Download Trust as a Moderator of In-Degree Centrality in the Context of

The Centrality Efficiency Index: A New Social Network Analysis Measure
Scott Droege, Ph.D.
Western Kentucky University
Department of Management
1906 College Heights Blvd. #11058
Bowling Green, KY 42101-1058
Phone: 270-745-6033
E-Mail: [email protected]
Lily C. Dong
Assistant Professor of Marketing
University of Alaska
School of Management (Marketing Area)
P.O. Box 756080
Fairbanks, AK 99775
Phone: 907-474-1993
E-Mail: [email protected]
ABSTRACT
This research develops a new measure of communication efficiency—the centrality efficiency
index (CEI)— be examining the ratio of actual centrality to potential centrality. The CEI has two
purposes. One, it can be a useful measurement for calculating communication flow efficiency
through social networks with respect to central actors, Two, it provides a way to calculate the
degree to which trust moderates closeness centrality of actors responsible for dispensing
sensitive information to actors with lower degrees of centrality.
2
Introduction
Social network centrality measures contribute to our understanding of communication flows
within social structures (Ibarra, 1993). In general, centrality refers to actors who are in a central
position within a social network (Brass, 1995). Although a number of centrality measures have
been proposed, the present research focuses on one specific centrality measure, closeness, which
is a global measure of an actor's centrality (Poulin, Boily, & Mâsse, 2000).
There are two goals of this research. One is to develop a useful measurement for
calculating communication flow efficiency through social networks with respect to central
actors. The second goal is to provide a method to calculate the degree to which trust moderates
closeness centrality of actors responsible for dispensing sensitive information to actors with
lower degrees of centrality.
The research is organized into four sections. First, a theoretical overview of the role of
centrality and trust in the communication process is provided. Second, propositions are
developed regarding trust as a moderator of closeness centrality; that is, trust moderates the
relationship between communication flows and the closeness centrality possessed by an
organizational actor. Further, the CEI and its use in gauging the extent to which trust provides
this moderating relationship are proposed. Third, managerial implications and future research
directions are suggested.
Theoretical Background
This section focuses on three areas: (1) closeness centrality in social networks; (2) vulnerability,
trust, and opportunism; and (3) intra-organizational communication flows.
Closeness Centrality
Operationally, centrality is the number of ties an actor possesses to others in a social network.
This is further weighted by the number of ties the latter actors possess to other actors (Emirbayer
& Goodwin, 1994). Centrality explains the relative connectedness of an actor. For example, if
one considers communication flows in a social network, an actor high in centrality would have
access to a large amount of information by virtue of his or her central position. Communications
with others would be "close" to the actor with high centrality. Even though communication may
not flow directly to the central actor, that actor would have access to the information via the
closeness of others to whom the actor is connected.
Closeness centrality further defines centrality by specifying the position that an actor
occupies in a social network. It indicates reachability; that is, an actor's ability to easily reach or
connect to others by being connected closely enough that the actor has access to others’
information. Closeness centrality is a straightforward measurement that simply calculates the
average of the direct and indirect links to all others in the network relative to the focus actor
(Brass, 1995).
Vulnerability, Trust, and Opportunism
Vulnerability may be viewed as two side of the same coin. On one side is trust. Doney, Cannon,
and Mullen refer to trust as the "willingness to rely on another party and to take action in
2
3
circumstances where such action makes one vulnerable to the other party" (1998: 604). This
assumes rationality on the part of the trustor: "The elements confronting the potential trustor are
nothing more or less that the considerations a rational actor applies in deciding whether to place
a bet" (Coleman, 1990: 99). In other words, trust can be viewed as the rational choice to make
oneself vulnerable to another. If one willingly becomes vulnerable, then a rational actor would
only place himself or herself in that vulnerable position if he or she believed that positive, or at
least neutral, outcomes would result.
The other side of the coin is opportunism, defined by Williamson's (1975, 1981) wellknown phrase of self-seeking with guile. Although Williamson's unit of analysis focused on
interfirm interaction and contract law, the basis of his approach in transaction cost analysis
allows one to consider opportunism from an intraorganizational level—the level of analysis that
is considered in this paper. Williamson (1981) suggests that the two behavioral assumptions of
bounded rationality and the potential for opportunism give rise to the ever-present potential of
vulnerability. When an actor willingly exposes himself or herself to vulnerability, that individual
has chosen, whether consciously or not, to trust another (Eisenhardt, 1989) and become exposed
to opportunistic behavior. Thus, the threat of opportunistic behavior provides a disincentive to
trusting behavior.
