Related papers: Fitch Graph Completion
Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. It is often believed that heterophilous graphs are challenging for standard message-passing graph neural networks…
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and…
Node classification is a classical graph machine learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs…
We investigate structural and algorithmic advantages of a directed version of the well-researched class of distance-hereditary graphs. Since the previously defined distance-hereditary digraphs do not permit a recursive structure, we define…
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic generalizations of enumerative results due to B\'ina and…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
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…
Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
The inference of gene regulatory networks (GRNs) is a foundational stride towards deciphering the fundamentals of complex biological systems. Inferring a possible regulatory link between two genes can be formulated as a link prediction…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
Let $G$ be a graph and $A$ be its adjacency matrix. A graph $G$ is invertible if its adjacency matrix $A$ is invertible and the inverse of $G$ is a weighted graph with adjacency matrix $A^{-1}$. A signed graph $(G,\sigma)$ is a weighted…
Gene innovation is a key mechanism on the evolution and phenotypic diversity of life forms. There is a need for tools able to study gene innovation across an increasingly large number of genomic sequences to maximally capitalise our…
Gene gains and losses have shaped the gene repertoire of species since the universal last common ancestor to species today. Genes in extant species were gained at different historical times via de novo creation of new genes, duplication of…
Phylogenetic reconstruction aims at finding plausible hypotheses of the evolutionary history of genes or species based on genomic sequence information. The distinction of orthologous genes (genes that having a common ancestry and diverged…
A graph $G$ realizes the degree sequence $S$ if the degrees of its vertices is $S$. Hakimi gave a necessary and sufficient condition to guarantee that there exists a connected multigraph realizing $S$. Taylor later proved that any connected…
The complex pattern of presence and absence of many genes across different species provides tantalising clues as to how genes evolved through the processes of gene genesis, gene loss and lateral gene transfer (LGT). The extent of LGT,…
A digraph is attached to any evolution algebra. This graph leads to some new purely algebraic results on this class of algebras and allows for some new natural proofs of known results. Nilpotency of an evolution algebra will be proved to be…
A directed graph $D$ is singly connected if for every ordered pair of vertices $(s,t)$, there is at most one path from $s$ to $t$ in $D$. Graph orientation problems ask, given an undirected graph $G$, to find an orientation of the edges…
Graph Neural Networks (GNNs) have become the de-facto standard tool for modeling relational data. However, while many real-world graphs are directed, the majority of today's GNN models discard this information altogether by simply making…