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Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
In recent years, the Graph Model has become increasingly popular, especially in the application domain of social networks. The model has been semantically augmented with properties and labels attached to the graph elements. It is difficult…
Graph representation plays an important role in the field of financial risk control, where the relationship among users can be constructed in a graph manner. In practical scenarios, the relationships between nodes in risk control tasks are…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
We study property testing of directed acyclicity in the unidirectional bounded-degree oracle model, where a query to a vertex reveals its outgoing neighbors. We prove that there exist absolute constants $d_0\in\mathbb{N}$ and…
There has been recent growing interest in graph theoretical properties known as r- and (r,s)-robustness. These properties serve as sufficient conditions guaranteeing the success of certain consensus algorithms in networks with misbehaving…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…
Given a graph $G$, we define ${\bf bcg}(G)$ as the minimum $k$ for which $G$ can be contracted to the uniformly triangulated grid $\Gamma_{k}$. A graph class ${\cal G}$ has the SQG${\bf C}$ property if every graph $G\in{\cal G}$ has…
The "slope-number" of a graph $G$ is the minimum number of distinct edge slopes in a straight-line drawing of $G$ in the plane. We prove that for $\Delta\geq5$ and all large $n$, there is a $\Delta$-regular $n$-vertex graph with…
A directed graph $D$ is singly connected if for every ordered pair of vertices $(s,t)$, there is at most one path from $s$ to $t$ in $D$. Graph orientation problems ask, given an undirected graph $G$, to find an orientation of the edges…
We introduce the concept of shallow directed minors and based on this a new classification of classes of directed graphs which is diametric to existing directed graph decompositions and width measures proposed in the literature. We then…
Random graph null models have found widespread application in diverse research communities analyzing network datasets, including social, information, and economic networks, as well as food webs, protein-protein interactions, and neuronal…
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…
Graph neural networks (GNNs) have attracted considerable attention due to their diverse applications. However, the scarcity and quality limitations of graph data present challenges to their training process in practical settings. To…
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…
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
We investigate the impact of a high-degree vertex in Tur\'{a}n problems for degenerate hypergraphs (including graphs). We say an $r$-graph $F$ is bounded if there exist constants $\alpha, \beta>0$ such that for large $n$, every $n$-vertex…