To avoid oversimplifying the issue, one must recognize that trust and opportunism have
affective and cognitive components (Smith, Haynes, Lazarus, & Pope, 1996) and involve more
than rational decisions as might be inferred from Williamson's (1975) definition. Indeed,
cognitive trust can serve as an antecedent to affect-based trust (McAllister, 1995). Affective trust
involves the emotional processes of care and concern for others; cognitive trust involves one's
beliefs regarding the dependability and reliability of others (Kramer, 1999; McAllister, 1995)
and is more similar to the rational actor perspective of trust.
Trust forms by a variety of mechanisms. In some situations, an actor trusts another based
on the other's degree of perceived reliability (Kramer, 1999; McAllister, 1995) or the belief that
the other's intentions show concern (Ring & Van de Ven, 1994). In other situations, it is not the
individual per se in whom trust is placed. Rather, it is the specific context of the communication
that regulates the degree of trust. For example, the explicit role served by one in whom trust is
placed can serve as a basis for trust (Kramer, Brewer, & Hanna, 1996) as well as the perceived
reliability and competence of the one in whom trust is placed (Szulanski, 1996). Burt and Knez
(1996) suggest that the necessity for an actor to maintain his or her reputation serves as a basis of
trust. Further, organizations may impose formal sanctions that discourage actors from taking
advantage of the trust placed in them (Shapiro, Sheppard, & Cheraskin, 1992). Another cognitive
trust formation mechanism occurs when trust is based simply on another's similarity to oneself.
The assumption is that similar others are more trustworthy than nonsimilar others (Jones &
George, 1998). Finally, "institutional trust," or the social norms and environment of the
organization, can engender trusting behavior (McKnight, Cummings, & Chervany, 1998).
Intra-Organizational Communication Flows
The flow of communication within an organization can have far-reaching effects. Obtaining
crucial information when needed is an issue of major consequence (Zander & Kogut, 1995). The
efficient flow of communication from one actor to another reduces the time one must spend
searching for critical information (Zack, 1999). Efficient access to information thus enhances the
downstream productivity of organizational activities. Opportunism can interfere with efficient
3
4
communication of information among individual actors. Williamson suggests that opportunism
may take the form of "strategic manipulation of information" (1975:26). When this occurs, trust
declines in the actor who acted opportunistically. Future transactions with that actor will tend to
be avoided, even if that actor holds an otherwise central position.
Propositions
Trust has been recognized as an influential component of social exchange and
cooperation in which "trust lubricates cooperation" (Nahapiet & Ghoshal, 1998), with low trust
inhibiting cooperative behavior (Gambetta, 1988). Individuals in low trust situations may
consider the risks of opportunism from another party to be greater than the potential benefits
derived from transferring crucial information to others (Jones & George, 1998). In Szulanski's
(1996) discussion of "internal stickiness," she suggests that difficult relationships among
individuals are a primary impediment to transfer of best practices. Similarly, the current research
suggests that relationships characterized by low trust result in rerouting of communication flows
through actors who are higher in trust but less central in a social network. Low trust results in
communication that must flow through potentially longer, less efficient routes. In these
situations, a possible negative effect can be the inefficient transfer of information among
organizational actors.
Buskens (1998) adds to this the role of trust in buyer-seller situations. Viewing trust as
the dependent variable, he examines in-degree and out-degree centrality metrics of information
accessibility and suggests that the level of centrality degree, both in-degree and out-degree,
influence trust. We propose an extension of this line of thinking: trust influences centrality and
serves as an antecedent moderating variable of centrality measures.
The specific centrality measure on which this research focuses attention is closeness
centrality due to its function as a global evaluator of centrality (Freeman, 1979). As a measure of
reachability, closeness is a centrality measure that explains an actor's ability to easily connect to
others. In other words, closeness centrality explains the links within a network placing an actor
in a central location such that he or she has access to information and could potentially pass that
information along to others. Higher closeness centrality requires fewer links or steps necessary to
move information from one location to another. Although closeness does not require that an
actor be situated between two others, it determines how accessible others are by means of direct
and indirect links within a network. The average of the direct and indirect links to all others in
the network determines an actor's closeness centrality (Brass, 1995).
