Network Brokerage: How the Social Network Around You Creates Competitive Advantage for Innovation and Top-Line Growth

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1 Network rokerage: How the Social Network Around You reates ompetitive Advantage for Innovation and Top-Line Growth For text on this session, see hapters 1 and 2 in rokerage and losure (including adjunct bits from Neighbor Networks). Appendices: I. xample Network Questionnaire for a Web Survey (pages 24-25, from 21, Neighbor Networks) Network rokerage (page 1) II. Network Metrics (pages 26-3, from 1992, Structural Holes, and 21, Neighbor Networks) III. NetDraw Quick Start -- making your own sociograms and benchmark network metrics (page 31) IV. Network ndogeneity -- avelas-smith-leavitt experiments (pages 32-33, 1949 Leavitt dissertation, 1951 Leavitt, Some effects of certain communication patterns upon group performance ) V. National Differences in usiness ulture (pages 34-36) This handout was prepared as a basis for discussion in executive education (opyright 216 Ronald S. urt, all rights reserved). To download work referenced here, or research/teaching materials on related topics, go to

2 Sociogram of the Org hart for a Large U Healthcare Organization O -Suite Heir Apparent Other, Respondent Other, NonRespondent ill ob Network rokerage (page 2) Figure 1.1 in urt (216, Structural Holes in Virtual Worlds).

3 Sociogram of Senior Leadership in the Healthcare Organization Asia US Lines indicate frequent and substantive work discussion; heavy lines especially close relationships. U and merging Markets ill ob Front Office Network rokerage (page 3) O -Suite Heir Apparent Other Senior Person ack Office R&D Figure 1.2 in urt (216, Structural Holes in Virtual Worlds).

4 To begin, the "network" around a person is a pattern of relationships with and between colleagues. This worksheet is completed in four steps: (1) In the oval, write the name of a significant colleague. The colleague could be your most valuable subordinate, your most difficult, your boss, an important source of support, or a key contact in another organization. Who doesn't matter. It just has to be someone you know well enough to know their key contacts. (2) In the squares, write the name of the five contacts with whom the person in the oval has the most frequent and substantial business contact. (3) Draw a line between any pair of contacts that are connected in the sense that the two people speak often enough that they have some familiarity with current issues in one another's work. SOIOGRAM graphic image of a network in which dots represent nodes (a person, group, etc.) and lines represent connections Network rokerage (page 4) (4) ompute network density. ount the number of lines between contacts (TIS). Divide by the number possible (n[n-1]/2, where n is the number of contacts, which is 5 if you entered five contacts). Multiply by 1 and round to nearest percent. DNSITY = Appendix I contains an illustrative survey webpage used to gather network data.

5 Z-Score Relative Performance (compensation, evaluation, promotion) Social apital of rokerage Manifest as better ideas, more-positive evaluations, higher compensation, earlier promotion, and faster teams. Now, establish the empirical fact that the people we will discuss as "network brokers" enjoy achievement and rewards higher than their peers. rokers are distinguished on the horizontal axis. Network rokerage (page 5) large, open Robert Network onstraint () many Structural Holes few ircles are average z-score performance (Z) for a five-point interval of network constraint () within each of eight study populations. Dashed line goes through mean values of Z for intervals of. old line is performance predicted by the natural log of. small, closed ames From Figure 1.8 in rokerage and losure. Data pooled across eight study-population graphs in Appendix II on measuring network constraint.

6 Network rokerage (page 6) Z-Score Relative Performance (compensation, evaluation, promotion) large, open Robert Performance Indicator (compensation, evaluation, promotion rate) median network constraint (35 points) Social apital of rokerage performance Manifest as higher better ideas, than more-positive evaluations, higher compensation, expected earlier promotion, and faster teams. performance lower than expected Human apital et al. (e.g., job rank, age, geography, kind of work, division, education, etc.) Z = ln() -2.5 r = Network onstraint () many Structural Holes few ircles are average z-score performance (Z) for a five-point interval of network constraint () within each of eight study populations. Dashed line goes through mean values of Z for intervals of. old line is performance predicted by the natural log of. small, closed ames Achievement and rewards are distinguished on the vertical axis, measuring the extent to which a person is doing better than his or her peers. From Figure 1.8 in rokerage and losure. Data pooled across eight study-population graphs in Appendix II on measuring network constraint.

7 Network rokerage (page 7) Z-Score Relative Performance (compensation, evaluation, promotion) large, open Robert median network constraint (35 points) Social apital of rokerage Manifest as better ideas, more-positive evaluations, higher compensation, earlier promotion, and faster teams. rokerage is a large percentage of explained performance differences. Z = ln() -2.5 r = Network onstraint () many Structural Holes few ircles are average z-score performance (Z) for a five-point interval of network constraint () within each of eight study populations. Dashed line goes through mean values of Z for intervals of. old line is performance predicted by the natural log of. small, closed ames 28% 17% 33% 2% 9% 55% 1% 81% 64% rokerage ontributes "Slightly More than Half" of Predicted Variance in Performance Differences between Managers: Network constraint (white), job rank (red), and other factors (striped). First pie is investment banker compensation and analyst election to the All-America Research Team. Second pie is supply-chain and HR manager compensation in corporate bureaucracies. Third pie is early promotion to senior job rank in a large electronics firm. Graph is from Figure 1.8 in rokerage and losure. Data are pooled across eight management populations. Pie charts are from Figure 2.4 in Neighbor Networks. On causal order, see Appendix IV.

