Related papers: How to cool a graph

Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…

Various graphs such as web or social networks may contain up to trillions of edges. Compressing such datasets can accelerate graph processing by reducing the amount of I/O accesses and the pressure on the memory subsystem. Yet, selecting a…

The burning number $b(G)$ of a graph $G$ was introduced by Bonato, Janssen, and Roshanbin [Lecture Notes in Computer Science 8882 (2014)] for measuring the speed of the spread of contagion in a graph. They proved for any connected graph $G$…

We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…

We consider the problem of finding the graph on which an epidemic cascade spreads, given only the times when each node gets infected. While this is a problem of importance in several contexts -- offline and online social networks,…

We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel…

Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…

In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…

We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…

We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the…

Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…

In this paper we present a novel approach for anonymizing Online Social Network graphs which can be used in conjunction with existing perturbation approaches such as clustering and modification. The main insight of this paper is that by…

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor…

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

Global transport and communication networks enable information, ideas and infectious diseases now to spread at speeds far beyond what has historically been possible. To effectively monitor, design, or intervene in such epidemic-like…

In this paper we elaborate upon a measure of node influence in social networks, which was recently proposed by Vassio et al., IEEE Trans. Control Netw. Syst., 2014. This measure quantifies the ability of the node to sway the average opinion…

We study thermal transport in folded graphene nanoribbons using molecular dynamics simulations and the non-equilibrium Green's function method. It is found that the thermal conductivity of flat graphene nanoribbons can be modulated by…

Motivated by recently discovered privacy attacks on social networks, we study the problem of anonymizing the underlying graph of interactions in a social network. We call a graph (k,l)-anonymous if for every node in the graph there exist at…

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…

In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the…