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An introduction to networks
An overview of a network as a collection of connected elements. Different types of networks are illustrated as well as a way to represent them mathematically.
The degree distribution of a network
The degree distribution is introduced as a simplified measure that characterizes one aspect of a network's structure.
One of the simplest types of networks
An introduction and motivation behind one of the simplest types of networks, the Erd
We can view a random network as a member of an ensemble of networks determined by a probability distribution.
The absurd high dimensionality of random graphs
The space of random networks is so ridiculously large that one needs to take drastic measures to make it manageable.
Evidence for additional structure in real networks
Real networks seems to have additional structure than that captured by a random network with independent edges.
Small world networks
Small world networks are those that have a relative small mean path length but high transitivity.
Generating networks with a desired degree distribution
Overview of algorithms that allow one to generate networks with a prescribed degree distribution
Connecting network structure to dynamical properties
An exploration of the influence of network structure on the properties of dynamical processes taking place on networks.
The master stability function approach to determine the synchronizability of a network
The master stability function approach allows one to analyze how network structure influences the stability of the completely synchronous state..
The stability of the asynchronous state as function of largest eigenvalue
The network influences the stability of the asynchronous state through the largest eigenvalue of the adjacency matrix.
Generating networks with a desired second order motif frequency
An approach to generating networks with given frequency of second order connection motifs.