8 The Returns to rokerage Aggregate to ompanies, Industries, and ommunities People with phone networks that span structural holes live in communities higher in socio-economic rank Networks are defined by land-line & mobile phone calls (map to left). Socio-economic rank is UK government index of multiple deprivation (IMD) based on local income, employment, education, health, crime, housing, and environmental quality (graph below). Units are phone area codes. Network rokerage (page 8) figures from agle, Macy, and laxton (21, Science), Network diversity and economic development

9 Network rokerage (page 9) And the Network ffect Is vident in oordination between Organizations Supplier evaluation: Leaders in 32 key supplier organizations were interviewed about their experience with a leading American telecom ("the company"). For larger suppliers, two or three agents were interviewed (e.g., Foxconn, Samsung, Sharp, Toshiba). The agents were asked to describe their experience with respect to company forecast accuracy and volatility in the company's development cycle (3 meets requirements, 2 satisfactory, or 1 unacceptable). The vertical axis is the average evaluation of the telecom company from each key supplier. Supplier valuation of Telecom (mean eval of forecast accuracy and development cycle volatilty) (1 = unacceptable, 2 = satisfactory, 3 = meets requirement r = -.44 t = P <.1 Network onstraint on est-onnected Procurement Manager Assigned to the Supplier (lowest network constraint score among managers for whom the supplier is where manager spends the most time) Supplier PO in telecom: The 55 managers in procurement support (no direct supplier contact) were asked to indicate their involvement in company operations with each of the 32 key suppliers. A manager could say that a supplier is one "on which I spend the most time," or "with which I have some direct contact," or "on which I work indirectly through other motorola employees" (or leave it blank if respondent had no contact with the supplier). For each of the 32 key suppliers, I identified the respondents who said they spend "most time" on the supplier, and selected the two respondents who had the most attractive network metrics defined by "frequent and substantive work contact" relations. The horizontal axis is the average network constraint score for the two best-connected procurement managers spending "most time" on the supplier providing the evaluation on the vertical axis.

10 HOW IT WORKS: Recombinant Sticky Information ontacts as Source vs. Portal YOU YOU YOU Network A Network Network Redundancy by ohesion YOU Network rokerage (page 1) ontact Redundancy Redundancy by Structural quivalence YOU A 7 6 & D 2 1 Robert Network onstraint ( = Σ j c ij = Σ j [p ij + Σ q p iqp qj] 2, i,j q) person 3:.42 = [.25+] 2 + [ ] 2 + [ ] 2 + [ ] ames Density Table Group A Group Group Group D Robert:.148 = [.77+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 from Figures 1.1 and 1.3 in urt (1992, Structural Holes) and Figure 1.2 in rokerage and losure

11 ridge & luster: Small World of Organizations & Markets A ames Robert Network rokerage (page 11) & D Network onstraint ( = Σ j c ij = Σ j [p ij + Σ q p iq p qj ] 2, i,j q) 85 5 person 3:.42 = [.25+] 2 + [ ] 2 + [ ] 2 + [ ] 2 Density Table Group A Group Group Group D Robert:.148 = [.77+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 + [.154+] 2 Network indicates distribution of sticky information, which defines advantage. From Figure 1.1 in rokerage and losure. For an HR treatment of the network distinction between Robert and ames, see in the course packet Kotter's classic distinction between "leaders" versus "managers." Robert ideally corresponds to the image of a "T-shaped manager," nicely articulated in Hansen's HR paper in the course packet.

12 Network rokerage (page 12) reate Value by ridging Structural Holes STIKY INFORMATION Information expensive to move because: (a) tacit, (b) complex, (c) requires other knowledge to absorb, or (d) interaction with sender, recipient, or channel. STRUTURAL HOL disconnection between two groups or clusters of people RIDG relation across structural hole NTWORK NTRPRNUR or "broker," or "connector:" a person who coordinates across a structural hole ROKRAG act of coordinating across a structural hole Here is the core network for a job FOR and AFTR the employee expanded the social capital of the job by reallocating network time and energy to more diverse contacts FOR 5 Research shows that employees in networks like the AFTR network, spanning structural holes, are the key to integrating operations across functional and business boundaries. In research comparing senior people with networks like these FOR and AFTR networks, it is the AFTR networks that are associated with more creativity, faster learning, more positive individual and team evaluations, faster promotions, and higher earnings. *Network scores refer to direct contacts. It is the weak contact connections (structural holes) in the AFTR network that provides the expanded social capital. The employee AFTR is more positioned at the crossroads of communication between social clusters within the firm and its market, and so is better positioned to craft projects and policy that add value across clusters constraint 2. constraint* 5 1 AFTR information breadth, timing, and arbitrage From Figure 1.4 in urt (1992, Structural Holes) and Figure 1.2 in rokerage and losure. See Appendix I on survey network data, Appendix II on measuring network constraint.

