Related papers: Signed graph embedding: when everybody can sit clo…
Several network embedding models have been developed for unsigned networks. However, these models based on skip-gram cannot be applied to signed networks because they can only deal with one type of link. In this paper, we present our signed…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
Social networks inherently exhibit complex relationships that can be positive or negative, as well as directional. Understanding balance in these networks is crucial for unraveling social dynamics, yet traditional theories struggle to…
Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…
The total graph is built by joining the graph to its line graph by means of the incidences. We introduce a similar construction for signed graphs. Under two similar definitions of the line signed graph, we define the corresponding total…
The median of a graph $G$ with weighted vertices is the set of all vertices $x$ minimizing the sum of weighted distances from $x$ to the vertices of $G$. For any integer $p\ge 2$, we characterize the graphs in which, with respect to any…
In the last decade or so, we have witnessed deep learning reinvigorating the machine learning field. It has solved many problems in the domains of computer vision, speech recognition, natural language processing, and various other tasks…
The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent…
Real-world data is often represented through the relationships between data samples, forming a graph structure. In many applications, it is necessary to learn this graph structure from the observed data. Current graph learning research has…
Is the enemy of an enemy necessarily a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be "balanced" were…
Positive and negative relations play an essential role in human behavior and shape the communities we live in. Despite their importance, data about signed relations is rare and commonly gathered through surveys. Interaction data is more…
Recently, graphs have been widely used to represent many different kinds of real world data or observations such as social networks, protein-protein networks, road networks, and so on. In many cases, each node in a graph is associated with…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency…
A signed graph is a pair $(G,\Sigma)$, where $G=(V,E)$ is a graph (in which parallel edges are permitted, but loops are not) with $V=\{1,\ldots,n\}$ and $\Sigma\subseteq E$. The edges in $\Sigma$ are called odd and the other edges of $E$…
The modeling of networks, specifically generative models, have been shown to provide a plethora of information about the underlying network structures, as well as many other benefits behind their construction. Recently there has been a…
A signed graph $\Sigma = (G, \sigma)$ is a graph where the function $\sigma$ assigns either $1$ or $-1$ to each edge of the simple graph $G$. The adjacency matrix of $\Sigma$, denoted by $A(\Sigma)$, is defined canonically. In a recent…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…
In many real-world networks, relationships often go beyond simple dyadic presence or absence; they can be positive, like friendship, alliance, and mutualism, or negative, characterized by enmity, disputes, and competition. To understand the…
Trace diagrams are structured graphs with edges labeled by matrices. Each diagram has an interpretation as a particular multilinear function. We provide a rigorous combinatorial definition of these diagrams using a notion of signed graph…