Related papers: Pacotte tree networks, graph theory and projective…
Graph theory provides a primary tool for analyzing and designing computer communication networks. In the past few decades, Graph theory has been used to study various types of networks, including the Internet, wide Area Networks, Local Area…
In recent years, methods from network science are gaining rapidly interest in economics and finance. A reason for this is that in a globalized world the interconnectedness among economic and financial entities are crucial to understand and…
We provide a finite equational presentation of graphs of treewidth at most three, solving an instanceof an open problem by Courcelle and Engelfriet. We use a syntax generalising series-parallel expressions, denoting graphs with a small…
We introduce evolving networks where new vertices preferentially connect to the more central parts of a network. This makes such networks compact. Finite networks grown under the preferential compactness mechanism have complex…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
Traceroute measurements are one of our main instruments to shed light onto the structure and properties of today's complex networks such as the Internet. This paper studies the feasibility and infeasibility of inferring the network topology…
A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life.' In this paper we use an…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
This article provides a taxonomy of current and past network modeling efforts. In all these efforts over the last few years we see a trend towards not only describing the network, but connected devices as well. This is especially current…
Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set $X$ of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization, that cannot be captured by trees. A variety of…
Virtual networks are an innovative abstraction that extends cloud computing concepts to the network: by supporting bandwidth reservations between compute nodes (e.g., virtual machines), virtual networks can provide a predictable performance…
Tree-child networks are an important network class which are used in phylogenetics to model reticulate evolution. In a recent paper, Pons and Batle (2021) conjectured a relation between tree-child networks and certain words. In this short…
The rich and varied ways that genetic material can be passed between species has motivated extensive research into the theory of phylogenetic networks. Features that align with biological processes, or with desirable mathematical…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…
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…
Research on probabilistic models of networks now spans a wide variety of fields, including physics, sociology, biology, statistics, and machine learning. These efforts have produced a diverse ecology of models and methods. Despite this…
We develop a notion of a dual of a graph, generalizing the definition of Goulden and Yong (which only applied to trees), and reproving their main result using our new notion. We in fact give three definitions of the dual: a graph-theoretic…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…