Related papers: Robust Topological Orderings for Directed Graphs
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…
We introduce new algebro-topological invariants of directed networks, based on the topological construction of the directed clique complex. The shape of the underlying directed graph is encoded in a way that can be studied mathematically to…
Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes…
In this paper we study termination of term graph rewriting, where we restrict our attention to acyclic term graphs. Motivated by earlier work by Plump we aim at a definition of the notion of simplification order for acyclic term graphs. For…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
Distributed peer-to-peer systems are widely popular due to their decentralized nature, which ensures that no peer is critical for the functionality of the system. However, fully decentralized solutions are usually much harder to design, and…
Wireless network topologies change over time and maintaining routes requires frequent updates. Updates are costly in terms of consuming throughput available for data transmission, which is precious in wireless networks. In this paper, we…
Directed graphs have been widely used in Community Question Answering services (CQAs) to model asymmetric relationships among different types of nodes in CQA graphs, e.g., question, answer, user. Asymmetric transitivity is an essential…
With emergence of blockchain technologies and the associated cryptocurrencies, such as Bitcoin, understanding network dynamics behind Blockchain graphs has become a rapidly evolving research direction. Unlike other financial networks, such…
Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.
Graph clustering has many important applications in computing, but due to the increasing sizes of graphs, even traditionally fast clustering methods can be computationally expensive for real-world graphs of interest. Scalability problems…
Given a static vertex-selection problem (e.g. independent set, dominating set) on a graph, we can define a corresponding temporally satisfying reconfiguration problem on a temporal graph which asks for a sequence of solutions to the…
Directed acyclic graphs have been used fruitfully to represent causal strucures (Pearl 1988). However, in the social sciences and elsewhere models are often used which correspond both causally and statistically to directed graphs with…
After a somewhat rocky start, geometry and topology have established a foothold in machine learning. Message passing, either on graphs or higher-order complexes, is one of the main drivers of geometric deep learning, and paradigms that were…
We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the…
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
The {\em acyclic chromatic number} of a graph is the least number of colors needed to properly color its vertices so that none of its cycles has only two colors. The {\em acyclic chromatic index} is the analogous graph parameter for edge…
Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…