![Page 1: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/1.jpg)
ETH Zurich – Distributed Computing – www.disco.ethz.ch
Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David Peleg
Homophily and the Glass Ceiling Effect in Social Networks
![Page 2: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/2.jpg)
![Page 3: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/3.jpg)
Do you notice something?
o o o o o
o o o o
![Page 4: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/4.jpg)
![Page 5: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/5.jpg)
What is happening?
The "glass ceiling"... is the unseen, yet unbreakable barrier that keeps minorities and women from rising to the upper rungs of the corporate ladder, regardless of their qualifications or achievements.
Federal Glass Ceiling Commission, US Government (1995)
![Page 6: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/6.jpg)
Unequal Entry Rates
Homophily
The Rich get Richer (Preferential Attachment)
PhD Students and their Advisor
![Page 7: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/7.jpg)
ρ
1-ρ
![Page 8: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/8.jpg)
![Page 9: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/9.jpg)
How does such a Network look like?
r = 0.5, ρ = 0.7
![Page 10: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/10.jpg)
How does such a Network look like?
r = 0.3, ρ = 1
![Page 11: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/11.jpg)
How does such a Network look like?
r = 0.3, ρ = 0
![Page 12: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/12.jpg)
How does such a Network look like?
r = 0.3, ρ = 0.7
![Page 13: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/13.jpg)
Glass Ceiling: How is it defined?
Tail glass ceiling: G(n) exhibits glass ceiling effect for the red nodes if: while:
![Page 14: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/14.jpg)
Does this Produce a Glass Ceiling?
r = 0.5, ρ = 0.7
![Page 15: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/15.jpg)
Does this Produce a Glass Ceiling?
r = 0.3, ρ = 1
![Page 16: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/16.jpg)
Does this Produce a Glass Ceiling?
r = 0.3, ρ = 0
![Page 17: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/17.jpg)
Does this Produce a Glass Ceiling?
r = 0.3, ρ= 0.7
![Page 18: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/18.jpg)
Formal Results
Theorem:
Let 0 < r < ½ and 0 < ρ < 1 then G(n, r, ρ) exhibits a glass ceiling effect (for any starting condition).
![Page 19: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/19.jpg)
Formal Results
Theorem: G(n, r, ρ) will not have glass ceiling effect in the following cases:
1. If the rate r = ½ (and for any value of ρ).
2. If ρ = 0 or ρ =1 (and for any value of r).
3. If a new vertex at time t selects its advisor uniformly at random from all nodes at time t-1 (and for any value of r and ρ).
![Page 20: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/20.jpg)
Proof Overview
1. Fast convergence of sum of degrees of red nodes in expectation (independent of starting condition)
2. High probability convergence
3. Power law degree distribution of each gender
![Page 21: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/21.jpg)
![Page 22: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/22.jpg)
![Page 23: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/23.jpg)
PhD and Supervisor Network
![Page 24: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/24.jpg)
PhD and Supervisor Network
![Page 25: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/25.jpg)
1.Definitions for glass celling effect in networks
2.Simple Mathematical model:
– Unequal entry rate, “rich get richer”, homophily
3.Proof for glass ceiling emergence
– three assumptions → glass ceiling
– any two assumptions → no glass ceiling.
4.Analyzed the DBLP
Summary
![Page 26: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/26.jpg)
Future Work
• Include nodes leaving the network
• Evaluate network with higher percentage of females
![Page 27: Homophily and the Glass Ceiling Effect in Social NetworksETH Zurich – Distributed Computing – Chen Avin, Barbara Keller, Zvi Lotker, Claire Mathieu, Yvonne-Anne Pignolet, David](https://reader033.vdocument.in/reader033/viewer/2022042006/5e6fd6094af1037c86220fe5/html5/thumbnails/27.jpg)
תודה רבה