The transfer of information to an actor with high closeness centrality involves the risk
that the actor will use the information opportunistically. For example, to gain power, the actor
may fail to pass along the information in its completeness to downstream actors who are
ultimately dependent on this central actor for the information. An actor may believe that the risk
of opportunism outweighs the benefits of using the closeness actor as a communication conduit.
The former actor may either withhold information or find an alternate route to the deliver the
information to the end user. With the development of alternate communication routes, the
closeness actor's necessity for communication declines in importance. As alternate
communication routes are formed, the closeness actor becomes less central to communication
within the network. That actor's closeness centrality subsequently declines.
Low trust in a closeness actor creates a downward spiral of information inaccessibility.
When trust is high, others have confidence that the closeness actor will not behave
4
5
opportunistically with information gained through the network. On the other hand, if trust is low,
actors will bypass that actor and develop alternate routes of communication. Communication
patterns will form that decrease the importance of the closeness actor's position. As trust
decreases and the actor is bypassed, that actor's closeness centrality decreases.
When trust is high, an actor's perception of the risk of opportunism is low. He or she is
therefore more willing to become vulnerable by entrusting others with sensitive information that
could potentially be used to the former actor's disadvantage. Goldberg (1980) suggests that the
threat of opportunism can be deliberately decreased through social forces such as improving the
quality of dyadic relationships or relational norms. When this occurs, those who trust others can
use the most efficient (the shortest) communication routes without fear of having their
vulnerability to opportunism exploited.
Actors who are trusted will be more frequently used as information transfer conduits.
Actors possessing high levels of closeness centrality will maintain those positions as long as trust
levels do not decline. In this case, there is no incentive from a vulnerability standpoint to find
alternate routes of communication. Subsequently, actors are likely to utilize the most efficient
communication routes through these trusted actors.
Schein's original definition of centrality is that centrality is “denotes the person's
objective position as measured by the degree to which company secrets are entrusted to him, by
ratings of others of his position, and by his actual power" (1971: 408). Schein's definition
provides two aspects of interest to the present discussion. First, centrality involves trust. Without
trust, one will likely have a decrease in his or her ability to successfully occupy a central position
in a network. In addition, centrality is, in part, a function of "ratings of others of his position."
Thus, an actor's centrality is partially a function of his or her ability to be trusted, which in turn,
leads to others rating that actor as a central player. Second, the phrase "secrets are entrusted to
him" denotes the transfer of confidential information to those who possess centrality. These
conditions are precisely those necessary to create the context needed for successful opportunism.
If one believes that opportunism is likely due to lack of trust in an actor, the latter actor's ability
to occupy a position of centrality is jeopardized. Therefore, in low trust situations in which
opportunism is perceived to be a significant threat, otherwise central actors will not occupy a
position of centrality. When this is the case, closeness centrality masks the most efficient routes
of communication. Closeness centrality measures actual routes, but not necessarily the most
efficient routes. Closeness, therefore, does not give any indication of the extent to which an
organization is using its communication networks efficiently.
A measure of potential closeness centrality would be useful to contrast with actual
closeness centrality to provide an index of communication efficiency with respect to closeness
centrality. One way to think of this is to envision communication efficiency as similar to capacity
utilization of production facilities. Capacity utilization measures the extent to which a company
utilizes its production facilities. The highest efficiency approaches 100 percent utilization of a
firm's facilities to maximize production and reduce costs associated with unused physical
resources. An index of potential versus actual closeness centrality could serve as a comparable
gauge of organizational efficiency of communication network utilization in transferring
information between and among actors. The ideal index would find the ratio of actual centrality
to potential centrality with respect to the geodesic (shortest path) distances between beginning
and ending points of communication flows. The closer the ratio approaches 1.0, the more
efficient the network. In other words, an ideal centrality efficiency index (CEI) would place
current actual centrality in the ratio's numerator. The denominator would show the shortest
5
6
reasonable path, given the organizational structure from the origin of information to the final
recipient of that information, where the final recipient is defined as that actor who makes a
decision based on the information provided. Therefore,
CEI = Actual Centrality / Potential Centrality
P1: A theoretical index of communication efficiency with respect to closeness centrality can be
calculated by measuring the ratio of actual centrality to potential centrality.
