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Correction

SOCIAL SCIENCES Correction for “A network’s gender composition and commu- nication pattern predict women’s leadership success,” by Yang Yang, Nitesh V. Chawla, and Brian Uzzi, which was first pub- lished February 5, 2019; 10.1073/pnas.1721438116 (Proc Natl Acad Sci USA 116:2033–2038). The authors note that part of the Acknowledgments section

appeared incorrectly. The acknowledgment “Multidisciplinary University Research Initiatives (MURI)–Defense Advanced Research Projects Agency (DARPA) Grant BAA-11-64” should instead appear as “the US Army Research Laboratory and US Army Research Office Grant W911NF-15-1-0577.”

Published under the PNAS license.

Published online March 25, 2019.

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A network’s gender composition and communication pattern predict women’s leadership success Yang Yanga,b, Nitesh V. Chawlac,d, and Brian Uzzia,b,1

aNorthwestern Institute on Complex Systems, Northwestern University, Evanston, IL 60208; bKellogg School of Management, Northwestern University, Evanston, IL 60208; cComputer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556; and dInterdisciplinary Center for Network Science and Applications, University of Notre Dame, Notre Dame, IN 46556

Edited by Greg J. Duncan, University of California, Irvine, CA, and approved November 26, 2018 (received for review December 11, 2017)

Many leaders today do not rise through the ranks but are recruited directly out of graduate programs into leadership positions. We use a quasi-experiment and instrumental-variable regression to understand the link between students’ graduate school social networks and placement into leadership positions of varying levels of authority. Our data measure students’ personal characteristics and academic performance, as well as their social network information drawn from 4.5 million email correspon- dences among hundreds of students who were placed directly into leadership positions. After controlling for students’ personal characteristics, work experience, and academic performance, we find that students’ social networks strongly predict placement into leadership positions. For males, the higher a male student’s centrality in the school-wide network, the higher his leadership- job placement will be. Men with network centrality in the top quartile have an expected job placement level that is 1.5 times greater than men in the bottom quartile of centrality. While centrality also predicts women’s placement, high-placing women students have one thing more: an inner circle of predominantly female contacts who are connected to many nonoverlapping third-party contacts. Women with a network centrality in the top quartile and a female-dominated inner circle have an expected job placement level that is 2.5 times greater than women with low centrality and a male-dominated inner circle. Women who have networks that resemble those of high-placing men are low- placing, despite having leadership qualifications comparable to high-placing women.

gender inequality | leadership | social network | computational social science | STEM

On July 20, 1969, Neil Armstrong became the first human to set foot on the moon, marking one of the most cele-

brated scientific achievements in history. However, his immortal words, “That’s one small step for man, one giant leap for mankind,” would never have been possible without Susan Fin- ley. Finley, a NASA engineer, rewrote the moon-landing code of Apollo 11’s failed computer minutes before the spacecraft touched down, averting what would have been a catastrophic crash landing (1). In the 50 y since Finley’s outstanding impact on the world, research has documented how the gender makeup of leaders impacts both organizational performance and equal- ity (2–5). Leaders in organizations play a large role in fill- ing job openings and establishing workplace cultures (2, 6). Female leadership has been associated with lower levels of gender discrimination (2, 7–9), supportive work–family-balance policies (6, 10–12), smaller gender-pay and -promotion gaps (13–15), and, in certain fields like science, technology, engineer- ing, and mathematics (STEM), better retention among women employees (16, 17).

Women’s and men’s leadership attainment has been linked to high-school academic training, gender norms, and mentorship relationships that differentially shape men’s and women’s aspi- rations and preparation for leadership (2, 7, 18). Nonetheless, research continues to explore reasons behind gender imbalances

in leadership (6, 19–21). A new channel into leadership posi- tions that diverges from traditional “up-through-ranks” channels is through placement into leadership positions directly out of graduate-school programs that are designed to provide future men and women leaders with indistinguishable levels of man- agerial and technical training required for leading. While these programs are fast-growing (22), knowledge about their link with men’s and women’s placement into leadership positions is nascent (23–25).

