相关论文: Point sets and functions inducing tangles of set s…

The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…

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 goal of data clustering is to partition data points into groups to minimize a given objective function. While most existing clustering algorithms treat each data point as vector, in many applications each datum is not a vector but a…

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…

In the present paper a novel graph-based approach to the shape decomposition problem is addressed. The shape is appropriately transformed into a visibility graph enriched with local neighborhood information. A two-step diffusion process is…

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…

This paper presents a graph bundling algorithm that agglomerates edges taking into account both spatial proximity as well as user-defined criteria in order to reveal patterns that were not perceivable with previous bundling techniques. Each…

Every end of an infinite graph $ G $ defines a tangle of infinite order in $ G $. These tangles indicate a highly cohesive substructure in the graph if and only if they are closed in some natural topology. We characterize, for every finite…

We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…

The area of Data Analytics on graphs promises a paradigm shift as we approach information processing of classes of data, which are typically acquired on irregular but structured domains (social networks, various ad-hoc sensor networks).…

We introduce a comprehensive data structure, tangle structure trees, which simultaneously displays all the $\mathcal{F}$-tangles of an abstract separation system for very general obstruction sets $\mathcal{F}$. It simultaneously also…

When the boundary of a familiar object is shown by a series of isolated dots, humans can often recognize the object with ease. This ability can be sustained with addition of distracting dots around the object. However, such capability has…

Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…

This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there…

Even though clustering trajectory data attracted considerable attention in the last few years, most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying…

Clustering is a fundamental problem in network analysis that finds closely connected groups of nodes and separates them from other nodes in the graph, while link prediction is to predict whether two nodes in a network are likely to have a…

We combine the two fundamental fixed-order tangle theorems of Robertson and Seymour into a single theorem that implies both, in a best possible way. We show that, for every $k \in \mathbb{N}$, every tree-decomposition of a graph $G$ which…

We prove a tangle-tree theorem and a tangle duality theorem for abstract separation systems $\vec S$ that are submodular in the structural sense that, for every pair of oriented separations, $\vec S$ contains either their meet or their join…