13 HOW IT WORKS: reativity and Innovation Are at the Heart of It Network rokerage (page 13) rokerage across Structural Holes reativity & Innovation (What should be done?) Achievement & Rewards (What benefits?) What in your work Adaptive Implementation improves the odds (How to frame it & who should be involved?) that you will discover the value of something you don't know you don't know? Alternative Perspective (how would this problem look from the perspective of a different group, or groups thinking out of the box is often less valuable than seeing the problem as it would look if you were inside a specific other box ) est Practice (something they think or do could be valuable in my operations) Analogy (something about the way they think or behave has implications for how I can enhance the value of my operations; i.e., look for the value of juxtapositioning two clusters, not reasons why the two are different so as to be irrelevant to one another you often find what you look for) Synergy (resources in our separate operations can be combined to create a valuable new idea/practice/product) from urt, "The social capital of structural holes" (22, The New conomic Sociology). The consequences of the information diversity associated with network brokerage is productively elaborated at length in economist Scott Page's 27 book, The Difference: How the Power of Diversity reates etter Groups, Firms, Schools and Societies.

14 FIRST AUTION: Returns to network brokerage are a probability, not a certainty. Access to structural holes merely "increases the risk of productive accident." Network rokerage (page 14) Patent co-authoring network from Lee Fleming & Matt Marx, "Managing creativity from rice elisle, "Pet display clothing" From Fleming & Marx, "Managing creativity in small worlds" (alifornia Management Review, 26) in small worlds" (alifornia Management Review, 26; see Fleming et al. 27 ASQ). (US Patent 5,91,666 granted May 11, 1999).

15 Advantage from Varied Perspectives: Information arbitrage is about framing as much as content. Problem vs. Paradox.* What point of view, or frame of reference, will make my idea attractive? The key is not to get "out of the box," so much as to see from within a different box.* Failure here could be a good idea over there. Network rokerage (page 15) arl Segerstrom, in hicago s 212 ADP, worked at Pfizer when the Viagra trials were run. arl sketched the story: Trials showed that the new drug was a failure as a heart medicine, so the trials were shut down and the test samples were recalled. Subjects were asked to return the test samples, and they usually do, but in this case, an unusually high proportion of subjects did not return the test samples. Someone asked, let s find out why they aren t returning the test samples, which revealed the profitable side-effect. Originally, minoxidil was used exclusively as an oral drug (with the trade name Loniten ) to treat high blood pressure. However, it was discovered to have an interesting side effect: hair growth. Minoxidil may cause increased growth or darkening of fine body hairs, or in some cases, significant hair growth. When the medication is discontinued, the hair loss will return to normal rate within 3 to 6 days. *The "problem vs. paradox" point is nicely elaborated by David Doltish, Peter airo, and ade owan in The Unfinished Leader (214). The "out of the box" point is nicely elaborated by Luc de rabandere (25), The Forgotten Half of hange: Achieving Greater reativity through hanges in Perception. See IDO on the saying "fail often to succeed sooner," and Firestein (216) Failure, on the critical role failure plays in successful science.

16 In short, network brokerage is a process by which people clear sticky-information markets. The rewards enjoyed by network brokers are compensation for clearing a market that would otherwise not clear. Therefore, variation between clusters/silos is essential to the value of brokerage. If there are no information differences between social clusters, then there is no value to moving information from one cluster to another. ompetition in open markets explicitly eliminates variation, though social clustering in networks usually indicates variation in understanding and practice. For example, P learning in the refining businesses Strong belief/culture/process/paradigm reinforce closed networks, and can obscure or blind people to variation between subgroups within the network. For example: Pfizer drug trial protocol Talent out of context (able musician in D.. metro train station) INSAD student teams oca ola as a distribution company versus custodian of the oca ola brand Network rokerage (page 16) "Hard" sciences & the negative correlation between age and contribution look for use of right-wrong versus productive-unproductive or interesting-uninteresting Personal experience is perhaps the most insidious blinder. Personal experience enriches understanding, but it can also limit understanding. Many people are trapped in their limited personal experience. They only hear/believe/understand knowledge consistent with what they ve already experienced. The power of understanding fundamental principles, and being able to re-frame problems in different ways, is that you can reason your way through challenges that involve experiences you have not yet had making you valuable beyond whatever experience life has happened to give you personally.

17 ven within Frame, Are You Thinking about the Work Productively? Modularity increases the risk of productive accident. Netscape s Navigator was released under open-source license in March 1998 as Mozilla. It was re-designed for modularity to make it more attractive to contributors. Networks below show module dependencies before and after the re-design. Propagation cost is the average percentage of code that must be updated following a change in any one module. Mozilla version propagation cost:* 17.35% Longitudinal volution of Mozilla Propagation ost* Mozilla version propagation cost: 2.78% Network rokerage (page 17) From Macormack, Rusnak,and aldwin, xploring the structure of complex software designs (26, Management Science).

