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Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to practical…
We revisit the concept of minimal rigidity as applied to soft repulsive, frictionless sphere packings in two-dimensions with the introduction of the jamming graph. Minimal rigidity is a purely combinatorial property encoded via Laman's…
We define the notion of affine rigidity of a hypergraph and prove a variety of fundamental results for this notion. First, we show that affine rigidity can be determined by the rank of a specific matrix which implies that affine rigidity is…
A graph $G = (V,E)$ is globally rigid in $\mathbb{R}^d$ if for any generic placement $p : V \rightarrow \mathbb{R}^d$ of the vertices, the edge lengths $||p(u) - p(v)||, uv \in E$ uniquely determine $p$, up to congruence. In this paper we…
Document dewarping is crucial for many applications. However, existing learning-based methods rely heavily on supervised regression with annotated data without fully leveraging the inherent geometric properties of physical documents. Our…
Given a weighted graph $G=(V,E,w)$, a partition of $V$ is $\Delta$-bounded if the diameter of each cluster is bounded by $\Delta$. A distribution over $\Delta$-bounded partitions is a $\beta$-padded decomposition if every ball of radius…
This paper presents a phenomenon which sometimes occurs in tetravalent bipartite locally dart-transitive graphs, called a Base Graph -- Connection Graph dissection. In this dissection, each white vertex is split into two vertices of valence…
Suppose a finite, unweighted, combinatorial graph $G = (V,E)$ is the union of several (degree-)regular graphs which are then additionally connected with a few additional edges. $G$ will then have only a small number of vertices $v \in V$…
The pivotal quality of proximity graphs is connectivity, i.e. all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are robust, i.e., they are able to function well even if they…
Motion planning is a fundamental problem of robotics with applications in many areas of computer science and beyond. Its restriction to graphs has been investigated in the literature for it allows to concentrate on the combinatorial problem…
Signed graphs are an emergent way of representing data in a variety of contexts where antagonistic interactions exist. These include data from biological, ecological, and social systems. Here we propose the concept of communicability for…
Local Irregularity Conjecture states that every simple connected graph, except special cacti, can be decomposed into at most three locally irregular graphs, i.e., graphs in which adjacent vertices have different degrees. The connected…
In this paper, we study the construction and transformation of two-dimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations,…
In matching theory, one of the most fundamental and classical branches of combinatorics, {\em canonical decompositions} of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known…
If we parameterize the positions of all vertices of a given graph in the plane such that distances between adjacent vertices are fixed, we obtain a moving graph. An L-linkage is a realization of a moving graph in 3D-space, by representing…
With the explosion of graph-structured data, link prediction has emerged as an increasingly important task. Embedding methods for link prediction utilize neural networks to generate node embeddings, which are subsequently employed to…
This paper is the first from a series of papers that provide a characterization of maximum packings of $T$-cuts in bipartite graphs. Given a connected graph, a set $T$ of an even number of vertices, and a minimum $T$-join, an edge weighting…
There have been recent advances in the analysis and visualization of 3D symmetric tensor fields, with a focus on the robust extraction of tensor field topology. However, topological features such as degenerate curves and neutral surfaces do…
A subset $D\subseteq V_G$ is a dominating set of $G$ if every vertex in $V_G\setminus D$ has a neighbor in $D$, while $D$ is a 2-dominating set of $G$ if every vertex belonging to $V_G\setminus D$ is joined by at least two edges with a…
A k-connected graph such that deleting any edge / deleting any vertex / contracting any edge results in a graph which is not k-connected is called minimally / critically / contraction-critically k-connected. These three classes play a…