Community Finding Clique Percolation MethodsBetweenness, Spectral Partition Methods
So far… We studied some basic network models: Erdos-Renyi: Random Graph. Watts-Strogatz: Small World. Barabasi-Albert: Scale-Free Networks. We also saw how to characterize the structure of networks by looking at different structural properties. Local Properties: Centrality Measures, Clustering, Topological Overlap, Motifs. Global Properties: Diameter, Giant Component, Degree Correlations.
We also Studied some dynamical consequences of Scale Free networks: Error-Attack Tolerance Vanishing Epidemic Threshold.
Vanishing Epidemic Threshold Random Network: Epidemic spreads if r >1 Random Network: Epidemic spreads if r > /
How predictable is an epidemic? i = 1 if is city has an infected individual and 0 otherwise. Overlap, measure similarity between the s describing different realizations of the simulation
High degree nodes difficult prediction, As there are many possible paths that spreading cant take. Heterogeneity in weight increases Predictability as there are some links That carry most of the traffic. (Effective degree is smaller)
High weight – High Betweenness Low weight – High Betweenness
Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007 Simple Contagion Process
Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007 Complex Contagion Process
Simple Contagion Process Complex Contagion Process Complex Contagions and the Weakness of Long Ties D Centola, M Macy - American Journal of Sociology, 2007 Watts-Strogatz type of Shortcuts increase the speed of spreading Watts-Strogatz type of slow or stop the spreading process