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

Hernan A. Makse - Shlomo Havlin

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

Hernan A. Makse - Shlomo Havlin

Obesity epidemic (?)

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

Obesity in USA increases with time

What we know on obesity ‘spreading’

1. Genetics2. Peer pressure

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

Our approach

• The physics of clustering is challenging

• Study obesity as a percolation process

• Use scaling analysis

• More properties

Obesity prevalence in USA

Percolation transition

Time evolution of obesity clusters

County obesity %

Largest clusters

County obesity %

Neighbors influence

(after Christakis, Fowler)

Distance-based correlations

The increase rate is also correlated

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

Limits

𝛽=𝛾2𝑑

High correlations: No correlations:

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

Spatial correlations (constant in time)

g =0.5Obesity

g =1.0Population

Digestive cancer mortality(Changes with time)

Time evolution of g

Weak correlations

Strong correlations

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

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