In programs that prepare graduates for leadership positions, a factor that is hypothetically related to a student’s placement is the student’s social network (21, 26), which can provide a job- seeker with key job-market information (21, 27, 28). Job-market information is of two types—public and private (21, 27, 29). Pub- lic information tends to include facts on who’s hiring and who has been hired, salaries across firms, company reputations, and other publicly available information important to job search and negotiations. By contrast, private information benefits job seek- ers by conveying personalized knowledge about an organization’s culture, unwritten rules, or sensitive and confidential impressions on how to present to recruiters or manage relationships (27, 28).

Different types of social-network ties access public and pri- vate information (30–32). Because public information generally involves diverse market-wide data, it tends to be scattered among students in the school-wide network (33). In such cases, weak ties (“acquaintances”) can be a primary source of public information because they are sufficient for passing on more or less fact-based information that requires little clarification to use effectively (30, 33). Conversely, because private information involves per- sonal experiences and biases, it is more likely to be passed

Significance

Graduate programs increasingly place women directly into leadership positions. For men, centrality in the school-wide student network predicts job-rank placement. Women’s place- ment is also predicted by centrality and the presence of a distinctive inner circle of women in their network. The inner circle of high-placing women displays an unusual network duality: The network has cliquish ties among women, but each woman is connected to a separate set of third-party contacts. This dual connectivity of strong and weak ties appears to pro- vide simultaneous access to gender-related tacit information important for women’s success as well as diverse job-market data needed for successful job search and negotiations.

Author contributions: Y.Y. and B.U. designed research; Y.Y., N.V.C., and B.U. performed research; Y.Y. and B.U. analyzed data; and Y.Y. and B.U. wrote the paper.y

The authors declare no conflict of interest.y

This article is a PNAS Direct Submission.y

Published under the PNAS license.y 1 To whom correspondence should be addressed. Email: [email protected]

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1721438116/-/DCSupplemental.y

Published online January 22, 2019.

www.pnas.org/cgi/doi/10.1073/pnas.1721438116 PNAS | February 5, 2019 | vol. 116 | no. 6 | 2033–2038

along by strong ties (“close friends”) who socially support each other and can interpret and trust one another’s information (29, 30, 32).

To study the link between the graduate-school network and leadership attainment, we collected data from a top-rated grad- uate program. The program, and others like it, trains men and women to be equally attractive technically and managerially for leadership positions. The sample included all n = 728 graduates, 542 men (74.5%) and 186 women (25.5%). Students’ social and communication networks were constructed from all 4.55 million anonymized, content-free emails sent among all students in the 2006 and 2007 classes. At this time, students used their school’s email service almost exclusively for their email correspondences. Students’ official transcripts provided data on gender, entrance- exam scores, grade point average (GPA), years of work experi- ence, undergraduate major, nationality, class year, and sociability (34) (SI Appendix, section 2). Our modeling triangulates multiple methods. First, we use fixed-effects regressions to find correla- tions between job attainment and student human capital and network characteristics. Second, we use instrumental variable (IV) regression and coarsened exact matching (CEM) within the context of a quasi-experiment to conduct causal inference tests (35, 36).

Variables in our analyses are defined as follows. The depen- dent variable is women and men’s “ranked job placement in leadership positions.” All graduates took leadership-level posi- tions. Because actual job-title data violate privacy guidelines, the institution provided a ranked percentile score [0.0–100] for each position based on the position’s normalized industry and region- specific salary (37). We followed standard practice and converted each job rank to a corresponding Z score, which is interpreted like the original ranked-percentile score (38).

