Related papers: Noncommutative Network Models
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
Recently, neural network architectures have been developed to accommodate when the data has the structure of a graph or, more generally, a hypergraph. While useful, graph structures can be potentially limiting. Hypergraph structures in…
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…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
This paper introduces a method to generate hierarchically modular networks with prescribed node degree list by link switching. Unlike many existing network generating models, our method does not use link probabilities to achieve modularity.…
How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. We…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
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…
The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their…
The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes,…
Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…
Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
We propose a general framework for modelling network data that is designed to describe aspects of non-exchangeable networks. Conditional on latent (unobserved) variables, the edges of the network are generated by their finite growth history…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…