Related papers: Complexity of the Multilevel Critical Node Problem
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
Given a graph $G$, guards are placed on vertices of $G$. Then vertices are subject to an infinite sequence of attacks so that each attack must be defended by a guard moving from a neighboring vertex. The m-eternal domination number is the…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…
Given a graph $G = (V, E)$, a non-empty set $S \subseteq V$ is a defensive alliance, if for every vertex $v \in S$, the majority of its closed neighbours are in $S$, that is, $|N_G[v] \cap S| \geq |N_G[v] \setminus S|$. The decision version…
Graph convolutional networks (GCNs) have been shown to be vulnerable to small adversarial perturbations, which becomes a severe threat and largely limits their applications in security-critical scenarios. To mitigate such a threat,…
Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information.…
The recent advancement in real-world critical infrastructure networks has led to an exponential growth in the use of automated devices which in turn has created new security challenges. In this paper, we study the robust and adaptive…
The problem of identifying important players in a given network is of pivotal importance for viral marketing, public health management, network security and various other fields of social network analysis. In this work we find the most…
Vertex classification -- the problem of identifying the class labels of nodes in a graph -- has applicability in a wide variety of domains. Examples include classifying subject areas of papers in citation networks or roles of machines in a…
We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after…
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value…
Explainable Graph Neural Network (GNN) has emerged recently to foster the trust of using GNNs. Existing GNN explainers are developed from various perspectives to enhance the explanation performance. We take the first step to study GNN…
Smart grids are vulnerable to cyber-attacks. This paper proposes a game-theoretic approach to evaluate the variations caused by an attacker on the power measurements. Adversaries can gain financial benefits through the manipulation of the…
We consider control of heterogeneous players repeatedly playing an anti-coordination network game. In an anti-coordination game, each player has an incentive to differentiate its action from its neighbors. At each round of play, players…
We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at…
An alternating graph is a directed graph whose vertex set is partitioned into two classes, existential and universal. This forms the basic arena for a plethora of infinite duration two-player games where Player~$\square$ and~$\ocircle$…
We investigate certified robustness for GNNs under graph injection attacks. Existing research only provides sample-wise certificates by verifying each node independently, leading to very limited certifying performance. In this paper, we…
Adversarial attacks to graph analytics are gaining increased attention. To date, two lines of countermeasures have been proposed to resist various graph adversarial attacks from the perspectives of either graph per se or graph neural…
Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been proposed. In this survey we describe a number of these models with particular…