18 Where did US time zones come from? Until 1883 each United States railroad chose its own time standards. The Pennsylvania Railroad used the "Allegheny Time" system. y 187 the Allegheny Time service extended over 2,5 miles with 3 telegraph offices receiving time signals. However, almost all railroads out of New York ran on New York time, and railroads west from hicago mostly used hicago time, but between hicago and Pittsburgh/uffalo the norm was olumbus time, even on railroads which did not run through olumbus. The Northern Pacific Railroad had seven time zones between St. Paul and the 1883 west end of the railroad at Wallula unction. Network rokerage (page 18) In 187 harles F. Dowd proposed four time zones based on the meridian through Washington, D for North American railroads. In 1872 he revised his proposal to base it on the Greenwich meridian. Sandford Fleming, a anadian, proposed worldwide Standard Time at a meeting of the Royal anadian Institute on February 8, leveland Abbe advocated standard time to better coordinate international weather observations and resultant weather forecasts, which had been coordinated using local solar time. In 1879 he recommended four time zones across the contiguous United States, based upon Greenwich Mean Time. The General Time onvention (renamed the American Railway Association in 1891), an organization of US railroads charged with coordinating schedules and operating standards, became increasingly concerned that if the US government adopted a standard time scheme it would be disadvantageous to its member railroads. William F. Allen, the onvention secretary, argued that North American railroads should adopt a five-zone standard, similar to the one in use today, to avoid government action. On October 11, 1883, the heads of the major railroads met in hicago at the Grand Pacific Hotel and agreed to adopt Allen's proposed system.... Standard time was not enacted into US law until the 1918 Standard Time Act.* *Text comes from October 24, 215 Wikipedia entry for "Standard time" (five zones include one east of astern zone). Map is Dowd's 1884 fifth version advocating to railroaders the adoption of standard time zones. ngraving of William Allen is from Frank Leslie's Popular Monthly (April 1884). For details on bureaucratic infighting over standard time, see artky, Selling the True Time (2, Stanford University Press).

19 Where did the M-16 come from? Discussion Question* Network rokerage (page 19) onsequential ideas are typically attributed to special people, geniuses, in part to make us feel less uncomfortable about our own ideas. True to form, an American armament expert describes ugene Stoner, the engineer who developed the M-16 assault rifle, as "an engineering genius of the first order." Another describes him as "the most gifted small-arm designer since rowning." (rowning patented the widely-adopted AR and 45 automatic.) 1. ased on the brief history video, how would you describe Stoner's genius? 2. What circumstances might allow you or your colleagues to be as creative? *Photos are from the video shown during the session. For discussion and references, see page 73 in rokerage and losure. For sampling on the dependent variable, see Rosenzweig, Misunderstanding the nature of company performance: the halo effect and other business delusions, 27 alifornia Management Review.

20 rokerage, Good Ideas, and Innovation Network rokerage (page 2) Management valuation of Idea's Value G G G G G G G G G G G Y = a + b ln() udge 1 udge 2 ombined G G G G a^ G ^ b t Network onstraint () on Manager Offering Idea ^ P(dismiss) 5.5 logit test statistic "... for those ideas that were either too local in nature,.1 incomprehensible, vague, or too whiny, I didn't rate them" ^ P(no idea) 11.2 logit test statistic Probability from Figure 2.1 in rokerage and losure (or Figure 5 in urt, "Structural holes and good ideas," 24 American ournal of Sociology)

