Corpo: The course will provide an introduction to the mathematical basis of Complex Networks and to their use to describe, analyze and model a variety of physical and economic situations.
LIST OF LECTURES
Lecture 1 Graph Theory Introduction:
Basic Definitions, Statistical Distributions, Universality, Fractals, Self-Organised Criticality
Lecture 2 Properties of Complex Networks:
Scale-Invariance of Degree Distribution, Small-World Effect, Clustering
Lecture 3 Applications:
Internet, WWW, Socio-technological systems, Economics, Biology
Lecture 4 Communities:
Community Detections, Algorithms to explore Graphs
Lecture 5 Different kind of graphs:
Vertices differences, Layered Vertices, Trees and Taxonomies
Lecture 6 Ranking:
Hierarchies, Spanning Trees,HITS, PageRank,
Lecture 7 Static Models of Graphs:
Erdos-Renyi, Small World
Lecture 8 Dynamical Models of Graphs:
Barabasi-Albert, Configuration models
Lecture 9 Fitness models:
Fitness model and Self-Organised Fitness Model
Lecture 10 Basic Ingredients of Models:
Growth Preferential Attachments, Log Normal Distribution, Multiplicative Noise