins with a general overview of some of the definitions and philosophical positions social network theory and analysis espouse followed by a discussion of a few specific topics and tools where network analysis could provide additional insight for sport management scholars. 1 Overview of Social Network Theory and Analysis Broadly conceived, the term network is often understood as the webs of relationships in which people or entities are embedded. In some senses, the word network is used to describe such things as organizations aligning together to form interorganizational networks or a type of flexibly designed network structure (e.g., the regional businesses of Silicon Valley) that an organization should embrace to remain competitive in today s business markets. From a different perspective, the phrase

3 340 Quatman and Chelladurai social network often takes on a metaphorical sense as in what someone should build to get a job or move up in the workforce. What many people do not realize, however, is that beneath the surface of these trendy metaphors, the term network can invoke much richer and more robust meanings and functions. In fact, an entire academic discipline related to the science, math, and application of this deeper utility and understanding of networks has emerged over the last quarter of a century or so. The practices and findings of this emergent discipline are often tied to the phrases social network theory and analysis which come together under an umbrella approach called the network perspective or network paradigm. 1 Concurrent with the advances made in the science and math behind the network perspective, a number of disciplines have embraced the techniques of social network analysis as it has widespread applicability for scholars and practitioners in fields ranging from physics and sociology to management, marketing, and education (Freeman, 2004). History and Evolution Although the network approach has only received recognition as a distinct research tradition over the last decade or so, many of its theoretical underpinnings and practices have been around for a long time. For example, the network approach s conceptual roots stem from a number of the structural ideas raised by well-known sociological thinkers such as Emile Durkheim, Georg Simmel and anthropologist Radcliffe-Brown (Freeman, 2004; Scott, 2001). Their research efforts often centered on understanding the structure and impact of relational webs or networks of social relationships between and among individuals, and the results of their studies ultimately inspired a desire and need in a number of scholars to translate the contextual metaphors of relational webs and networks to a more concrete and measurable area of study. Around 1933, driven by a special interest in understanding group dynamics, a psychiatrist by the name of Jacob Moreno and a psychologist by the name of Helen Jennings, developed the groundwork for a field of measurement called sociometry (Freeman, 2004; Wasserman & Faust, 1994). Sociometry essentially provided a means for depicting the interpersonal structure of groups using sociograms which showed people (or more generally any units of interest) represented as points and the relationships between units as lines connecting points in two-dimensional space. Before long, methodologists and mathematicians realized that these sociograms could be translated into matrices and analyzed using principles from graph theory; thus expanding the capabilities and insight the research approach could offer for scholars. Over the past several decades, a number of advances in sociological theory, mathematics, and computer technology helped the simplistic sociometric analyses of earlier times evolve into a much more sophisticated methodological approach called social network analysis. In fact, social network analysis as it is known today actually developed out of a bridging of practices in a variety of disciplines including anthropology, sociology, mathematics, and physics. As a result, both the approach and the applications are inherently interdisciplinary.

4 Social Network Theory and Analysis 341 Ontological, Epistemological, and Methodological Premises Ontologically, the network perspective encourages people to see the social world through a unique lens; particularly the relational properties present between and among entities. Epistemologically, social network theory and analysis suggest that we can come to know and understand the social world by taking the relational components of phenomena into consideration. Methodologically, social network analysis offers some unique tools to concretely measure and effectively analyze how the relational properties of a system affect a phenomena being studied. Emirbayer s (1997) Manifesto for a Relational Society and Wellman s (1988) Structural Analysis: From Metaphor to Substance offer fairly clear descriptions of how a network approach differs conceptually from other research perspectives. Emirbayer (1997) dissected sociological perspectives into two general approaches: a substantialist perspective and a relational perspective. 2 The substantialist perspective adopts the view that substances of various kinds (entities) constitute the fundamental units of the world and should serve as a starting point for systematic inquiry. In adopting this view, researchers often use units and levels of analyses corresponding to the attributes of autonomous, individual substances. Many of these studies employ what Emirbayer referred to as variable-centered analyses whereby conventional quantitative and statistical methods are used to study the associations among the attributes of the things, beings, or essences or the usefulness of one or more of the attributes in predicting the level of another attribute. Hence, using a substantialist perspective, researchers are often inclined to study the relationships between the attributes of substances rather than the actual, concrete relationships between the substances themselves. In contrast, researchers using a relational approach view the world as being comprised of systems of dynamic, unfolding relations rather than as static ties among inert substances. With this approach, the dynamic relations embedded within the unfolding processes become the primary units of analysis. Those that adopt a relational approach tend to believe that, Individual persons, whether strategic or norm following are inseparable from the transactional contexts within which they are embedded (Emirbayer, 1997, p. 287). In many cases, this is the type of view a number of qualitative research designs embody as they seek to understand cultures and phenomena from within a dynamic, contextual situation. Ultimately, Emirbayer provided a thorough account of the strengths and weaknesses of both approaches but makes a compelling argument toward the embracement and advancement of the relational perspective. Among other things, he provided a sound ontological and epistemological reasoning behind the theory and implications for a number of substantive and empirical applications. In particular, he makes a strong case for the value of social network theory and analysis noting that network methods are transactional or relational precisely because they involve a shift away from thinking about a concept as a singular categorical expression to regarding concepts as embedded in complex relational networks.... (p. 300). Wellman (1988) noted that while many social scientists profess to be studying social structure through attributional analyses, their inherent methodological individualism leads them to neglect social structure and the relations among