21 Some Good Ideas and Some Stinkers (4.5 value, 22 network constraint) I believe that we are doing a lot of posi>ve things to improve SM across the ompany (Professional Development, MMI, e- tools, Supplier Ra>ng System, etc.). However, our current organiza>on structure inhibits us from leading the Industry in SM effec>veness. Programs dictate our sources of supply. Therefore, cannot fully leverage our company buying power nor are we able to present a one ompany voice to our suppliers. If SM orgs reported directly to the orporate VP of SM, we would have more clout and be able to influence nterprise decisions. At a minimum, SM orgs should report dual solid line to both orp VP SM and the U General Manager. (4.5 value, 31 network constraint) We need to develop and train our SM people in the Subcontracts area to manage our cri>cal subcontractors. We need to ins>tute a standard process for subcontract management and a training program to deploy this process within SM across our loca>ons. We also need to have sufficient experienced subcontracts people available to support the program offices in order to adequately manage the subcontract process. (.5 value, 8 network constraint) My SixSigma Team was tasked with developing an easier method to get udgets and Targets posted, by part number, so that the buyers would not waste >me contac>ng individual SMs. This process requires u>lizing the Materials System and uyer Web System. The team ran into several roadblocks, but we iden>fied solu>ons to resolve those roadblocks. Some programming changes were required (none of which was extremely high cost). In addi>on, we tried to have all SMs directed to get all of their contracts loaded into the system by a certain cut- off date. We went through three or four cut- off date delays for various reasons, and each >me our team met the challenge. So much >me went by, however, the programmers were all diverted to the new SAP system. Without the programming changes, mee>ng the ini>al goals of the team (making ALL budgets and targets available to the buyers) is no longer possible. Therefore, the one thing I would change is to implement the changes that my team proposed. This would make the buyer more efficient and less frustrated. Network rokerage (page 21) (Dismissed, 61 network constraint) I would move ahead with NGPS system. From an opera>onal stand point, we have too many systems with weak batch and patch programs. Data does not flow smoothly. urrently, the procurement and AP func>ons are in NGPS/Oracle. We need to more data into the system (i.e., inventory) and have a integrated opera>on. Too much >me is spent inves>ga>ng errorant data. I would also move towards building a system which starts with item master disciplines. Where did the Gate 4 material and SM labor es>mates for an in- house proposal come from? I believe the numbers did not come from SM in the last couple months. The Site xec. thinks they are too high. I need to inves>gate the source of the SM bid. (Dismissed, 71 network constraint) What we did change were procedures, processes, and spun up a 6 Sigma Team to address permanent fixes. The one thing I would like to see changed is the silo mode of opera>on. Things fall through the cracks when all players in differing opera>ons do not talk with one another. In this case three major opera>ons are owners of a piece of a larger process. The SM has the bondroom and stores and keeps par>al records. Manufacturing and Program Management have the repair/upgrade/modifica>on process. Property Management which is part of Quality has the computer system and the overall management of government property process. SM runs the Government/ustomer ondroom which stores all Govt/ust furnished material received. The DMA ustomer wrote a AR regarding several control issues rela>ng to receipt, shipment, and records of the property. See the discussion of Table 2 in urt, "Structural holes and good ideas," 24 American ournal of Sociology

22 Three Summary Points Network Structure Is a Proxy for the Distribution of Information For reasons of opportunity, shared interests, experience simple inertia organizations and markets drift toward the bridge-and-cluster structure known as a small world. Over time, information becomes "sticky" within clusters, different between clusters. In Which Network rokers Have a ompetitive Advantage ridge relations across the structural holes between clusters provide information breadth, timing, and arbitrage advantages, such that network brokers managing the bridges are at higher risk of productive accident in detecting and developing good ideas. They are the source of significant innovation in organizations and markets. In return, network brokers tend to be better compensated than peers, more widely celebrated than peers, and promoted more quickly to senior rank relative to peers; in short, brokers do better. Network rokerage (page 22) Three Points Follow from the Link between Network rokerage & Innovation - losed networks do not identify unintelligent managers so much as expert specialists. - Innovation is an import/export process. Value is not created at the innovation source. It is created each time productive knowledge produces innovation in a target audience. - Innovation depends on the network as well as the person. Innovation does not depend on individual genius so much as it depends on employees finding opportunities to broker knowledge from where it is routine to where it would create value.

23 Appendix Materials Network rokerage (page 23)

24 Appendix I: xample Network Questionnaire for a Web Survey for discussion of these slides and how to collect network data, Network rokerage (page 24) see Appendix A, "Measuring the Network," in Neighbor Networks. Figure A1 in Neighbor Networks

25 Appendix I, continued Network rokerage (page 25) Figure A2 in Neighbor Networks

26 Appendix II: Network Metrics* from urt, "Formalizing the argument," (1992, Structural Holes); "Gender of social capital" (1998, Rationality and Society); Appendix "Measuring Access to Structural Holes," (21, Neighbor Networks). Network brokerage is typically measured in terms of opportunities to connect people. When everyone you know is connected with one another, you have no opportunities to connect people. When you know a lot of people disconnected from one another, then you have a lot of opportunities to connect people. Opportunities should be emphasized in these sentences. None of the usual brokerage measures actually measures brokerage behavior. They index opportunities for brokerage. Reliability and cost underlie the practice of measuring brokerage in terms of opportunities. It is difficult to know whether or not you acted on a brokerage opportunity. One can know with more reliability whether or not you had an opportunity for brokerage. Acts of brokerage could be studied with ethnographic data, but the needed depth of data would be expensive, if not impossible, to obtain by the practical survey methods used to measure networks. Good reasons notwithstanding, the practice of measuring brokerage by its opportunities rather than its occurrence means that performance has uneven variance across levels of brokerage opportunities. Performance is typically low in the absence of opportunities. Performance varies widely where there are many opportunities: (1) because some people with opportunities do not act upon them and so show no performance benefit, (2) because it is not always valuable to move information between disconnected people (e.g., explain to your grandmother the latest technology in your line of work), or (3) because the performance benefit of brokerage can occur with just one key bridge relationship. A sociologist might do more creative work because of working through an idea with a colleague from economics, but that does not mean that she would be three times more creative if she also worked through the idea with a colleague from psychology, another from anthropology, and another from history. The above three points can be true of brokerage measured in terms of action, but under the assumption that people invest less in brokerage that adds no value, the three points are more obviously true of brokerage measured in terms of opportunities. It could be argued that people more often involved in bridge relations are more likely to have one bridge that is valuable for brokerage, and to understand how to use bridges to add value, but the point remains that the network measures discussed below index opportunities for brokerage, not acts of brokerage. Network rokerage (page 26) ridge ounts ridge counts are an intuitively appealing measure. The relation between two people is a bridge if there are no indirect connections between the two people through mutual contacts. Associations with performance have been reported measuring brokerage with a count of bridges (e.g., urt, Hogarth, and Michaud, 2:Appendix; urt, 22). onstraint I measure brokerage opportunities with a summary index, network constraint. As illustrated on the next page, network constraint begins with the extent to which manager i s network is directly or indirectly invested in the manager s relationship with contact j (urt 1992: hap. 2): c ij = (p ij + Σ q p iq p qj ) 2, for q i,j, where p ij is the proportion of i s network time and energy invested in contact See Appendix III to get free software to do these calculations for you. We use the software in the follow-on course, 396.

