Role models for complex networks

Role models for complex networks

We present a framework for automatically decomposing (“block-modeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image grap...

Complex Networks: Deterministic Models

The recent discovery that many networks associated with complex systems belong to a new category known as scale-free small-world has led to a surge in the number of new models for these systems. Many studies are based on probabilistic and statistical methods which capture well some of the basic properties of the networks. More recently, a deterministic approach has proven useful to complement a...

Farey graphs as models for complex networks

Farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as Farey graphs. These graphs were first introduced by Matula and Kornerup in 1979 and further studied by Colbourn in 1982 and they have many interesting properties: they are minimally 3-colorable, uniquely Hamiltonian, maximally outerplanar and perfect. In this paper we introduce a simple gener...

Complex networks: Models and dynamics

Modularity of Complex Networks Models

Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between vertices of different clusters. As a result, modularity is often used in optimization methods for detecting community structure in networks, and so it is an impo...