Introduction to Complex Networks - Loughborough University · [B3] Dynamical Processes on Complex Networks A. Barrat, M. Barthélémy, and A. Vespignani, Cambridge University Press

Introduction to Complex Networks

Samuel Johnson Warwick Mathematics Institute, and

Centre for Complexity Science, University of Warwick

Complexity

“Even the smallest insect, with its intricate structure, is far more complex than either an atom or a star.” Sir Martin Rees

Complexity

“The whole is more than the sum of its parts.”

Graph theory

Some real networks

Nodes and links

Nodes and links

Nodes and links

Nodes and links

Adjacency matrix

Node degree

Node degree

Node degree

Node degree

Node degree

Degree distribution

Degree distribution

Paths

Paths

Paths

Clustering

Key measures

Random graphs

Random graphs

Random graphs

Six degrees of separation?

Six degrees of separation?

Six degrees of separation?

Clustering

Watts-Strogatz model

Epidemics

Scale-free networks

Scale-free networks

Scale-free networks

Barabási-Albert model

Network robustness

Structure of networks

Dynamical processes on networks

Thank you for your attention! …and to A.-L. Barabási for making material available online