Related papers: A General Solution for Network Models with Pairwis…

Bottom-up layout algorithms for compound graphs are suitable for presenting the microscale view of models and are often used in model-driven engineering. However, they have difficulties at the macroscale where maintaining the overview of…

Deformations of knots and links in ambient space can be studied combinatorially on their diagrams via local modifications called Reidemeister moves. While it is well-known that, in order to move between equivalent diagrams with Reidemeister…

Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…

Most epidemic processes on networks can be modelled by a compartmental model, that specifies the spread of a disease in a population. The corresponding compartmental graph describes how the viral state of the nodes (individuals) changes…

In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…

Several `edge-discovery' applications over graph-based data models are known to have worst-case quadratic time complexity in the nodes, even if the discovered edges are sparse. One example is the generic link discovery problem between two…

Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…

In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…

Many natural, technological, and social systems incorporate multiway interactions, yet are characterized and measured on the basis of weighted pairwise interactions. In this article, I propose a family of models in which pairwise…

Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…

Knowledge hypergraphs generalize knowledge graphs using hyperedges to connect multiple entities and depict complicated relations. Existing methods either transform hyperedges into an easier-to-handle set of binary relations or view…

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…

We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the…

Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighbourhoods of nodes in hypergraphs. We establish their relationships to lattice…

There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable structured class, such as the class of all planar graphs. Here we consider a general 'bridge-addable' class of graphs - if a graph…

We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks…

In this paper, we address the model reduction problem for linear hybrid systems via the interconnection-based technique called moment matching. We consider two classical interconnections, namely the direct and swapped interconnections, in…

The spectral properties of traditional (dyadic) graphs, where an edge connects exactly two vertices, are widely studied in different applications. These spectral properties are closely connected to the structural properties of dyadic…

Networks are widely used to model the contact structure within a population and in the resulting models of disease spread. While networks provide a high degree of realism, the analysis of the exact model is out of reach and even numerical…