5 342 Quatman and Chelladurai individuals (p. 31). In his view, even some of the studies that do use a relational perspective often only employ a dyadic level of analysis. He argued that in using a dyadic approach, researchers still disregard structural form, making an implicit bet that they can adequately analyze ties in structural isolation, without reference to the nature of other ties in the network or how they fit together (p. 36). In essence, the network perspective espouses two general points of emphasis: (1) a consideration of the concrete relationships between entities over the relationships between their attributes, and (2) a focus on concrete social structure rather than isolated individual entities or dyads. Wellman (1988) expressed that over the course of time, network analyses have emerged as a distinctive form of social inquiry having five paradigmatic characteristics that provide its underlying intellectual unity (p. 20). The characteristics he described were: 1. Behavior is interpreted in terms of structural constraints on activity, rather than in terms of inner forces within units (e.g., socialization to norms ) that impel behavior in a voluntaristic, sometimes teleological, push toward a desired goal. 2. Analyses focus on the relations between units, instead of trying to sort units into categories defined by the inner attributes (or characteristics) of these units. 3. A central consideration is how the patterned relationships among multiple alters [actors] jointly affect network members behavior. Hence, it is not assumed that network members engage only in multiple duets with separate alters [actors]. 4. Structure is treated as a network of networks that may or may not be partitioned into discrete groups. It is not assumed a priori that tightly bounded groups are, intrinsically, the building blocks of the structure. 5. Analytic methods deal directly with the patterned, relational nature of social structure in order to supplement and sometimes supplant mainstream statistical methods that demand independent units of analysis (p. 20). A Complementary Approach to Inquiry As expressed by Denzin and Lincoln (2005), Guba and Lincoln (2005) and a number of other scholars, the integration of postmodern philosophies and various moments of qualitative, naturalistic inquiry have made it increasingly difficult to specifically and succinctly categorize research approaches into a particular paradigm or research tradition. The traditional distinctions between quantitative and qualitative research and the ontological, epistemological, and methodological assumptions they employ have collapsed into a blurring and blending of perspectives with an increased embracement of a desire to employ a wide range of interconnected interpretive practices, hoping always to get a better understanding of the subject matter at hand (Denzin & Lincoln, 2005, p. 4). The social network perspective tends to strongly reflect the blurring of paradigms as its ontological, epistemological, and methodological underpinnings draw

