Related papers: From Signed Networks to Group Graphs
We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and…
A gain graph is a triple (G,h,H), where G is a connected graph with an arbitrary, but fixed, orientation of edges, H is a group, and h is a homomorphism from the free group on the edges of G to H. A gain graph is called balanced if the…
From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…
In this paper we investigate the $directed$ $normalizing$ $graph$ associated with a group $G$, defined as the simple directed graph whose vertices are the elements of $G$, with an arrow from $x$ to $y$ whenever the subgroup $\langle x…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that…
This work analyzes the convergence properties of signed networks with nonlinear edge functions. We consider diffusively coupled networks comprised of maximal equilibrium-independent passive (MEIP) dynamics on the nodes, and a general class…
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
This note attempts to understand graph limits as defined by Lovasz and Szegedy (2006)} in terms of harmonic analysis on semigroups. This is done by representing probability distributions of random exchangeable graphs as mixtures of…
In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit,…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
Signed network is a kind of network that associates each edge a positive or negative sign which could express friendly or unfriendly relationship between individuals. When diseases spreading over the signed network, some unfriendly edges…
Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriad graph analytic tasks and applications. Most GNNs rely on the homophily assumption that nodes belonging to the same class are more…
We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.
Network systems have become a ubiquitous modeling tool in many areas of science where nodes in a graph represent distributed processes and edges between nodes represent a form of dynamic coupling. When a network topology is already known…
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…
A large portion of today's big data can be represented as networks. However, not all networks are the same, and in fact, for many that have additional complexities to their structure, traditional general network analysis methods are no…