Three variables—centrality, communication equality, and gen- der homophily—measured different aspects of a student’s net- work. For all network measures, nodes i and j were defined as connected if her or his email was reciprocal and greater than expected by chance (39–42) (group emails were omitted). Centrality in the school-wide network was measured by using Pagerank. Centrality scores were logged and standardized. Con- sistent with research, students displayed a median number of contacts of 12 (95%, CI = 11–13) (41, 42). Persons with the same centrality often have different network communication patterns and gender compositions (31). For example, students can email their network contacts relatively equally or unequally. Com- munication equality was measured by using Shannon entropy (43). When communication equality is low, a subset of i ’s alters receive an incommensurate share of i ’s email and stand out as relatively “strong” network ties (30, 39). When communication equality is high, i ’s alters receive roughly equivalent shares of i ’s email (all j ’s are relatively “weak” ties). Communication equal- ity is normally distributed (mean = 1.93, SD = 0.65). Gender homophily was measured as a student’s proportion of same- sex contacts compared with what was expected by chance using a Z score (44) (mean = 0.91, SD = 1.54). Compositionally, 76.2% of students had mixed-gender networks, 22.3% had all- male networks, and 1.3% had all-female networks (SI Appendix, Table S1). Detailed definitions of network variables can be found in SI Appendix, section 2.

Results Fig. 1 presents the coefficients and standard errors of a regres- sion of students’ ranked leadership-job placement on social- network characteristics and controls for student characteris- tics and performance, an industry-category dummy variable (SI Appendix, section 2), and an interaction between the dummy variable and all of the network variables.

Examining the associations between person-level variables and placement, Fig. 1 indicates that examination scores, GPA, work

experience, and sociability show no statistically significant rela- tionships with leadership-job placement. An explanation for the fact that employers do not seem to differentiate students on their personal traits is that graduate programs, unlike undergraduate programs, select relatively small numbers of students of nearly equivalent qualifications. Also noteworthy is the finding that pat- terns of leadership attainment do not appear to differ in STEM and non-STEM jobs (P = 0.943 and P = 0.993 for men and women) or display any significant variation across industries (see expanded table in SI Appendix, Table S2). This finding suggests that research that has speculated that STEM leadership positions are unique (20, 45) may nonetheless be able to draw on insights about women leaders found in non-STEM fields.

Controlling for other factors, we observe that students’ net- works strongly predict the placement level for both women and men. For men, only centrality is significantly related to job attain- ment. Roughly, a 10% increase in centrality on average for a man corresponds to an ∼ 29% unit increase in ranked job place- ment. Beyond centrality, neither communication patterns nor gender homophily predicts placement level for men. This finding suggests that male students who equally or unequally distribute their communications among their contacts have no difference in placement rank. Similarly, for men, an underrepresentation or overrepresentation of same-gender contacts is uncorrelated with placement level. Together, these patterns suggest that men’s networks relate to placement level principally via network centrality, which conceivably increases their access to diverse, publicly available job-market information in the school-wide network (21).

For women, centrality positively correlates with placement level. A 10% increase in centrality corresponds to an ∼ 59% unit increase in ranked job placement, suggesting that wide access to public information about the job market is also essential for women. The regression also indicates that communication patterns and gender compositions significantly predict women’s

Fig. 1. Fixed-effects regression of ranked job-level placement in leader- ship positions. Job-level placement is quantified with a rank percentile score. Blue/pink lines represent the regression coefficients and associ- ated 95% CIs for men/women. For men, only centrality in school-wide network predicts job-placement ranking. For women, centrality and the interaction between communication equality and gender homophily predict job-placement rankings.

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Fig. 2. Gender homophily and communication patterns predict women’s, but not men’s, job placements. Margins plots are estimated from coefficients reported in Fig. 1. Solid lines represent students whose networks have more same-gender contacts than expected by chance (i.e., same-gender “dominated” networks) and vice versa for dashed lines. A indicates that women have higher-ranked placements when they have female-dominated networks and communicate relatively evenly with the contacts in their network and vice versa for low-placing women. C demonstrates that high-placing women also have relatively stronger ties with the women in their network than do low-placing women (bar height is normalized for each group). B and C indicate that high- and low-placing men show no differences in their gender and communication patterns. See SI Appendix, section 5.2 for computational details. NS, not significant; **P < 0.01.

job-rank placement. Fig. 2 A and B presents the margin plots with 95% CI of women’s and men’s predicted placement level (Z score) for the interaction between communication equal- ity and gender homophily based on a split at the median level of the gender homophily. The figures indicate that communi- cation patterns and gender compositions significantly predict women’s placement level, but not men’s, although we cannot reject the null hypothesis that the corresponding coefficients are similar for both groups (SI Appendix, section 5.1.1). For women, the significant interaction indicates that women place higher the more women-dominated their network is (solid line) and the more they communicate relatively evenly with their contacts.