27 Illustrative Network and omputation A Network rokerage (page 27) onstraint measures the extent to which a network doesn't span structural holes F Network constraint measures the extent to which your network time and energy is concentrated in a single group. There are two components: (direct) a contact consumes a large proportion of your network time and energy, and (indirect) a contact controls other people who consume a large proportion of your network time and energy. The proportion of i s network time and energy allocated to j, p ij, is the ratio of z ij to the sum of i s relations, where z ij is the strength of connection between i and j, here simplified to zero versus one. contact-specific constraint (x1): A D F 4.3 c ij = (p ij + Σ q p iq p qj ) 2 1(1/36) q i,j D network data A D F 1. 1 gray dot total 39.9 = aggregate constraint ( = Σ j c ij )

28 j, p ij = z ij / Σ q z iq, and variable z ij measures the strength of connection between contacts i and j. onnection z ij measures the lack of a structural hole so it is made symmetric before computing p ij in that a hole between i and j is unlikely to the extent that either i or j feels that they spend a lot of time in the relationship (strength of connection between i and j versus strength of connection from i to j; see urt, 1992:51). The total in parentheses is the proportion of i s relations that are directly or indirectly invested in connection with contact j. The sum of squared proportions, Σ j c ij, is the network constraint index. I multiply scores by 1 to discuss integer levels of constraint. The network constraint index varies with three network dimensions: size, density, and hierarchy. onstraint on a person is high if the person has few contacts (small network) and those contacts are strongly connected to one another, either directly (as in a dense network), or through a central, mutual contact (as in a hierarchical network). The index,, can be written as the sum of three variables: Σ j (p ij ) 2 +2Σ j p ij (Σ q p iq p qj ) + Σ j (Σ q p iq p qj ) 2. The first term in the expression, -size in urt (1998), is a Herfindahl index measuring the extent to which manager i s relations are concentrated in a single contact. The second term, -density in urt (1998), is an interaction between strong ties and density in the sense that it increases with the extent to which manager i s strongest relations are with contacts strongly tied to the other contacts. The third term, -hierarchy in urt (1998), measures the extent to which manager i s contacts concentrate their relations in one central contact. See urt (1992:5ff.; 1998:Appendix) and orgatti, ones, and verett (1998) for discussion of components in network constraint. Size Network size, N, is the number of contacts in a person's network. In graph-theory discussions, the size of the network around a person is discussed as degree. For non-zero network size, other things equal, more contacts mean that a manager is more likely to receive diverse bits of information from contacts and is more able to play their individual demands against one another. Network constraint is lower in larger networks because the proportion of a manager s network time and energy allocated to any one contact (p ij in the constraint equation) decreases on average as the number of contacts increases. Network rokerage (page 28) Density Density is the average strength of connection between contacts: Σ z ij / N*(N-1), where summation is across all contacts i and j. Dense networks are more constraining since contacts are more connected (Σ q p iq p qj in the constraint equation). ontact connections increase the probability that the contacts know the same information and eliminate opportunities to broker information between contacts. Thus, dense networks offer less of the information and control advantage associated with spanning structural holes. Density is only one form of network closure, but it is a form often discussed as closure. Hypothetical networks in the figure on page 4 illustrate how constraint varies with size, density, and hierarchy. Relations are simplified to binary and symmetric in the networks. The graphs display relations between contacts. Relations with the person at the center of the network are not presented (that person at the center is referenced by various labels such as "you," "ego," or "respondent"). The first column in the figure contains examples of sparse networks (zero density). No contact is connected with other contacts. The third column of the figure contains maximum-density networks (density = 1). very contact has a strong connection with each other contact. At each network size, constraint is lower in the sparse-network column.

