Related papers: When can splits be drawn in the plane?

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final…

Detection of curvilinear structures in images has long been of interest. One of the most challenging aspects of this problem is inferring the graph representation of the curvilinear network. Most existing delineation approaches first…

Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…

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…

We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a…

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…

When artificial neural networks have demonstrated exceptional practical success in a variety of domains, investigations into their theoretical characteristics, such as their approximation power, statistical properties, and generalization…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…

Biological networks provide insight into the complex organization of biological processes in a cell at the system level. They are an effective tool for understanding the comprehensive map of functional interactions, finding the functional…

1-planar graphs are graphs that can be drawn in the plane such that any edge intersects with at most one other edge. Ackerman showed that the edges of a 1-planar graph can be partitioned into a planar graph and a forest, and claims that the…

Polyploidization is an important evolutionary process which affects organisms ranging from plants to fish and fungi. The signal left behind by it is in the form of a species' ploidy level (number of complete chromosome sets found in a cell)…

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…

Methods for detecting community structure in networks typically aim to identify a single best partition of network nodes into communities, often by optimizing some objective function, but in real-world applications there may be many…

In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…

Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order…

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…

We study the problem of visualizing phylogenetic networks, which are extensions of the Tree of Life in biology. We use a space filling visualization method, called DAGmaps, in order to obtain clear visualizations using limited space. In…

Bipartite networks provide an effective resource for representing, characterizing, and modeling several abstract and real-world systems and structures involving binary relations, which include food webs, social interactions, and…

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…

Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets:…