Related papers: Signed graph embedding: when everybody can sit clo…
A signed graph is a pair $(G,\sigma)$, where $G$ is a graph and $\sigma: E(G)\rightarrow \{-, +\}$, called signature, is an assignment of signs to the edges. Given a signed graph $(G,\sigma)$ with no negative loops, a balanced…
There is a well-known way to describe a link diagram as a (signed) plane graph, called its Tait graph. This concept was recently extended, providing a way to associate a set of embedded graphs (or ribbon graphs) to a link diagram. While…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices $s,t$ ($s \neq t$), there is a neighbor vertex of $s$ that is closer to $t$ than to $s$ in the Euclidean distance. Greedy drawings are important in the…
A signed graph is a graph where each edge receives a sign, positive or negative. The signed graph model has been used in many real applications, such as protein complex discovery and social network analysis. Finding cohesive subgraphs in…
Signed graphs are widely used to analyze complex systems such as social, political, and biological networks. The notion of balance, a key concept of signed graphs, reflects the stability of relationships. While it has been extensively…
Social networks involve both positive and negative relationships, which can be captured in signed graphs. The {\em edge sign prediction problem} aims to predict whether an interaction between a pair of nodes will be positive or negative. We…
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…
The index of a signed graph is the largest eigenvalue of its adjacency matrix. For positive integers $n$ and $m\le n^2/4$, we determine the maximal index of complete signed graphs with $n$ vertices and $m$ negative edges. This settles (the…
Let $G$ be a graph and $A$ be its adjacency matrix. A graph $G$ is invertible if its adjacency matrix $A$ is invertible and the inverse of $G$ is a weighted graph with adjacency matrix $A^{-1}$. A signed graph $(G,\sigma)$ is a weighted…
A signed graph $(G, \sigma)$ is a graph $G$ along with a function $\sigma: E(G) \to \{+,-\}$. A closed walk of a signed graph is positive (resp., negative) if it has an even (resp., odd) number of negative edges, counting repetitions. A…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
The study of social networks is a burgeoning research area. However, most existing work deals with networks that simply encode whether relationships exist or not. In contrast, relationships in signed networks can be positive ("like",…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. The existence of greedy drawings has been…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
An ordered graph is a graph with a total order over its vertices. A linear layout of an ordered graph is a partition of the edges into sets of either non-crossing edges, called stacks, or non-nesting edges, called queues. The stack (queue)…