29 Network rokerage (page 29) Hierarchy Density is a form of closure in which contacts are equally connected. Hierarchy is another form of closure in which a minority of contacts, typically one or two, stand above the others for being more the source of closure. The extreme is to have a network organized around one contact. For people in job transition, such as M..A. students, that one contact is often the spouse. In organizations, hierarchical networks are sometimes built around the boss. Hierarchy and density both increase constraint, but in different ways. They enlarge the indirect connection component in network constraint (Σ q p iq p qj ). Where network constraint measures the extent to which contacts are redundant, network hierarchy measures the extent to which the redundancy can be traced to a single contact in the network. The central contact in a hierarchical network gets the same information available to the manager and cannot be avoided in manager negotiations with each other contact. More, the central contact can be played against the manager by third parties because information available from the manager is equally available from the central contact since manager and central contact reach the same people. Network constraint increases with both density and hierarchy, but density and hierarchy are empirically distinct measures and fundamentally distinct with respect to social capital because it is hierarchy that measures social capital borrowed from a sponsor. To measure the extent to which the constraint on a person is concentrated in certain contacts, I use the oleman-theil inequality index for its attractive qualities as a robust measure of hierarchy (urt, 1992:7ff.). Applied to contact-specific constraint scores, the index is the ratio of Σ j r j ln(r j ) divided by N ln(n), where N is number of contacts, r j is the ratio of contact-j constraint over average constraint, c ij /(/N). The ratio equals zero if all contact-specific constraints equal the average, and approaches 1. to the extent that all constraint is from one contact. Again, I multiply scores by 1 and report integer values. In the first and third columns on the next page, no one contact is more connected than others, so all of the hierarchy scores are zero. Non-zero hierarchy scores occur in the middle column, where one central contact is connected to all others who are otherwise disconnected from one another. ontact A poses more severe constraint than the others because network ties are concentrated in A. The oleman-theil index increases with the number of people connected to the central contact. Hierarchy is 7 for the three-contact hierarchical network, 25 for the five-contact network, and 5 for the ten-contact network. This feature of hierarchy increasing with the number of people in the hierarchy turns out to be important for measuring the social capital of outsiders because it measures the volume of social capital borrowed from a sponsor, which strengthens the association with performance (this point is the focus of the later session on outsiders having to borrow network access from a strategic partner). Note that constraint increases with hierarchy and density such that evidence of density correlated with performance can be evidence of a hierarchy effect. onstraint is high in the dense and hierarchical three-contact networks (93 and 84 points respectively). onstraint is 65 in the dense five-contact network, and 59 in the hierarchical network; even though density is only 4 in the hierarchical network. In the ten-contact networks, constraint is lower in the dense network than the hierarchical network (36 versus 41), and density is only 2 in the hierarchical network. Density and hierarchy are correlated, but distinct, components in network constraint.

30 roker Networks Partner Networks lique Networks Partners Small Networks contacts density x 1 hierarchy x 1 constraint x 1 from: A nonredundant contacts betweenness (holes) A A D A Network Hierarchy rokers Network Density liques A A A Network onstraint Network rokerage (page 3) Larger Networks contacts density x 1 hierarchy x 1 constraint x 1 from: A D nonredundant contacts betweenness (holes) Still Larger Networks contacts density x 1 hierarchy x 1 constraint x 1 nonredundant contacts betweenness (holes) D D To keep the diagrams simple, relations with ego are not presented D decreases with number of contacts (size), increases with strength of connections between contacts (density), and increases with sharing the network (hierarchy). This is Figure 2.8 in urt (216, Structural Holes in Virtual Worlds, cf. Figure.2 in Neighbor Networks). Graph above plots density and hierarchy for 1,989 networks observed in six management populations (aggregated in Figure 2.4 in Neighbor Networks to illustrate returns to brokerage). Dot-circles are executives (MD or more in finance, VP or more otherwise). Hollow circles are lower ranks. xecutives have significantly larger, less dense, and less hierarchical networks.

31 Network rokerage (page 31) *node data id ego A D F *tie data from to tie ego A 1 ego 1 ego 1 ego D 1 ego 1 ego F 1 A 1 A 1 F A 1 D 1 Appendix III: NetDraw Quick Start Making your own sociograms and computing network metrics for a group, project, organization, or market 1. DOWNLOAD TH FR NTWORK SOFTWAR, NTDRAW ( download, then click on the "xe only" option) 2. TYP TH 21 LINS TO TH RIGHT INTO YOUR WORD PROSSOR AND SAV AS A TT FIL NDING IN.vna The 21 lines are a roster of people in the network followed by a roster of relations (e.g., ego has a relation to person A at strength 1). These data define the network illustrating network constraint on page 37 in this handout. 3. LOAD TH.vna FIL INTO NTDRAW ( File menu, open option, then VNA text file and omplete ) 4. GNRAT A SPATIAL DISPLAY OF TH NTWORK ( Layout menu, graph theoretic layout option, then spring embedding ). YOU SHOULD GT TH SOIOGRAM LOW. (See next page for basic nets discussed in this course.) Now play around to learn the wide capabilities of the software. lick and drag a node to move it and its relations around. Remove arrows by clicking on the arrow button to the right of the row of command buttons just above the sociogram display. Save the sociogram to a file for editing, pasting, and printing ( File menu, save diagram as option, then metafile ). For more complex edits, such as computing network metrics ( Analysis menu, structural holes option, then ego network model and save the data), see the short user guide you can download on the page where you clicked "xe only." If you are not comfortable using new software, it might be wise to bring in someone who can play with the software then brief you. FOR TT PLAINING TH NTWORK MTRIS, see Appendix II in this handout. aution: Some versions of NetDraw compute incorrect values of network constraint for isolates. Network constraint is infinite for isolates, so constraint should be its maximum of one. Some versions of NetDraw report a value of zero for infinity. This issue is not likely an issue for you since you probably have contacts, else you wouldn't be using the software. D ego A F

