Related papers: Algebraic connectivity of layered path graphs unde…

Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a…

A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for…

To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus. Such algebras are related to factorizations of polynomials over…

Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be…

Graph Neural Networks (GNNs) as deep learning models working on graph-structure data have achieved advanced performance in many works. However, it has been proved repeatedly that, not all edges in a graph are necessary for the training of…

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes…

In this paper, we study crucial elements of a complex network, namely its nodes and connections, which play a key role in maintaining the network's structure and function under unexpected structural perturbations of nodes and edges removal.…

In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…

Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…

In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes, so that nodes may be in more than one community. We do this by making a node…

Network-based modeling of complex systems and data using the language of graphs has become an essential topic across a range of different disciplines. Arguably, this graph-based perspective derives its success from the relative simplicity…

When drawing graphs whose edges and nodes contain text or graphics, such informa tion needs to be displayed without overlaps, either as part of the initial layout or as a post-processing step. The core problem in removing overlaps lies in…

This paper revisits two classical distributed problems in anonymous networks, namely spanning tree construction and topology recognition, from the point of view of graph covering theory. For both problems, we characterize necessary and…

Graphs and hypergraphs combine expressive modeling power with algorithmic efficiency for a wide range of applications. Hedgegraphs generalize hypergraphs further by grouping hyperedges under a color/hedge. This allows hedgegraphs to model…

Dynamic Connectivity is a fundamental algorithmic graph problem, motivated by a wide range of applications to social and communication networks and used as a building block in various other algorithms, such as the bi-connectivity and the…

The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically…

We consider questions related to the existence of spanning trees in graphs with the property that after the removal of any path in the tree the graph remains connected. We show that, for planar graphs, the existence of trees with this…

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…

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…