6 Social Network Theory and Analysis 343 from a variety of perspectives and philosophical traditions. For example, it is often noted that network theory and analysis can be located in or outside of conventional understandings of quantitative and qualitative research processes as they tend to intertwine quantitative and qualitative philosophies, data collection, analysis techniques and interpretation practices. Although, network analysis techniques can invoke a consideration of statistical relationships among variables much like mainstream quantitative methods, network analysis consists of a body of qualitative measures of network structure (Scott, 2001; p. 3). Further, by supplementing quantitative analyses with qualitative and graphical data the network approach tends to stay close to the data instead of working at a more abstract level as inferential statistics would compel a researcher to do (Kilduff & Tsai, 2005). Depending on the research question at hand and the philosophies and training a researcher possesses, social network theory and analysis can be viewed as a distinct research perspective or one that is used alongside some of the other broad research paradigms such as positivism, interpretivism, and critical approaches. Some studies only employ network theories or concepts while working with or within one of the other paradigms, whereas others adopt a network perspective in its entirety (i.e., from the philosophies behind it to the distinct methodological tools it espouses). Applying a Network Perspective Given the differences in emphasis, the network perspective offers some unique advantages to the research process. For example, network approaches allow for: (1) a concrete vitality for several difficult-to-define constructs an attribute which can greatly facilitate measurability and interpretation of data (Emirbayer, 1997; Wasserman & Faust, 1994); (2) simultaneous analysis of multiple levels of relational data thus providing some fluidity between micro-,meso-, and macro- linkages (Kilduff & Tsai, 2003); and (3) a unique integration of quantitative, qualitative, and graphical data producing an intuitive, thorough, and rich analysis of phenomena (Scott, 2001). To illustrate and further clarify these advantages, the upcoming sections provide descriptions of a few research contexts that lend themselves well for implementing a network perspective and an account of some of the processes associated with carrying out a network study. The purpose of these sections is to provide the reader with transparent examples and a basic understating of the applicability of the network approach. Research Contexts Social network studies often seek to uncover patterns of interaction between and among actors or entities in a system, determine the conditions under which those patterns arose, or attempt to identify the consequences of the structural patterns. The utility and applicability of social network theory and analysis is very broad and has been embraced by researchers in a number of fields. Several papers and texts provide quite extensive reviews and a variety of contextual examples of the uses of social network theory and analysis for research purposes such as: (1) Blackshaw and Long (1998) for leisure and tourism; (2) Brass, Galaskiewicz, Greve, and Tsai (2004) and Parkhe, Wasserman, and Ralston, Kilduff and Tsai (2005) for management and

7 344 Quatman and Chelladurai organizational behavior topics; and (3) Iacobucci (1996) for marketing contexts. Although an in-depth review of how other fields have employed social network analysis and the insights they have gained as a result of such studies is outside the scope of this article, we will attempt here to provide several examples of contexts and ways social network analysis might be relevant to topics of interest for sport management scholars. For example, Stern (1996) discussed how network concepts can help us understand the differences between cooperation, competition, and conflict in organizational relationships with specific implications for relational marketing. From a different perspective, Nixon (1993) tendered a number of sport-specific examples of how social network theory and analysis might provide unique insight for sport sociology and other related fields pertaining to such topics as coaching burnout, organizational analyses, and racial stacking. For example, Nixon (1993) noted how the kinds and amount of support flowing from coaches social support networks can impact their interactions, behavior, and attitudes. He further expressed: It would seem fruitful... to use a network approach to combine managerial recruitment and stacking research traditions with the tradition focusing on the social contact theory of racial integration (e.g., Chu & Briffey, 1985) to determine how the racial composition of teams, stacking, and various dimensions of social relation. (p. 319). For those interested in organizational behavior and management topics, probably the most popular and notable applications of social network theory and analysis are embodied by the notion of social capital. Generally, social capital is fundamentally based upon the value and benefits of social connections. The network-related organizational and management literatures offer some interesting insight in such contexts as how people get jobs and how they can move up the workforce hierarchy (Brass, 1995; Brass et al., 2004). Within these topical areas, the organizational behavior literature also taps into several different workforce diversity issues. For example, Mehra, Kilduff, and Brass (1998) found evidence that racial minorities are often clustered in the peripheries of organizations networks, and Brass (1985) found evidence that gender segregation is present in the informal networks of organizations. Other applications of a network perspective include work on strategic alliances and interorganizational partnerships (e.g., Burt, 1992; Uzzi, 1997), board interlocks (e.g., Mizruchi, 1996), flows of information and diffusion of innovation (e.g., Rogers, 2003), and power and influence (e.g. Brass, 1985; Burt, 1992). Scholars have also considered how the informal networks of an organization can affect the workflow in an organization (Brass et al., 2004; Krackhardt & Hansen, 1993). In addition, using a network perspective, researchers have been able to explain variance in such traditional organizational outcomes as individuals performance, job satisfaction, job commitment, turnover, group structure, leadership effectiveness, and the opportunities and constraints on ethical behaviors (Brass, 1995; Brass et al., 2004). Given the breadth of work carried out in fields related to sport management, it seems that social network theory and analysis could be very useful tools for sport management scholars. In fact, several scholars from the field of sport management

