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Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
The families EPT (resp. EPG) Edge Intersection Graphs of Paths in a tree (resp. in a grid) are well studied graph classes. Recently we introduced the graph classes Edge-Intersecting and Non-Splitting Paths in a Tree ENPT, and in a Grid…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
In the last decade it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks: separable elements, with connections (or interactions) between certain pairs of them.…
The edge betweenness centrality of an edge is loosely defined as the fraction of shortest paths between all pairs of vertices passing through that edge. In this paper, we investigate graphs where the edge betweenness centrality of edges is…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with…
Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that…
A road map can be interpreted as a graph embedded in the plane, in which each vertex corresponds to a road junction and each edge to a particular road section. We consider the cartographic problem to place non-overlapping road labels along…
Most graph neural network models rely on a particular message passing paradigm, where the idea is to iteratively propagate node representations of a graph to each node in the direct neighborhood. While very prominent, this paradigm leads to…
A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness; computing shortest paths or geodesics yields measures of network connectivity that can…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
Graph embedding is a powerful method in parallel computing that maps a guest network $G$ into a host network $H$. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
In this paper, we define a class of auxiliary graphs associated with simple undirected graphs. This class of auxiliary graphs is based on the set of spanning trees of the original graph and the edges constituting those spanning trees. A…
The interaction between transitivity and sparsity, two common features in empirical networks, implies that there are local regions of large sparse networks that are dense. We call this the blessing of transitivity and it has consequences…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…