On Network Theory Borgatti, Stephen P.; Halgin, Daniel S.
Organization science (Providence, R.I.),
09/2011, Volume:
22, Issue:
5
Journal Article
Peer reviewed
Research on social networks has grown considerably in the last decade. However, there is a certain amount of confusion about network theory-for example, what it is, what is distinctive about it, and ...how to generate new theory. This paper attempts to remedy the situation by clarifying the fundamental concepts of the field (such as the network) and characterizing how network reasoning works. We start by considering the definition of network, noting some confusion caused by two different perspectives, which we refer to as realist and nominalist. We then analyze two well-known network theories, Granovetter's strength of weak ties theory Granovetter, M. S. 1973. The strength of weak ties.
Amer. J. Sociol.
78
(6) 1360-1380 and Burt's structural holes theory Burt, R. S. 1992.
Structural Holes: The Social Structure of Competition
. Havard University Press, Cambridge, MA, to identify characteristic elements of network theorizing. We argue that both theories share an underlying theoretical model, which we label the network flow model, from which we derive additional implications. We also discuss network phenomena that do not appear to fit the flow model and discuss the possibility of a second fundamental model, which we call the bond model. We close with a discussion of the merits of model-based network theorizing for facilitating the generation of new theory, as well as a discussion of endogeneity in network theorizing.
Centrality and network flow Borgatti, Stephen P.
Social networks,
2005, 2005-1-00, 20050101, Volume:
27, Issue:
1
Journal Article
Peer reviewed
Centrality measures, or at least popular interpretations of these measures, make implicit assumptions about the manner in which traffic flows through a network. For example, some measures count only ...geodesic paths, apparently assuming that whatever flows through the network only moves along the shortest possible paths. This paper lays out a typology of network flows based on two dimensions of variation, namely the kinds of trajectories that traffic may follow (geodesics, paths, trails, or walks) and the method of spread (broadcast, serial replication, or transfer). Measures of centrality are then matched to the kinds of flows that they are appropriate for. Simulations are used to examine the relationship between type of flow and the differential importance of nodes with respect to key measurements such as speed of reception of traffic and frequency of receiving traffic. It is shown that the off-the-shelf formulas for centrality measures are fully applicable only for the specific flow processes they are designed for, and that when they are applied to other flow processes they get the “wrong” answer. It is noted that the most commonly used centrality measures are not appropriate for most of the flows we are routinely interested in. A key claim made in this paper is that centrality measures can be regarded as generating expected values for certain kinds of node outcomes (such as speed and frequency of reception) given implicit models of how traffic flows, and that this provides a new and useful way of thinking about centrality.
Research in organizational learning has demonstrated processes and occasionally performance implications of acquisition of declarative (know-what) and procedural (know-how) knowledge. However, ...considerably less attention has been paid to learned characteristics of relationships that affect the decision to seek information from other people. Based on a review of the social network, information processing, and organizational learning literatures, along with the results of a previous qualitative study, we propose a formal model of information seeking in which the probability of seeking information from another person is a function of (1) knowing what that person knows; (2) valuing what that person knows; (3) being able to gain timely access to that person's thinking; and (4) perceiving that seeking information from that person would not be too costly. We also hypothesize that the knowing, access, and cost variables mediate the relationship between physical proximity and information seeking. The model is tested using two separate research sites to provide replication. The results indicate strong support for the model and the mediation hypothesis (with the exception of the cost variable). Implications are drawn for the study of both transactive memory and organizational learning, as well as for management practice.
Over the past decade, there has been an explosion of interest in network research across the physical and social sciences. For social scientists, the theory of networks has been a gold mine, yielding ...explanations for social phenomena in a wide variety of disciplines from psychology to economics. Here, we review the kinds of things that social scientists have tried to explain using social network analysis and provide a nutshell description of the basic assumptions, goals, and explanatory mechanisms prevalent in the field. We hope to contribute to a dialogue among researchers from across the physical and social sciences who share a common interest in understanding the antecedents and consequences of network phenomena.
The concept of centrality is often invoked in social network analysis, and diverse indices have been proposed to measure it. This paper develops a unified framework for the measurement of centrality. ...All measures of centrality assess a node's involvement in the walk structure of a network. Measures vary along four key dimensions: type of nodal involvement assessed, type of walk considered, property of walk assessed, and choice of summary measure. If we cross-classify measures by type of nodal involvement (radial versus medial) and property of walk assessed (volume versus length), we obtain a four-fold polychotomization with one cell empty which mirrors Freeman's 1979 categorization. At a more substantive level, measures of centrality summarize a node's involvement in or contribution to the cohesiveness of the network. Radial measures in particular are reductions of pair-wise proximities/cohesion to attributes of nodes or actors. The usefulness and interpretability of radial measures depend on the fit of the cohesion matrix to the one-dimensional model. In network terms, a network that is fit by a one-dimensional model has a core-periphery structure in which all nodes revolve more or less closely around a single core. This in turn implies that the network does not contain distinct cohesive subgroups. Thus, centrality is shown to be intimately connected with the cohesive subgroup structure of a network.
