Related papers: Minimal Construction of Graphs with Maximum Robust…
For any fixed integer $R \geq 2$ we characterise the typical structure of undirected graphs with vertices $1, ..., n$ and maximum degree $R$, as $n$ tends to infinity. The information is used to prove that such graphs satisfy a labelled…
We study the robustness of interdependent networks where two networks are said to be interdependent if the operation of one network depends on the operation of the other one, and vice versa. In this paper, we propose a model for analyzing…
Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
In several applications in distributed systems, an important design criterion is ensuring that the network is sparse, i.e., does not contain too many edges, while achieving reliable connectivity. Sparsity ensures communication overhead…
Much of our commerce and traveling depend on the efficient operation of large scale networks. Some of those, such as electric power grids, transportation systems, communication networks, and others, must maintain their efficiency even after…
In varying degree distributions, we investigate the optimally robust networks against targeted attacks to nodes with higher degrees. In considering that a network tends to have more robustness with a smaller variance of degree…
In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model…
A networked dynamical system is composed of subsystems interconnected through prescribed interactions. In many engineering applications, however, one subsystem can also affect others through "unintended" interactions that can significantly…
Graph Neural Networks (GNNs) have shown their great ability in modeling graph structured data. However, real-world graphs usually contain structure noises and have limited labeled nodes. The performance of GNNs would drop significantly when…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
Motivated by problems modeling the spread of infections in networks, in this paper we explore which bipartite graphs are most resilient to widespread infections under various parameter settings. Namely, we study bipartite networks with a…
Despite the exploding interest in graph neural networks there has been little effort to verify and improve their robustness. This is even more alarming given recent findings showing that they are extremely vulnerable to adversarial attacks…
The adversarial robustness of Graph Neural Networks (GNNs) has been questioned due to the false sense of security uncovered by strong adaptive attacks despite the existence of numerous defenses. In this work, we delve into the robustness…
Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…