Related papers: Trees = Networks ?!?
The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…
Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted…
In Chapter 1 we fully characterise pairs of finite graphs which form a gap in the full homomorphism order. This leads to a simple proof of the existence of generalised duality pairs. We also discuss how such results can be carried to…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such as social…
Networks have in recent years emerged as an invaluable tool for describing and quantifying complex systems in many branches of science. Recent studies suggest that networks often exhibit hierarchical organization, where vertices divide into…
Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…
In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…
We extend to infinite graphs the matroidal characterization of finite graph duality, that two graphs are dual iff they have complementary spanning trees in some common edge set. The naive infinite analogue of this fails. The key in an…
The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
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.…
As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…
In phylogenetics, evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In…
In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
The investigation of social networks is often hindered by their size as such networks often consist of at least thousands of vertices and edges. Hence, it is of major interest to derive compact structures that represent important…
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
We study an abstract notion of tree structure which lies at the common core of various tree-like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested subsets of a set, tree-decompositions of graphs and…