Related papers: Noncommutative Network Models
Networks can be combined in various ways, such as overlaying one on top of another or setting two side by side. We introduce "network models" to encode these ways of combining networks. Different network models describe different kinds of…
In this thesis, we present a flexible framework for specifying and constructing operads which are suited to reasoning about network construction. The data used to present these operads is called a \emph{network model}, a monoidal variant of…
We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
In this paper we define and study the notion of a monoidal network, which consists of a commutative ring $R$ and a collection of groups $\Gamma_I$, indexed by the ideals of $R$, with $\Gamma_I$ acting on the quotient $R/I$ and satisfying a…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
Modeling networks can serve as a means of summarizing high-dimensional complex systems. Adapting an approach devised for dense, weighted networks, we propose a new method for generating and estimating unweighted networks. This approach can…
The structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit…
Modular meta-learning is a new framework that generalizes to unseen datasets by combining a small set of neural modules in different ways. In this work we propose abstract graph networks: using graphs as abstractions of a system's subparts…
Complex networks have become powerful mechanisms for studying a variety of realworld systems. Consequently, many human-designed network models are proposed that reproduce nontrivial properties of complex networks, such as long-tail degree…
Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…