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The edge removal problem studies the loss in network coding rates that results when a network communication edge is removed from a given network. It is known, for example, that in networks restricted to linear coding schemes and networks…
We study the network dismantling problem, which consists in determining a minimal set of vertices whose removal leaves the network broken into connected components of sub-extensive size. For a large class of random graphs, this problem is…
Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical…
Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…
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…
Traditional network disruption approaches focus on disconnecting or lengthening paths in the network. We present a new framework for network disruption that attempts to reroute flow through critical vertices via vertex deletion, under the…
The process of destroying a complex network through node removal has been the subject of extensive interest and research. Node loss typically leaves the network disintegrated into many small and isolated clusters. Here we show that these…
We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…
The connectivity structure of a network can be very sensitive to removal of certain nodes in the network. In this paper, we study the sensitivity of the largest component size to node removals. We prove that minimizing the largest component…
Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most $k$ edges from a given input graph (of small treewidth) so that the resulting graph avoids a set…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…
Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these…
We address the general problem of how best to attack and destroy a network by node removal, given limited or no prior information about the edges. We consider a family of strategies in which nodes are randomly chosen, but not removed.…
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 link prediction in networks whose edge structure may vary (sufficiently slowly) over time. This problem, with applications in many important areas including social networks, has two main variants: the first, known…
Network dismantling is a relevant research area in network science, gathering attention both from a theoretical and an operational point of view. Here, we propose a general framework for dismantling that prioritizes the removal of nodes…
In this paper, we investigate some basic connectivity problems in directed graphs (digraphs). Let $G$ be a digraph with $m$ edges and $n$ vertices, and let $G\setminus e$ be the digraph obtained after deleting edge $e$ from $G$. As a first…
In the fully dynamic edge connectivity problem, the input is a simple graph $G$ undergoing edge insertions and deletions, and the goal is to maintain its edge connectivity, denoted $\lambda_G$. We present two simple randomized algorithms…
We study a Stackelberg variant of the classical Most Vital Links problem, modeled as a one-round adversarial game between an attacker and a defender. The attacker strategically removes up to $k$ edges from a flow network to maximally…
This paper studies the relation between node deletion and algebraic connectivity for graphs with a hierarchical structure represented by layers. To capture this structure, the concepts of layered path graph and its (sub)graph cone are…