Pages similar to: Generating networks with a desired second order motif frequency
- 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 - Random networks
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. - Scale-free networks
Scale-free networks are those that have a power law degree distribution. - 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.