Related papers: CSD Homomorphisms Between Phylogenetic Networks
The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN…
Convolutional neural networks often dominate fully-connected counterparts in generalization performance, especially on image classification tasks. This is often explained in terms of 'better inductive bias'. However, this has not been made…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…
Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a…
Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…
Bayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents…
Network visualization allows a quick glance at how nodes (or actors) are connected by edges (or ties). A conventional network diagram of "contact tree" maps out a root and branches that represent the structure of nodes and edges, often…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
We compare three basic kinds of discrete mathematical models used to portray phylogenetic relationships among species and higher taxa: phylogenetic trees, Hennig trees and Nelson cladograms. All three models are trees, as that term is…
Finding meaningful communities - subnetworks of interest within a large scale network - is a problem with a variety of applications. Most existing work towards community detection focuses on a single network. However, many real-life…
Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any biological justification. Here, we show that…
A connected dominating set (CDS) in a graph is a dominating set of vertices that induces a connected subgraph. Having many disjoint CDSs in a graph can be considered as a measure of its connectivity, and has various graph-theoretic and…
Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…
Phylogenetic networks are a special type of graph which generalize phylogenetic trees and that are used to model non-treelike evolutionary processes such as recombination and hybridization. In this paper, we consider {\em unrooted}…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
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…
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…