32 Most Distributed Leadership (slow, happy) Appendix IV: Network ndogeneity Independent Network ffect A Most entralized Leadership (fast, unhappy) D D D A A A D IRL (5.4 sec) HAIN (53.2 sec) Y-NTWORK (35. sec) WHL (32. sec) N N Happy N N Happy N N Happy N N Happy A A A A Network rokerage (page 32) D Avg D Avg D Avg D Avg The four networks are from the avelas-leavitt experiments on leadership in task groups. The WHL is a traditional bureaucracy in which is in charge. The other three networks involve distributed leadership (all five people in the IRL;,, and D in the HAIN; and D in the Y-NTWORK). More distributed leadership is associated with more messages, slower task completion, and greater enjoyment. Speed, messages, and enjoyment scores are from Leavitt (1951). Number of contacts (N) and network constraint (N) are computed from binary ties in the sociograms (number of contacts equals number of non-redundant contacts in these structures). Figure 2.4 in urt (216, Structural Holes in Virtual Worlds)

33 ehavioral and Opinion orrelates of Network rokers Mean Messages Sent Answer messages Information messages Mean njoyment Score njoyment after first trial njoyment after last trial Times ited as Group Leader Network onstraint Network onstraint Network onstraint ( ) Network rokerage (page 33) A. Network brokers tend to distribute answers, people in moderately constrained positions tend to be conduits for informational messages. Data are from Leavitt (1949: Table 3, following page 62).. Network brokers are least happy initially, but eventually become the most pleased with the experience. Data are from Leavitt (1949:Table 29, pages 6-61; "How did you like your job in the group?).. The final outcome, by the end of the experiment, is that network brokers are most likely to be recognized as the unofficial group leader. Data are from Leavitt (1949: Table 8, page 38; Did your group have a leader? If so, who? ). Figure 2.5 in urt (216, Structural Holes in Virtual Worlds)

34 Network rokerage (page 34) from urt, Hogarth, and Michaud "The social capital of French and American managers" (2, Organization Science) olleague Relations Predating ntry into the Firm French Manager Years in the Firm American Manager Years in the Firm Years Acquainted with ontact Years in the Firm to 1 11 to 2 Over 2 Total Number olleagues French Managers % Known efore Firm 26% 15% 5% 11% Mean Years Known Number olleagues American Managers % Known efore Firm 81% 42% 6% 55% Mean Years Known Appendix V: National Differences in usiness ulture

35 Distinctions etween Kinds of Relations (relations close together reach the same contacts) Network rokerage (page 35) distant difficult American Managers less than monthly other less close knew before monthly 3-9 subordinate buy-in valued daily 1+ close supervisor discuss exit weekly discuss personal 1-2 esp close socialize other subordinate distant difficult French Managers less than monthly 1-2 monthly less close knew before close from Figure 1.7 in rokerage and losure (cf. Figure A3 in Neighbor Networks) 3-9 buy-in valued 1+ daily discuss esp personal close discuss exit weekly socialize supervisor

36 Network Returns for ntrepreneurs in the Renewal of the hinese conomy Network rokerage (page 36) Predicted Probability of ompany Patents (for 77 electronic firms with R&D departments) Network onstraint many Structural Holes few r =.84 Sample of 7 hinese O entrepreneurs in 212. Networks are key contacts during important events in company history, most valuable current contacts, most valuable senior employee, and most difficult contact. mean network size network density non-redundant contacts network constraint (x1) mean percent family frequency (days) years known contacts mean number of employees year company founded NOT The above graph contains the 77 electronics companies with R&D departments. The Y axis is from a logit equation predicting whether or not each of the 7 companies had filed for patents (73% had not filed for patents). The predictors include years since founding (.79 z-score), number of company employees (2.35 z-score), whether the company had an R&D department (9.19 z-score), log network constraint (-2.97 z-score, P <.1), an adjustment for lower patenting in textiles, transportation equipment, and medicine manufacturing (-2.17 z-score), and an adjustment for a weaker network effect in the lower patenting industries (2.16 z-score). For contextual background on the sample Os, see Nee and Opper, apitalism from elow: Markets and Institutional hange in hina (212, Harvard University Press). Also see Merluzzi (213, "Social apital in Asia," Social Science Research). 1% % % O's cite no nuclear or extended family! (61%)

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