8 Social Network Theory and Analysis 345 have already investigated network-related concepts in some of these areas. For example, consider the studies of Cousens and Slack (1996, 2005) who investigated interorganizational networks in North American professional sport leagues. These two papers make compelling arguments for both the theoretical value and insight provided by the network theories. Nonetheless, while both articles were insightful and progressive in their own right, neither fully integrated the methodological tools supplied by network analysis to analyze and interpret the data; many of which were not even available when the 1996 article was written. Through the use of specific network methods, their work might be expanded to include a more extensive, intuitive, and direct means of analyzing, interpreting, and reporting the network-related concepts their studies investigated. Similarly, Babiak (2003) conducted a case study on the dynamics, challenges, and complexities of interorganizational partnerships of a Canadian Nationals Sport Centre. Given the complex nature of the study s broader interests, Babiak (2003) opted to use a dyadic level of analysis rather than a network level of analysis in her investigation although she did emphasize the importance of considering network features beyond the dyadic level. In fact, she noted that a network analysis may very well have been an effective and compelling method to have used. In a different context, Sagas and Cunningham (2005) considered network structural properties and the role race plays in the differences in career success of assistant football coaches. Working within a positivist frame but using a critical lens, their work used a postitivistic, quantitative approach for analyzing various network properties. In essence, they used a variation of what is referred to in the social network literature as an ego-centric approach. 3 While frequently used and effectively applied, the ego approach actually violates some of the deeper philosophies of a true relational approach. Namely, it focuses only on the direct ties of a person s contacts, and ignores the person s indirect ties and ties amongst an individual s contacts. In other words, like Babiak (2003), their approach can be likened to studying multiple dyadic relationships around a single subject. Consequently, their work could easily and effectively be expanded using various methodological tools the network paradigm offers. Having said these things, in no way do we mean to take away from the quality or findings of any of these scholars works as they are quite novel and are consistent with the findings and practices often used in the organizational and management discourses. We are merely attempting to show how the ideas they suggested might be replicated and extended in future studies using some of the more sophisticated methodological tools the network approach provides. The sport management studies listed here investigated a number of the well-developed network concepts and theories, however, they did not employ social network analysis per se. In the forthcoming sections of this paper, we will draw upon these examples to demonstrate and model the advances and extensions social network analysis could provide for future research endeavors. Operational Practices The primary source behind the methodological advantages that social network theory and analysis provide is a novel application of graph theory. Using the graph theoretical principles of points to represent actors in a system and edges to represent

9 346 Quatman and Chelladurai relational ties between the actors in a system, social network analysis fosters a unique mathematical formalism as well as provides a concrete and relatively intuitive means for studying the relationships among actors. In a network approach, actors can be characterized by any type of entity embedded within a larger system of entities (Wasserman & Faust, 1994). In the social sciences, the entities of interest are often individual people or groups of people acting as a unit (e.g., individuals in an organization, organizations in a market, markets in an industry, etc.). In a network approach, researchers also have the freedom to operationalize the ties or relationships of interest between the actors. For example, a researcher might investigate such things as friendship ties between employees in an organization or resource exchange ties between organizations in a market. Under these operational definitions, the corresponding edges and nodes can then be modeled, quantified, and analyzed to investigate a network s structural properties. Defining a social system and studying phenomena in these regards can be somewhat liberating for a researcher because it imparts a universal lens for defining social structural properties (e.g., density, cohesion, embeddedness) across time, space, and context. In this way, the social network perspective provides a formalized vocabulary to represent relational concepts and structural properties in precise and consistent ways. In fact, as Wasserman and Faust (1994) asserted, The methods of network analysis provide explicit formal statements and measures of social structural properties that might otherwise be defined only in metaphorical terms (p. 17). This precision and consistency of vocabulary allows for a unique opportunity to integrate formal mathematical models as a basis for empirical testing and theoretical development. Incidentally, it is useful to use the graph theoretical premises to clarify how a network approach differs from traditional approaches in its underlying assumptions. In Figure 1a, individuals and dyads of individuals are shown as embedded within a larger network structure and, thus, the structure of a social system possesses Figure 1a A network illustration with the direction and intensity of ties.

