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Eigenvalues of a graph are of high interest in graph analytics for Big Data due to their relevance to many important properties of the graph including network resilience, community detection and the speed of viral propagation. Accurate…

We study spreading processes in temporal graphs, i. e., graphs whose connections change over time. These processes naturally model real-world phenomena such as infectious diseases or information flows. More precisely, we investigate how…

Graphs are a widely used data structure for collecting and analyzing relational data. However, when the graph structure is distributed across several parties, its analysis is particularly challenging. In particular, due to the sensitivity…

For a graph $G$ and a non-negative integral weight function $w$ on the vertex set of $G$, a set $S$ of vertices of $G$ is $w$-safe if $w(C)\geq w(D)$ for every component $C$ of the subgraph of $G$ induced by $S$ and every component $D$ of…

Graph Attention Networks(GATs) are useful deep learning models to deal with the graph data. However, recent works show that the classical GAT is vulnerable to adversarial attacks. It degrades dramatically with slight perturbations.…

Graphs in many applications, such as social networks and IoT, are inherently streaming, involving continuous additions and deletions of vertices and edges at high rates. Constructing random walks in a graph, i.e., sequences of vertices…

Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…

We consider activated random walk (ARW), an interacting particle system and prototypical model of self-organized criticality in a setting which combines mean-field behavior with the geometry of an arbitrary graph, which we call the village…

This paper studies the eigenvalue distribution of the Watts-Strogatz random graph, which is known as the "small-world" random graph. The construction of the small-world random graph starts with a regular ring lattice of n vertices; each has…

Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which…

Graph Neural Networks (GNNs) are widely used and deployed for graph-based prediction tasks. However, as good as GNNs are for learning graph data, they also come with the risk of privacy leakage. For instance, an attacker can run carefully…

A detailed analysis of three species-rich ecosystem food webs has shown that they display scale-free distributions of connections. Such graphs of interaction are in fact shared by a number of biological and technological networks, which…

Although powerful graph neural networks (GNNs) have boosted numerous real-world applications, the potential privacy risk is still underexplored. To close this gap, we perform the first comprehensive study of graph reconstruction attack that…

The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…

Graphical passwords (GPWs) have been studied over 20 years. We are motivated from QR codes that can be considered GPWs, are successfully applied in today's world. However, one need such GPWs that can be use conveniently and have higher…

As the study of graph neural networks becomes more intensive and comprehensive, their robustness and security have received great research interest. The existing global attack methods treat all nodes in the graph as their attack targets.…

This work focuses on developing an effective meta-heuristic approach to protect against simultaneous attacks on nodes of a network modeled using a graph. Specifically, we focus on the $k$-strong Roman domination problem, a generalization of…

With a simple attack and repair evolution model, we investigate the stability and structural changes of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to…

Deep neural networks (DNNs) have been widely applied to various applications, including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to…

Coding schemes with extremely low computational complexity are required for particular applications, such as wireless body area networks, in which case both very high data accuracy and very low power-consumption are required features. In…