Related papers: Hierarchical Partial Planarity
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…
Complex networks are made up of vertices and edges. The latter connect the vertices. There are several ways to measure the importance of the vertices, e.g., by counting the number of edges that start or end at each vertex, or by using the…
We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…
The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…
We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs…
We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…
As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
Network visualization is essential for many scientific, societal, technological and artistic domains. The primary goal is to highlight patterns out of nodes interconnected by edges that are easy to understand, facilitate communication and…
A temporal graph is a graph in which edges are assigned a time label. Two nodes u and v of a temporal graph are connected one to the other if there exists a path from u to v with increasing edge time labels. We consider the problem of…
Suppose a graph has no large balanced bicliques, but has large minimum degree. Then what can we say about its induced subgraphs? This question motivates the study of degree-boundedness, which is like $\chi$-boundedness but for minimum…
Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…
Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
It was recently shown \cite{STV} that satisfiability is polynomially solvable when the incidence graph is an interval bipartite graph (an interval graph turned into a bipartite graph by omitting all edges within each partite set). Here we…
In this paper we deepen the understanding of the connection between two long-standing Graph Drawing open problems, that is, Simultaneous Embedding with Fixed Edges (SEFE) and Clustered Planarity (C-PLANARITY). In his GD'12 paper Marcus…