Related papers: When can splits be drawn in the plane?
A clutter consists of a finite set and a collection of pairwise incomparable subsets. Clutters are natural generalisations of matroids, and they have similar operations of deletion and contraction. We introduce a notion of connectivity for…
In many ways, graphs are the main modality of data we receive from nature. This is due to the fact that most of the patterns we see, both in natural and artificial systems, are elegantly representable using the language of graph structures.…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
We use graphical methods to probe neural nets that classify images. Plots of t-SNE outputs at successive layers in a network reveal increasingly organized arrangement of the data points. They can also reveal how a network can diminish or…
Complex network theory has shown success in understanding the emergent and collective behavior of complex systems [1]. Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks [2-6]---in…
Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest $k$ such that the graph is $k$-splittable into a planar graph. A $k$-split operation…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…
Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…
Complex models, such as neural networks (NNs), are comprised of many interrelated components. In order to represent these models, eliciting and characterising the relations between components is essential. Perhaps because of this, diagrams,…
Can expressiveness of a drawing be traced with a computer? In this study a neural network (perceptron) and a support vector machine are used to classify line drawings. To do this the line drawings are attributed values according to a…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node…
We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in…