10 Social Network Theory and Analysis 347 some very unique features. For example, there are a number of nodes that are more isolated than others (e.g., 6, 25 and the dyad of 11 and 14), several nodes which possess more ties to different nodes than others (e.g., 3, 5, 18, and 19), and a few nodes that possess more central positions in the network than others (e.g., 3, 15, and 19). The network view fundamentally asserts that these varying features could potentially have significant implications on phenomena of interest and therefore should be taken into account. Social network approaches also allow researchers to investigate several different attributes of relational ties between actors. Thus, instead of simply considering whether or not a tie is present, a researcher can examine additional implications from network configurations. For example, a network investigation can incorporate such things as the intensity (often measured by strength or frequency of interaction) and direction of ties (often used to represent the direction of effect). In Figure 1a, intensity is represented by the thickness of lines, however, the intensity can actually be quantified as a continuous variable for more complex analyses. In addition, a single population of actors can also be used to examine the multiplexity of ties between actors. The multiplexity of a tie refers to the extent to which two actors are linked together by more than one relationship. For example, a network of employees can be drawn to include multiple ties at once such as lines representing friendship ties and lines representing instrumental ties. Figure 1b illustrates a network diagram with the consideration of multiplex ties. Imagine the dashed lines to represent one type of relationship (e.g., information exchange), the dotted lines to represent another type of relationship (e.g., friendship), and the solid lines as still another type of relationship (e.g., proximity of desks). The attributes of the ties (i.e., directionality, intensity, and multiplexity) do not have to be considered mutually exclusively. That is, a network can be examined from any and all of these perspectives simultaneously. Figure 1b Illustration of a network with multiplex ties.

11 348 Quatman and Chelladurai Sampling Although random sampling is critical to most conventional studies, it is often not of interest or particular use in many network studies. Wasserman and Faust (1994) noted that contrary to random samples, network studies often necessitate full data on the presence or absence of social relations among all, or at best, most of the members of a bounded population. Therefore, one of the major threats to the validity of any network study is a researcher s determination of boundary specification for the actors to be included in the analysis. In other words, an imperfect representation of the true underlying structure is based upon the extent to which actors who may indeed be relevant to the construct of interest are ignored. A dataset that is missing actors who actually serve as key structural people in the network (e.g., a person like node 3 in Figure 1a.) can potentially portray a very distorted representation of the true structural configuration. Thus, the structural quality of the participants in the study tends to be of greater importance than the quantity or random assessment of participants. 4 Network scholars have developed a number of strategies and techniques for actor enumeration and boundary specification (see for e.g., Laumann, Marsden, & Prensky, 1983; Scott, 2000; Wasserman & Faust, 1994). Data Collection Much like conventional studies, network analytic methods can employ a number of different approaches for gathering data including (but not limited to): questionnaires, interviews, observations, archival sources, and experiments. The main difference between network data collection methods and conventional methods is the type of data and phenomena the instruments are designed to capture. For example, on a questionnaire or in an interview, a researcher might ask such questions as who do you go to for advice and how often do you go to that person for advice? Using an observation approach, a researcher might watch for behavioral examples of relationships such as which people talk to each other and how often they talk to each other. Analysis As a network approach deals with unique theoretical ideas and questions that are very different from the conventional approaches, traditional statistical and data analytic procedures are generally not directly applicable for exploring and testing network data and theories. Consequently, network analysts have developed a body of methods specifically designed for investigating relational concepts and properties. These methods offer some unique analytical advantages. For example, one benefit of embracing a network perspective is the ability to simultaneously include multiple levels of analysis of relational data. The network perspective allows for such an analysis because it assumes that the world is comprised of networks of networks. Therefore, a researcher can analyze networks within networks at the same time within a single study as illustrated in Figure 2. In any case, two broad approaches are used for analyzing and interpreting network data: visualization and quantification. The first approach, visualization, should be relatively apparent as it was used earlier in articulating the characteristics of the network paradigm. Analysis from this approach entails visually inspecting

12 Social Network Theory and Analysis 349 Figure 2 Illustration of a network within a network. the data for meaningful patterns. To aid in the visualization process, many social network software packages offer drawing tools which use various algorithms to find ways of drawing networks so that structural patterns are easier for the human eye to catch. 5 The programs also usually provide ways for manipulating the views and extracting parts of the network to allow a researcher to focus in on areas of interest. This is particularly useful when the number of actors and ties in a network of interest are rather large. For example, Figure 3 provides a visual image of a randomly generated network of 1,000 actors in the software program Pajek obtained under the Fruchterman Reingold 2D layout. While working in the software program, we can zoom in on certain areas and extract out parts of the network to investigate the structural features in greater detail. To illustrate the utility of visual analysis, consider some of the features of Figure 3. It is clear that there is a large relatively connected group of nodes (located in the center); there are a number of nodes which are isolates or outliers from the larger connected main network; and some nodes are connected to other nodes but they are not collectively tied to the larger connected network group (these appear as smaller overlapping groups of nodes tied together but not tied to the larger network group). Hence, one conclusion that may be drawn from even this superficial observation of the network is the fact that although a number of isolates and disjointed subgroups are present in the network, there is one connected group of actors which is significantly larger than the rest of the groups. 6 In other words, let us say this picture represented the data corresponding to the informal friendship network of a sport organization, and you were interested in studying where the women and racial/ethnic minorities fall amongst the nodes. You could add an attribute partition (i.e., dummy code the nodes into colored groups) and see where the nodes that correspond with your various groupings fall in the picture. A pattern might emerge (similar to that of Mehra et al., 1998 or Brass,