Fig. 2C further indicates that high-placing women have rel- atively stronger relationships with the women in their network than do low-placing women. Seventy-seven percent of high- placing women have an inner circle of strong ties to two or three women who communicate intensely with one another. By contrast, low-placing women have a male-dominated network and relatively weak ties with the women in their network. The regression estimate of the impact of these network differences for women’s placement implies that woman with a network centrality in the top quartile and a female-dominated inner circle have an expected job placement level that is 2.5 times greater than a woman with low centrality and a male-dominated inner circle.

The positive link for high-placing women between their inner circle and leadership attainment is striking. Cliquish, homoge- neous networks normally hurt job-search and promotion oppor- tunities (29, 33, 46). In this context, how does an inner circle benefit high-placing women? One possible account is that while the inner circle is made up of a small cluster of tightly inter- linked women, each woman simultaneously has nonoverlapping third-party contacts; the former provide gender-specific private information and support, while the latter provide job-market information scattered among separate contacts in the larger school network. To explore this hypothesis, we counted the num- ber of uniquely new contacts added with each inner-circle contact at the time the relationship formed (Fig. 3 A and B). Consis- tent with our hypothesis, Fig. 3C demonstrates that each new inner-circle contact of a high-placing woman, although cliquishly connected, provides connections to an unusually large number

of new contacts that were unreachable through her previous contacts. By contrast, the strong-contacts of low-performing women and all men lack this network duality—they provide redundant paths to contacts already reachable via their cur- rent network connections. Specifically, each inner-circle contact of high-placing women puts them in reach of (i.e., fewer hops away from) nearly twice as many new contacts as that of either low-placing women or all men (P < 0.01).

Quasi-experimental Causal Inferences. The above results demon- strate robust correlations between a student’s graduate-school social network and his or her ranked leadership-job placement. In observational data, unobserved individual differences could account for both variations in students’ social networks and ranked placement. An experiment could account for unobserved differences; however, an experiment is impossible because stu- dents’ careers may be unintentionally harmed (23). As an alternative, we used a quasi-experimental design (QED) that implemented IV regression and CEM to test for causal infer- ence. Both methods support a causal inference between social networks and ranked job placement.

Our QED exploits exogenous variation in students’ chances of forming inner circles to implement an IV estimator for our inner circle. The QED had the following design based on prior studies conducted in similar educational settings (47, 48). Before classes began, all incoming students were randomly assigned to one of nine roughly equivalently sized “home sections.” Randomized assignment to a home section equalized student characteristics across home sections on all observable characteristics, includ- ing gender, nationality, entrance-examination scores, years of work experience, GPA, and industry background. For exam- ple, if women made up 25% of the entire incoming class, each home section had ∼ 25% women students in it, who were drawn randomly from the full set of women in the incoming class. SI Appendix, Fig. S1 verifies that home sections had no observable differences per the randomization.

Because students take their first-quarter classes exclusively with their home-section-mates, most students initially form a network that includes contacts predominantly from their home section rather than from their nonhome sections. Beginning with second-quarter classes, students are differentially exposed, depending on the classes to which they are assigned, to male

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Fig. 3. High-placing women have an inner circle in their networks that dis- tinguishes them from low-placing women. A highlights the functions of the inner circle of high-placing women. An inner-circle contact provides a high- placing woman with access to diverse sets of contacts by connecting her to an usually large number of new, nonoverlapping contacts that would be unreachable through contacts already in her network. B shows that, on average, low-placing women lack this inner circle. The strongest contacts in a low-placing woman’s network connect her to overlapping contacts. C quantifies the average number of unique contacts reached through friends- of-friends in the networks of high- and low-placing men and women. Two “hops” is equivalent to friends-of-friends, while three hops is equivalent to friends-of-friends-of-friends. High-placing women have significantly bet- ter reach to diverse, nonoverlapping contacts than low-placing women (see SI Appendix, section 5.3, Figs. S6 and S7 for additional tests). **P < 0.01; ***P < 0.001; NS, not significant.

and female students from outside their home section. The level of exposure a student has to nonhome-section students depends on an auction system that assigns students to classes. As part of the class-auction system, students bid for classes they want, but bidding outcomes are unpredictable, and stu- dents end up being assigned, in varying degrees, to classes they did not choose to be part of, and in those classes, meet new students from other home sections that they did not expect to meet.