Clearly, such a measure would be quite difficult to obtain in practice due to the possible number
of network configurations. As the number of actors in a network increases, there is an
exponential increase in the possible number of network configurations. However, a realistic and
reasonable proxy of this theoretically ideal index may be constructed using easily obtainable
measures. By placing closeness in the numerator and a measure of potential centrality in the
denominator, a reasonable estimate of CEI may be calculated. An individual's closeness
centrality in a connected network (Ccs) can be calculated using the formula:
Ccs = (N-1) / ∑d (i,j)
where N = the total number of actors in the network and d(i,j) = the path distance between actors
i and j. Therefore, a formula that approaches the values one would obtain with the theoretical
CEI is given by:
CEI =
(N-1) / ∑d (i,j)
Potential centrality
The measurement of potential centrality is more difficult. However, Valente and Foreman
(1998) have developed a formula they refer to as relative point integration. Relative point
integration is the ratio between integration—the actor's connectedness in the network—and
radiality—how well that actor's ties reach out into the network. In essence, relative point
integration measures connectedness and reach. An integrated actor is easily reached by others,
while an actor high in radiality is able to reach out into the network. By considering both the
ability to reach as well as the ability to be reached, a broad measure of the potential for one to
possess a high level of centrality is available.
Using relative point integration in the denominator of the CEI provides a rough measure
of actual centrality versus potential centrality. The relative point integration is calculated by:
I'(k) = I(k) / max(RDjk)
j,k
Placing this in the denominator of the CEI results in:
CEI =
(N-1) / ∑d (i,j)
I(k) / max(RDjk)
j,k
6
7
Thus,
P2: A reasonable proxy of the theoretical index of communication efficiency with respect to

 (x  x) / /(x  x)
closeness centrality is given by: CEI  N 1)/  d(i, j) /
i
i
Managerial Implications and Future Research Directions

Trust is an admittedly difficult construct to define (Bigley & Pearce, 1998). When applied to
social networks and communication flows, the degree of difficulty is further exacerbated.
However, despite the inherent difficulties, trust can serve as an important organizational resource
(Gallivan, 2001).
Efficient and effective transfer and use of information is a potentially valuable
organizational resource (Appleyard, 1996). When viewed as a resource, effective utilization of
trust becomes a managerial concern. Managers should view trust as they do other intangible
resources. The inefficient use of network patterns for locating information can be costly.
Consequently, if managers can enhance the level of trust throughout a network, information
search costs should decline.
This article is a first step toward developing a centrality efficiency index to measure
communication flow efficiency in social networks viewing trust as a moderating variable. The
next step would be to further hone the CEI and determine whether it is valid and reliable by
adding error terms. In addition, there may be other measure of centrality that would be better
suited to a measurement of communication efficiency. Structural holes—actors connected to
otherwise disconnected others (Burt, 1992)—may be an appropriate construct for determining
communication efficiency. Using structural holes in a CEI may be an alternative way to capture
the nature of crucial information transfer within networks. Other moderators should also be
considered. In addition to trust, constructs such as relational norms, competition within and
between intrafirm work groups and business units, and organizational structure may be brought
to bear.
Nevertheless, the CEI provides a starting point for further work. A robust measure of
communication efficiency within social networks should enhance managerial consulting practice,
particularly for those consultants and managers involved with firms undergoing downsizing,
restructuring, and other drastic measures that affect employee's perceptions of security. A valid,
reliable measure of the extent to which trust moderates this relationship would shed light on the
efficiency with which information is transferred as organizations undergo such disruptive
changes.
An index of the actual versus the potential communication flows would ideal, but this
ideal is limited by the impracticality of direct measurement of communication flows. However,
this research has proposed that the CEI can serve as a reasonable substitute. The CEI, by
approximating an index of efficiency, could be useful in analyzing the extent of factors that
moderate communication flow efficiency. Thus, considering trust as a moderator, one would
expect a direct relationship between trust and CEI. As trust increases, one would expect CEI to
increase. As trust decreases, one would expect CEI to decrease.
7
8
References
Appleyard, M. M. (1996). ‘How does knowledge Flow? Interfirm patterns in the semiconductor
industry’, Strategic Management Journal, Vol. 17, Winter Special Issue, pp 137-154.
Bigley, G. A., & Pearce, J. L. (1998), ‘Straining for shared meaning in organization science:
Problems of trust and distrust’, Academy of Management Review, Vol 32, No 3, pp 405422.
Brass, D. J. (1995), ‘A social network perspective on human resources management’, Research
in Human Resources Management, Vol 13, pp 39-79, JAI Press, Inc.
Burt, R. S. 1992, ‘Structural Holes: The Social Structure of Competition’, Cambridge, MA:
Harvard University Press.
Buskens, V. (1998), ‘The social structure of trust’, Social Networks, Vol 20, pp 265-289.