13 350 Quatman and Chelladurai Figure 3 Illustration of a randomly generated global network. 1995) where the women and racial/ethnic minorities are grouped into certain areas of the structure (e.g., mostly isolates or in the periphery of the network). Although visualization can be an excellent tool, it can be somewhat difficult to draw conclusions and make sense of a network simply through visual inspection. Visualization can be especially challenging for networks with a large number of actors or networks that include the intensity, directionality, or multiplexity of ties. To address these concerns, social network analysis provides a means for quantifying many of the structural features of a network. Network quantification stems from the ability to translate the network diagrams into actor-by-actor sociomatrices. To demonstrate, in a dichotomous relationship between actors, a 1 can be inserted into all boxes in the matrix where a relationship is present between the actors and a 0 can be inserted where there is no relationship present. Table 1 displays how dichotomous relationships between actors 1-7 in Figure 1a would be translated into a sociomatrix. The same approach could be followed to translate the direction of ties such that a tie directed from one actor to the next would equate to a 1. Likewise, to incorporate the intensity of ties, you would follow the same procedure only the value of the numbers would follow a continuous pattern of values (e.g., 1 to 5). Social network software programs can use algorithms to read and manipulate the sociomatrices obtained for calculating various structural properties.

14 Social Network Theory and Analysis 351 Table 1 Translation of Actors 1 7 from Figure 1 Into a Sociomatrix Exploring obtained network structures through the quantified measurement techniques allows researchers to be much more concise as well as precise in their interpretations. However, at times, the outputs of the quantified measures can also become unwieldy and somewhat abstract. Therefore, combining visualization and quantified assessments throughout the analysis process tends to provide the best conceptual understanding of a network s patterns and allows the researcher to stay close to the data. To provide some context for the relevance of such visualization and quantification techniques, we draw upon the work of Cousens and Slack (1996). Throughout the article, the authors describe a number of ego-networks (one focal actor and the ties that actor possesses with other actors) and the antecedents leading to the establishment of new ties. A majority of the examples are described in words rather than visuals or numbers. The use of visualization and quantification techniques might have increased the intuitive understanding of the phenomenon as well as the ease of analyzing and interpreting the data. In addition, the richness in conveying the examples might also have been improved through the integration of the representation of the multiplexity, intensity, and directionality of ties in a global rather than ego-network approach which are facilitated by the recently developed analytical software and algorithms. As another example, consider the work of Babiak (2003) which might be extended to consider how the concrete structure of an organization s place in the network lends support to or deters the organization in terms of power and gatekeeping roles. If Figure 1a were to represent a network of organizational partnerships, nodes 8 and 10 could possess very different constraints and opportunities than say nodes 21 or 25 as they would be in a strong position to take advantage of serving as a broker or gatekeeper between other nodes in the network. Sport management scholars might also consider the social network literature on informal networks within an organization. While managers often pride themselves on their extensive knowledge and understanding of the strengths and weaknesses of their employees and their acute sense of who gets along with who and who works well together, the reality of their perceptions are often superficial at best (Krackhardt & Hanson, 1993). Krackhardt and Hanson (1993) contended that using social network analysis, managers and researchers alike can translate fairly accurate information about the informal networks into maps showing how work and advancement actually take place in an organization.

