Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute,...

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Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute, City College of New York Hernan A. Makse - Shlomo Havlin

Transcript of Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute,...

Page 1: Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute, City College of New York Hernan A. Makse - Shlomo.

Clustering and spreading of behavior and opinion in social networksLazaros GallosLevich Institute, City College of New York

Hernan A. Makse - Shlomo Havlin

Page 2: Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute, City College of New York Hernan A. Makse - Shlomo.

Clustering and spreading of behavior in social networksLazaros GallosLevich Institute, City College of New York

Hernan A. Makse - Shlomo Havlin

Page 3: Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute, City College of New York Hernan A. Makse - Shlomo.

Obesity epidemic (?)

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BMI and obesity

The Body Mass Index (BMI) is a standard measure of human body fat

BMI>30 is generally accepted as the obesity threshold

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Obesity in USA increases with time

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What we know on obesity ‘spreading’

1. Genetics2. Peer pressure

(Christakis and Fowler, NEJM, 2007)3. Spatial clustering

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Our approach

• The physics of clustering is challenging

• Study obesity as a percolation process

• Use scaling analysis

• More properties

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Obesity prevalence in USA

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Percolation transition

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Time evolution of obesity clusters

County obesity %

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Largest clusters

County obesity %

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Neighbors influence

(after Christakis, Fowler)

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Distance-based correlations

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The increase rate is also correlated

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Spatial correlations:

Scaling theory of Growth

• Standard theory of Gibrat assumes random

growth

• Scaling concepts introduced by the H.E. Stanley

group

(Stanley, Nature, 1996) for the growth of

companies

• Extended to more properties (e.g. cities)

Growth rate:

𝛽=𝛾2𝑑

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Limits

𝛽=𝛾2𝑑

High correlations: No correlations:

b =0, g =0 b =0.5 , g=2 (in 2d)

Page 17: Clustering and spreading of behavior and opinion in social networks Lazaros Gallos Levich Institute, City College of New York Hernan A. Makse - Shlomo.

Spatial correlations (constant in time)

g =0.5Obesity

g =1.0Population

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Digestive cancer mortality(Changes with time)

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Time evolution of g

Weak correlations

Strong correlations

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Phase diagram

Uncorrelated

Random walk

Human activity

Economy

City growth

Population

Mortality

Cancer mortality

Obesity

Diabetes

Inactivity

Lung cancer

g /d11/21/4

Weak

correlationsStrong

correlations

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Conclusions

• Strong spatial correlations in obesity spreading

• Obesity clusters grow faster than the population growth

• Scaling analysis quantifies the degree of spatial correlations

• Exponents are related

Three main universality classes based on spatial correlations