Related papers: When can splits be drawn in the plane?
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
Cities can be seen as the epitome of complex systems. They arise from a set of interactions and components so diverse that is almost impossible to describe them exhaustively. Amid this diversity, we chose an object which orchestrates the…
The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear…
In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a phylogenetic…
Real-world networks are often complex and large with millions of nodes, posing a great challenge for analysts to quickly see the big picture for more productive subsequent analysis. We aim at facilitating exploration of node-attributed…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
In the paper we show that the bibliographic data can be transformed into a collection of compatible networks. Using network multiplication different interesting derived networks can be obtained. In defining them an appropriate normalization…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
Networks are one of the most powerful structures for modeling problems in the real world. Downstream machine learning tasks defined on networks have the potential to solve a variety of problems. With link prediction, for instance, one can…
Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better…
Because networks can be used to represent many complex systems, they have attracted considerable attention in physics, computer science, sociology, and many other disciplines. One of the most important areas of network science is the…
We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by…
Networks are a natural and popular mechanism for the representation and investigation of a broad class of systems. But extracting information from a network can present significant challenges. We present NetzCope, a software application for…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
The analysis of networks, aimed at suitably defined functionality, often focuses on partitions into subnetworks that capture desired features. Chief among the relevant concepts is a 2-partition, that underlies the classical Cheeger…
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 study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
Directed graphs are widely used to model data flow and execution dependencies in streaming applications. This enables the utilization of graph partitioning algorithms for the problem of parallelizing computation for multiprocessor…