15 352 Quatman and Chelladurai In these regards, imagine Figure 3 to represent data collected about the informal networks of employees in an organization. The lines between nodes (i.e., individual employees) represent friendship ties among them. Given this informal network structure, we could attempt to answer such questions as does someone s location in the informal network relate to their overall job satisfaction (i.e., are isolates less satisfied than those in the more central parts of the network)? Likewise, as has often been postulated, social network analysis provides a means for operationalizing the good old boys network. General Connectivity Patterns and Obtaining Structural Variables In general, almost all network studies are first concerned with various aspects of the general connectivity patterns of an obtained network structure. With a general understanding of the connectivity patterns in a network, a researcher can gather a sense of what additional properties are important to explore in greater depth. Table 2 provides a list (though not exhaustive) of some of the general connectivity considerations a researcher may choose to explore through quantification and visualization measures. In many cases, almost all of the properties assessed using social network software produce distributions of structural features which can be translated into structural variables. For instance, one might be interested in seeing if the salary of an employee is significantly related to the number and type of ties an employee possesses in the informal network. Pajek enables a researcher to obtain distributions for a number of nodal structural properties (e.g., in-degree or centrality) as well as a distribution of things such as node attributes (e.g., salary). The resulting distributions can then be imported into conventional statistical software programs such as SPSS and SAS and used in the form of traditional quantitative analytical techniques. Timing and Network Dynamics Ontologically, social network analysis assumes that networks are almost always dynamic in nature and continually changing. That is to say, new actors are continually being added to the network, others may stop being active in the network, and the relationships between any two actors may cease to exist at any point in time. This point was greatly emphasized in Cousens and Slack (2005) as they explored the evolution of field-level change in North American major league professional sport over time. Hence, timing and network dynamics are important considerations in many network investigations, and this is yet another area where the methodological developments of the social network paradigm can be quite useful. One simple technique for incorporating time analyses is to block the data into designated time periods. Figures 4a-c provide illustrations of a hypothetical process of network evolution from a random generation process. Of course, the actual changes in network structure for real-world data may or may not exhibit structural trends similar to the randomly generated networks. Nonetheless, these illustrations do provide a thematic similarity to some of the structural trends in the inter-organizational networks described by Cousens and Slack (1996) and (2005); namely increases in the number of partnerships and a tighter system of coupling (increases in the density of ties between organizations in the field).

16 Social Network Theory and Analysis 353 Table 2 Network Analysis Considerations Single Network Considerations Degree Number of direct links with other nodes In-degree Number of directional ties leading to the node from other nodes (incoming ties) Out-degree Number of directional ties coming from the node toward other nodes (outgoing ties) Isolate A node which has no links or relatively few links to other nodes Closeness Extent to which a node is close to or can reach all other nodes in the network Betweenness Extent to which a node serves as a mediator or a necessary connector between two other nodes Star An node that is highly central to other nodes, which in turn are not highly connected to each other (e.g., actor C in Figure 1 would be a star) Peripheral actor A node that is located on the outer parts of the network as compared to all other nodes Central actor A node that is located in the inner parts of the network as compared to all other nodes Partial Network Considerations Dyad The relationship between two nodes in a network Triad The relationship(s) between three nodes in a network Symmetry The reciprocity and direction of ties Component Connected subset of network nodes and links Subgroups The presence of connected (and in some cases densely connected) subsets of nodes Whole Network Considerations Density Ratio of the number of present ties to the number of possible ties in the network Size Number of actors in the network Connectivity or reachability The extent to which actors in the network are linked to one another by direct or indirect ties (the ability to reach one node from another) Cohesion The extent to which a network can remain connected even when various nodes are removed from the network Conceptualizing Social Influence and Diffusion Patterns The network approach is also useful for conceptualizing processes of social influence and patterns of diffusion across a system of actors. In most cases, the obtained structure of any network analytic study can be viewed as an underlying structure for the transfer of anything through a system of actors. For example, it is useful for studying such things as diffusion of innovation across organizations, the spread of a rumor through employees in an organization, or something such as word-of-mouth or socialization processes in consumer behavior. In the case of Sagas and Cunningham (2005), this might have played out in terms of a person s social network of contacts serving as sources or references for job opportunities.

17 Figure 4a Illustration of network evolution stage 1. Figure 4b Illustration of network evolution stage 2. Figure 4c Illustration of network evolution stage