These procedures create random variation in a student’s expo- sure to nonhome-section male and female students, and these nonhome-section classmates are likely to have connections that don’t overlap with the student’s current connections. This ran- dom variation is used to create an IV that can be used to predict the likelihood of having a network with an inner cir- cle. In IV regression, causal inferences are supported when a valid instrument correlates with the explanatory variable, but not with other determinants of the dependent variable. Here, our explanatory variable is the “inner circle” (measured as Commu- nication Equality × Gender Homophily), and our instrument is the degree of exposure a student has to same-gender class- mates from their nonhome sections. Our reasoning behind this instrument is that the inner circle of high-placing women has high clustering among her same-gender contacts and high diver-

sity of third-party contacts. High clustering is more likely when a student is put into classes that have relatively high numbers of same-gender classmates. High diversity is more likely if those same-gender contacts have nonoverlapping connections. While we cannot directly test the exclusion restriction that our instru- ment is unrelated to the dependent variable through a channel other than our explanatory variable (i.e., the inner circle), we stress that our IV derives from a quasi-random assignment procedure that is beyond a student’s control.

Fig. 4 presents the results of the two-stage least-squares (2SLS) regression analysis. The results support our regression findings (Fig. 1). Looking at the link between a student’s expo- sure level to same-gender contacts from other sections and having an inner circle, Fig. 4 indicates a significant first-stage relationship between our IV and explanatory variable for both women (P = 0.002) and men (P = 0.004), a finding consistent with expectations. Fig. 4 reports the link between job placement and a student’s inner circle based on the first-stage fitted values of the inner circle. These 2SLS estimates indicate that having an inner circle strongly and positively predicts women’s ranked job placement (P = 0.026). By contrast, the 2SLS estimates indi- cate that an inner circle has a null effect on men’s ranked job placement (P = 0.670). A CEM also confirmed the IV regression results (49, 50) (see SI Appendix, section 4 for details).

Discussion Leadership positions are increasingly filled by graduates of pro- grams that prepare leaders with the skills needed to be directly hired into positions of leadership. Our study used a quasi- experiment to isolate and test for causal inference in leadership attainment based on human and social capital variables. We found that a graduate-school network predicts placement in leadership positions for male and female students alike, but high- placing women have distinctive networks. High-placing women tend to have an inner circle of contacts who are cliquish in terms of gender, yet diverse in terms of having contacts whose contacts are nonoverlapping. IV regression and CEM analysis further support the causal inference that high-placing women have a

Fig. 4. IV regression of leadership-job placement on women’s and men’s inner circles. B reports estimates of the first-stage regression, where a student’s observed inner circle is regressed on the instrumental variable explained in the text. A reports 2SLS estimates of leadership-job place- ment on the fitted values of inner circle from the first-stage regression. We observe that leadership-job placement is significantly associated with the inner circle of women only. All regressions include the controls described in Fig. 1. The first-stage F statistic indicates that weak instrument patholo- gies are unlikely to be a concern (36). OLS, ordinary least squares. *P < 0.05; **P < 0.01.

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distinctive inner-circle network that predicts their placement level in a leadership position.

Theoretically, the association between an inner circle and job placement both supports and challenges current thinking. Research on women in leadership has argued that getting lead- ership positions on par with men is not dependent on working harder, but working smarter (51). One interpretation of our findings is that working smarter means having a network that addresses the dual concerns of women leaders—simultaneous access to public information and private, gender-specific infor- mation (51). We find that the high-placing women have this kind of network duality, but low-placing women have networks that resemble men’s networks—they have high network centrality, but not an inner circle.

