Related papers: The Sackin Index of Simplex Networks

Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…

Phylogenetic inference, the task of reconstructing how related sequences evolved from common ancestors, is a central objective in evolutionary genomics. The current state-of-the-art methods exploit probabilistic models of sequence evolution…

Acyclic networks are a class of complex networks in which links are directed and don't have closed loops. Here we present an algorithm for transforming an ordinary undirected complex network into an acyclic one. Further analysis of an…

Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…

In this work, we answer an open problem in the study of phylogenetic networks. Phylogenetic trees are rooted binary trees in which all edges are directed away from the root, whereas phylogenetic networks are rooted acyclic digraphs. For the…

Billey et al. [arXiv:1507.04976] have recently discovered a surprisingly simple formula for the number $a_n(\sigma)$ of leaf-labelled rooted non-embedded binary trees (also known as phylogenetic trees) with $n\geq 1$ leaves, fixed (for the…

Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted…

In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…

Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which…

Phylogenetic networks are useful in representing the evolutionary history of taxa. In certain scenarios, one requires a way to compare different networks. In practice, this can be rather difficult, except within specific classes of…

For a given set $\mathcal{L}$ of species and a set $\mathcal{T}$ of triplets on $\mathcal{L}$, one wants to construct a phylogenetic network which is consistent with $\mathcal{T}$, i.e which represents all triplets of $\mathcal{T}$. The…

A spanning tree $T$ in a graph $G$ is a sub-graph of $G$ with the same vertex set as $G$ which is a tree. In 1981, McKay proved an asymptotic result regarding the number of spanning trees in random $k$-regular graphs. In this paper we prove…

Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…

A phylogenetic tree is an acyclic graph with distinctly labeled leaves, whose internal edges have a positive weight. Given a set of n leaves, the collection of all phylogenetic trees with this leaf set can be assembled into a metric cube…

Driven by the need for better models that allow one to shed light into the question how life's diversity has evolved, phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees,…

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…

Simplicial complexes describe collaboration networks, protein interaction networks and brain networks and in general network structures in which the interactions can include more than two nodes. In real applications, often simplicial…

Phylogenetic networks are important for the study of evolution. The number of methods to find such networks is increasing, but most such methods can only reconstruct small networks. To find bigger networks, one can attempt to combine small…

Here we show that, given a set of clusters C on a set of taxa X, where |X|=n, it is possible to determine in time f(k).poly(n) whether there exists a level-<= k network (i.e. a network where each biconnected component has reticulation…

Network science is a powerful framework allowing to model complex systems, it is capable to describe and take into account the intricate web of connections existing among the constituting basic element of the system. Recently scholars have…