18 Social Network Theory and Analysis 355 Three common considerations in network diffusion studies include: the presence of multiple paths, clustering patterns, and the role of structurally significant actors. The presence of multiple paths in a network (i.e., connectivity patterns that allow you to reach one node from another in more ways than one) can significantly increase the likelihood of diffusion (Rogers, 2003; Moody & Leahey, 2006) in that multiple paths allows for information (or whatever the topic of interest is for the researcher) to spread even if a particular node or tie does not contribute to the diffusion process. Multiple paths can also increase the inclination of an individual to adopt because of the possibility that more than one of their social contacts have already adopted. From a different perspective, scholars also contend that relationships in realworld networks tend to cluster or clump around certain features (Moody and Leahey, 2006). For example, in the informal networks of an organization, there might be various cliques or social circles that can be differentiated. As such, network clustering can make diffusion through a network lumpy. That is, while an innovation can diffuse fairly easily within the clusters, certain actors in a network might have to serve as brokers to connect two or more clusters in order for an innovation to continue to spread (which can potentially slow or even stop the progression of diffusion). For example, as mentioned earlier, nodes 8 and 10 in Figure 1a, might serve as the best bridge for an innovation to diffuse from the bottom half of the cluster (nodes 9, 10, 15, 16, 17, 19, and 21) to the top half of the cluster (nodes 8, 12, 13, 18, and 22). It is also common to consider the substantial influence of certain actors who are located in positions that are structurally more accessible to elements in the network as well as being conduits for the spread of things through the network. Conversely, certain actors might be located in structurally disadvantaged places for both spreading and receiving information. In this regard, a network calculation that is useful for studying diffusion properties is closeness centrality, an index of how close the actor is to all of the other actors in a set. The more an actor is considered central, the more the actor is located in an advantageous location. In contrast, a peripheral actor is in a disadvantageous location in terms of access to information. Pajek makes the assessment of centrality measures extremely easy and very intuitive. Although these measures are continuous in nature, one can partition the results into ranks and then have the program diagram the partitions with the ties in tact. Figure 5 provides a visual image of the closeness centrality scores assessed on a randomly generated network. Moreover, the distributions obtained during these assessments can be imported into conventional statistics packages to study such things as the correlation between centrality and other variables of interest. 7 Network manipulation also allows us to identify cohesive subgroups (i.e., clusters of densely connected individuals within a network). The premise here is that members of a cohesive subgroup are likely to communicate with one another frequently either directly or indirectly through intermediaries within the subgroup. Therefore, the transfer of information between individuals in a cohesive subgroup is more likely to occur than between isolates or individuals who are not in the cohesive subgroup. Figure 6 provides a visual image of the type of graph one might obtain through network analysis.

19 Figure 5 Illustration of closeness centrality partitioned into 10 categories. Figure 6 Illustration of several cohesive subgroups. 356

20 Social Network Theory and Analysis 357 Summary and Conclusions Social network theory and analysis provide leverage and insight for philosophically, theoretically, and empirically investigating a diverse range of questions. The description of applications and methodological tools provided in this paper are by no means exhaustive or comprehensive in terms of the utility of social network theory and analysis. It is also important to note that the intent of this paper is not to suggest that the traditional approaches and methodologies be abandoned but rather to encourage the integration and synthesis of both traditional research approaches and the network perspective for a greater understanding of the multi-faceted dimensions and topics of interest to sport management scholars. Sport management researchers philosophical views of the utility, strengths, and weaknesses of social network theory and analysis will likely vary greatly depending on the ontological, epistemological, and methodological stances to which they subscribe. In reading this paper a number of scholars may question the unique values that social network analysis may be able to offer or be unconvinced that network analysis can move beyond simply describing relationships. However, we believe that most scholars who read this paper will be able to find ways to beneficially integrate social network theory and analysis into their future research endeavors. It is hoped that in the near future scholars would undertake the application of network theory to investigate the phenomenon of their interest. Such work would be the first to demonstrate the relevance and utility of social network theory and social network analysis to sport management. In doing so, we strongly encourage those who might undertake a social network approach to go beyond simply describing the relationships that they uncover. The greatest breakthroughs and most significant contributions are likely to come from those who find ways to think, theorize, and find appropriate applications that consider the nature of the relationships that exist and what those relationships might hold for the phenomena they are seeking to understand. In other words, researchers applying the network analysis should go beyond the description of relationships among entities of interest and attempt to explain the how and why of the observed relationships and the factors (e.g., power dynamics) which forge the observed relationships. In addition, we believe that social network analysis of phenomena of interest in sport management can contribute to knowledge generation in other fields of study because both social network analysis and sport management are interdisciplinary in nature. Although the field of social network analysis itself draws collaboration from sociologists, mathematicians, physicists, and computer scientists, sport management serves as a catalyst in bringing together applied fields such as physical education, health education, fitness promotion, recreation, and coaching and theoretical fields such as sociology, psychology, philosophy, communications, organizational theory, organizational behavior, and marketing. Furthermore, as Wolfe et al. (2005) articulated, sport provides opportunities to observe, accurately measure, and compare variables of interest over time and to test hypotheses with highly motivated respondents in quasi-laboratory conditions (p. 185). For these reasons, sport management network studies could serve as a veritable nexus for the advancement of knowledge and collaboration of scholars across the boundaries of traditionally bounded disciplines.