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Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…
In recent years, a new interest for the use of graph-theory based networks has emerged within the field of cognitive science. This has played a key role in mining the large amount of data generated by word association norms. In the present…
Galled trees are studied as a recombination model in theoretic population genetics. This class of phylogenetic networks has been generalized to tree-child networks, normal networks and tree-based networks by relaxing a structural condition.…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Networks are ubiquitous in biology and computational approaches have been largely investigated for their inference. In particular, supervised machine learning methods can be used to complete a partially known network by integrating various…
We describe Galois connections which arise between two kinds of combinatorial structures, both of which generalize trees with labelled leaves, and then apply those connections to a family of polytopes. The graphs we study can be imbued with…
Graph decompositions are the natural generalisation of tree decompositions where the decomposition tree is replaced by a genuine graph. Recently they found theoretical applications in the theory of sparsity, topological graph theory,…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…
Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Inspired by the growth dynamics of the protist \textit{Physarum polycephalum}, we employ a formalism that describes adaptive, incompressible Hagen-Poiseuille flows on channel networks to identify graphs connecting different nodes within…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…
The concept of pendant-tree connectivity, introduced by Hager in 1985, is a generalization of classical vertex-connectivity. In this paper, we study pendant-tree connectivity of line graphs.