Unlike prior work on social networks and job attainment, we find that cliquish networks are not associated with poor job placement. Prior work has found that network relationships based on homophily and high clustering, where friends of friends are friends of each other, work against professional success by putting job seekers in echo chambers that lack the informational breath and diversity that supports a successful job search. By con- trast, we find that women leaders who have an inner circle of high clustering and high diversity, they appear to reconcile the dual employment challenges that women have to face in male- dominated jobs. In male-dominated settings, women need to gain trustworthy, gender-relevant information about job cultures and social support and wide access to diverse public job-market information. For male graduates, placement depends only on their network centrality—which provides a high level of public job information. Thus, the processes identified in this study— a first examination of women’s placement from graduate school directly into leadership positions, reveal patterns that may help women’s and men’s attainment of influential leadership positions in all jobs.

Another implication for network theory posed by our work concerns network formation. Preferential attachment theory argues that strategically oriented persons should connect to the best-connected persons. However, for women’s job attainment in leadership positions, the best choice is not simply to connect to the best-connected person. Such a process is likely to raise a stu- dent’s centrality but fail to create an inner circle, which doesn’t focus on contacts who have lots of connections but contacts who have nonoverlapping connections.

Areas of future research concern whether women directly attaining leadership positions out of graduate school continue to develop special networks that benefit the firm, their career success, and the success of the personnel they manage. Studies show that when women work with a higher percentage of female supervisors, they report more gender equality (9); family and organizational support (12); and smaller gender pay gaps (13). Yet some research finds that when women view women leaders as threats to power, the presence of women leaders can back- fire, particularly in firms with relatively low proportions of senior

women (10). Thus, one hypothesis is that graduate-school net- works may increase the proportions of senior women in firms and expose aspiring women leaders to each other, reducing expecta- tions of threat. Another area of future research focuses on two theoretical explanations for the impact of networks on job-search information and social support. In our analysis, unfortunately, we do not have data that allow us to definitively say in what relative proportion social support and information are active in women’s networks or how they possibly interact with one another. While our measures focused on communication volume in our net- works, leaning our explanation of the findings toward the role of information in networks, more research is needed on the role of social support.

Susan Finley launched her career at the Jet Propulsion Lab- oratory in 1958. Her career success is partly attributed to an inner circle of women contacts that formed in college, expanded at NASA, and was instrumental in providing information and social support beneficial to her leadership success. Today, she is involved in developing the software that will land the first women and men on Mars.

Materials and Methods Data. Our data came from a top-ranked business school in the United States. The data include all 4.55 million email messages sent by students from two classes. During this time window, the host institution verified that stu- dents almost exclusively used the school’s email service rather than personal email accounts to communicate with each other. Individual attribute data on undergraduate major, entrance examination scores, gender, and so on, as well as student performance (GPA, industry placement, and job-rank placement, etc.) came directly from the programs registrar records and stu- dent transcripts. See SI Appendix, sections 1 and 2 for additional details. All data in the study were anonymized by a third party before being analyzed. Northwestern University Institutional Review Board approved this study (no. STU00002048).

Measures. Ranked job-placement and network variables were defined in the text (see SI Appendix, section 2 for details). Control variables for individual student characteristics were collected directly from stu- dents’ official transcripts. Detailed information on control variables and interactions among variables can be found in SI Appendix, sections 2 and 5.1.

Methods. To address whether the observed network features could be explained by chance interactions, we constructed 10,000 surrogate networks where the degree centrality sequence (52) of the actual network is pre- served and links are placed at random (44, 52) (see SI Appendix, section 3 for details).

ACKNOWLEDGMENTS. We thank Ben Jones, Chris Skovron, Yuan (Tanya) Tian, two anonymous reviewers, and the editor for helpful comments on the manuscript. This work was supported by the Northwestern University Insti- tute for Complex Systems, Multidisciplinary University Research Initiatives (MURI)–Defense Advanced Research Projects Agency (DARPA) Grant BAA- 11-64, and NIH Award R01GM112938. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the social policies, either expressed or implied, of DARPA or the U.S. government.

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