An analysis is conducted on the robustness of measures of centrality in the face of random error in the network data. We use random networks of varying sizes and densities and subject them ...(separately) to four kinds of random error in varying amounts. The types of error are edge deletion, node deletion, edge addition, and node addition. The results show that the accuracy of centrality measures declines smoothly and predictably with the amount of error. This suggests that, for random networks and random error, we shall be able to construct confidence intervals around centrality scores. In addition, centrality measures were highly similar in their response to error. Dense networks were the most robust in the face of all kinds of error except edge deletion. For edge deletion, sparse networks were more accurately measured.
In this paper, we review and analyze the emerging network paradigm in organizational research. We begin with a conventional review of recent research organized around recognized research streams. ...Next, we analyze this research, developing a set of dimensions along which network studies vary, including direction of causality, levels of analysis, explanatory goals, and explanatory mechanisms. We use the latter two dimensions to construct a 2-by-2 table cross-classifying studies of network consequences into four canonical types: structural social capital, social access to resources, contagion, and environmental shaping. We note the rise in popularity of studies with a greater sense of agency than was traditional in network research.
This paper reviews the growing body of work on network dynamics in organizational research, focusing on a corpus of 187 articles—both “micro” (i.e., interpersonal) and “macro” (i.e., ...interorganizational)—published between 2007 and 2020. We do not see “network dynamics” as a single construct; rather, it is an umbrella term covering a wide territory. In the first phase of our two-phase review, we present a taxonomy that organizes this territory into three categories: (1) network change (i.e., the emergence, evolution, and transformation of network ties and structures), (2) the occurrence of relational events (i.e., modeling the sequence of discrete actions generated by one actor and directed towards one or more other actors), and (3) coevolution (i.e., the process whereby network and actor attributes influence each other over time). Our review highlights differences between network dynamics based on relational states (e.g., a friendship) and relational events (e.g., an email message), examines the drivers and effects of network dynamics, and in a methodological appendix, clarifies the assumptions, strengths, and weaknesses of different analytical approaches for studying network dynamics. In the second phase of our review, we critically reflect on the findings from the first phase and sketch out a rough agenda for future research, organized in terms of four overarching themes: the interplay between the dynamics of social networks conceived as relational states and relational events, mechanisms underlying network dynamics, outcomes of network dynamics, and the role of cognition.
•Closeness centrality has two common interpretations: one based on efficiency and one based on independence.•Closeness-as-independence (being independent of) and betweenness centrality (being ...depended upon) are dual indices based on a shared dependency relation.•Duality is not preserved in valued networks.•Duality can be maintained with a novel definition of distance.•Thus, closeness-as-independence and closeness-as-efficiency are actually two indices that agree on non-valued networks.
Betweenness centrality is generally regarded as a measure of others’ dependence on a given node, and therefore as a measure of potential control. Closeness centrality is usually interpreted either as a measure of access efficiency or of independence from potential control by intermediaries. Betweenness and closeness are commonly assumed to be related for two reasons: first, because of their conceptual duality with respect to dependency, and second, because both are defined in terms of shortest paths.
We show that the first of these ideas – the duality – is not only true in a general conceptual sense but also in precise mathematical terms. This becomes apparent when the two indices are expressed in terms of a shared dyadic dependency relation. We also show that the second idea – the shortest paths – is false because it is not preserved when the indices are generalized using the standard definition of shortest paths in valued graphs. This unveils that closeness-as-independence is in fact different from closeness-as-efficiency, and we propose a variant notion of distance that maintains the duality of closeness-as-independence with betweenness also on valued relations.
The network perspective is rapidly becoming a lingua franca across virtually all of the sciences from anthropology to physics. In this paper, we provide supply chain researchers with an overview of ...social network analysis, covering both specific concepts (such as structural holes or betweenness centrality) and the generic explanatory mechanisms that network theorists often invoke to relate network variables to outcomes of interest. One reason for discussing mechanisms is to facilitate appropriate translation and context‐specific modification of concepts rather than blind copying. We have also taken care to apply network concepts to both “hard” types of ties (e.g., materials and money flows) and “soft” types of ties (e.g., friendships and sharing‐of‐information), as both are crucial (and mutually embedded) in the supply chain context. Another aim of the review is to point to areas in other fields that we think are particularly suitable for supply chain management (SCM) to draw network concepts from, such as sociology, ecology, input–output research and even the study of romantic networks. We believe the portability of many network concepts provides a potential for unifying many fields, and a consequence of this for SCM may be to decrease the distance between SCM and other branches of management science.
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