Class 04: Scale-free properties

7 outubro 2021, 15:30 • Francisco Correia dos Santos

• Topics: Analysis of the degree distributions of biological (PPI, metabolic networks, etc.), social (email, co-authorship, online communities, sexual interaction networks, etc.) and technological networks (WWW, airport, Internet, etc.). Power-law degree distributions. Scaling of the maximum degree. Scale-free: what does it mean? Nth moments of power-law degree distributions.  Ultra-small world properties. Exponents of real-world networks: why is nature in such a limited range? Fitting power-laws: the Clauset et al. Method (& code). Configuration model

LAB01

4 outubro 2021, 17:00 • Francisco Correia dos Santos

In-class development of the course's project. Gephi and NetworkX. Problem set 1.

Class 03: Random Graphs and WS model

4 outubro 2021, 15:00 • Francisco Correia dos Santos

Topics discussed: Stanley Milgram small-world experiments, the Erdos-Renyi model, Erdos number, Average degree, degree dist., clustering coeff. of an ER graph, scaling of the maximum degree, the emergence of a giant component in random graphs.

Topics: Watts & Strogatz paper on Small-world networks (Nature, 1998), dependence on the clustering and average-path length, Homogeneous-small worlds and rewiring of networks without altering the degree dist.See also Newman's review, The Structure and Function of Complex Networks, and search for the Watts-Strogatz small-world model. 

Apoio ao Projecto e à resolução dos problem sets.

4 outubro 2021, 11:00 • Francisco Miguel Enxerto Sena

Apoio ao Projecto e à resolução dos problem sets.

Apoio ao Projecto e à resolução dos problem sets.

1 outubro 2021, 15:00 • Francisco Miguel Enxerto Sena

Apoio ao Projecto e à resolução dos problem sets.