Coleman, J. S. (1990). ‘Foundations of Social Theory’. Cambridge, MA: Belknap Press of
Harvard University.
Doney, P. M., Cannon, J. P., & Mullen, M. R. (1998), ‘Understanding the influence of national
culture on the development of trust’, Academy of Management Review, Vol 23, No 3, pp
601-621.
Eisenhardt, K. (1989), ‘Agency theory: An assessment and review’, Academy of Management
Journal, Vol 14, pp 57-74.
Emirbayer, M., & Goodwin, J. (1994), ‘Network analysis, culture, and the problem of agency’,
American Journal of Sociology, Vol 99, No 6, pp 1411-1454.
Freeman, L. C. (1979). ‘Centrality in Social Networks: I. Conceptual Clarification. Social
Networks,’ Vol 1, pp 215-239.
Gambetta, D. (1988), ‘Trust: Making and Breaking Cooperative Relationships’, Oxford,
England: Basil Blackwell.
Goldberg, V. P. (1980), ‘Relational exchange’, American Behavioral Scientist, Vol 23, pp 337352.
Ibarra, H. (1993), ‘Network centrality, power, and innovation involvement: Determinants of
technical and administrative roles’, Academy of Management Journal, Vol 36, pp 471501.
Jones, G. R., & George, J. M. (1998), ‘The experience and evolution of trust: Implications for
cooperation and teamwork’, Academy of Management Review, Vol 23, No 3, pp 531-547.
Kramer, R. M. (1999), ‘Trust and distrust in organizations: Emerging perspectives, enduring
questions’, Annual Review of Psychology, Annual, pp 569-598.
Kramer, R. M., Brewer, M. B., & Hanna, B. A. (1996), ‘Collective trust and collective action:
The decision to trust as a social decision’, In R. M. Kramer, & T. R. Tyler (Eds.), Trust in
Organizations: Frontiers in Theory and Research, pp 357-389. Thousand Oaks, CA:
Sage Publications, Inc.
McAllister, D. J. (1995), ‘Affect- and cognition-based trust as foundations for interpersonal
cooperation in organizations’, Academy of Management Journal, Vol 38, No 1, pp 2460.
McKnight, D. H., Cummings, L. L., & Chervany, N. L. (1998), ‘Initial trust formation in new
organizational relationships’, Academy of Management Review, Vol 23, No 3, pp. 473491.
Nahapiet, J., & Ghoshal, S. (1998), ‘Social capital, intellectual capital, and the organizational
advantage’, Academy of Management Review, Vol 23, No 2, pp. 242-266.
8
9
Poulin, R., Boily, M. C., & Mâsse, B. R. (2000), ‘Dynamical systems to define centrality in
social networks’, Social Networks, Vol 22, pp 187-220.
Ring, P. S., & Van de Ven, A. H. (1994), ‘Developmental processes of cooperative
interorganizational relationships’, Academy of Management Review, Vol 19, pp 90-118.
Schein, E. H. (1971), ‘The individual, the organization, and the career: A conceptual scheme’,
Journal of Applied Behavioral Science, Vol 7, pp 401-426.
Shapiro, D. L., Sheppard, B. H., & Cheraskin, L. (1992), ‘Business on a handshake’, Negotiation
Journal, Vol 8, No 4, pp 365-377.
Smith, C. A., Haynes, K. N., Lazarus, R. S., & Pope, L. K. (1996), ‘In search of the "hot"
cognitions: Attributions, appraisals, and their relations to emotion’, Journal of
Personality and Social Psychology, Vol 65, pp 916-929.
Szulanski, G. (1996), ‘Exploring internal stickiness: Impediments to the transfer of best practices
within the firm’, Strategic Management Journal, Vol 17, No S2, pp 27-44.
Williamson, O. E. (1975), ‘Comparative economic organization: The analysis of discrete
structural alternatives’, Administrative Science Quarterly, Vol 36, pp 269-296.
Williamson, O. E. (1981), ‘The economics of organization: The transaction cost approach’,
American Journal of Sociology, Vol 87, No 3, pp 548-577.
Zack, M. H. (1999), ‘Managing codified knowledge’, Sloan Management Review, Vol 40, No 4,
pp. 45-58.
Zander, U., & Kogut, B. (1995), ‘Knowledge and the speed of transfer and imitation of
organizational capabilities: An empirical test’, Organization Science, Vol 6, pp 76-92.
9