Related papers: Graph Theory Based Approach to Characterize Self I…
Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$. A…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a…
We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…
Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly…
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
Packing and covering problems for metric spaces, and graphs in particular, are of essential interest in combinatorics and coding theory. They are formulated in terms of metric balls of vertices. We consider a new problem in graph theory…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
Atom arrangement plays a critical role in determining material properties. It is, therefore, essential for materials science and engineering to identify and characterize distinct atom configurations. Currently, crystal structures can be…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Metal-organic frameworks (MOFs) are highly interesting and tunable materials. By incorporating spatial defects into their atomic structure, MOFs can be finetuned to exhibit precise chemical functionalities, extending their applicability in…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
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…
We investigate experimentally and numerically the defect configurations emerging when a cholesteric liquid crystal is confined to a spherical shell. We uncover a rich scenario of defect configurations, some of them non-existent in nematic…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
Graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. When graph side information is not available, the node correspondence is estimated on the sole basis of network…
Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…