Related papers: A survey of graph burning
Our understanding of the dynamics of complex networked systems has increased significantly in the last two decades. However, most of our knowledge is built upon assuming pairwise relations among the system's components. This is often an…
We study feature propagation on graph, an inference process involved in graph representation learning tasks. It's to spread the features over the whole graph to the $t$-th orders, thus to expand the end's features. The process has been…
We present a general approach to study the flooding time (a measure of how fast information spreads) in dynamic graphs (graphs whose topology changes with time according to a random process). We consider arbitrary converging Markovian…
\emph{Uncertain Graph} (also known as \emph{Probabilistic Graph}) is a generic model to represent many real\mbox{-}world networks from social to biological. In recent times analysis and mining of uncertain graphs have drawn significant…
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…
We initiate the study of deterministic distributed graph algorithms with predictions in synchronous message passing systems. The process at each node in the graph is given a prediction, which is some extra information about the problem…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
The burning number conjecture states that the burning number of a connected graph is at most $\lceil \sqrt{n} \rceil.$ While the conjecture is unresolved, Land and Lu proved that the burning number of a connected graph is at most $…
In order to improve the resilience of computer infrastructure against cyber attacks and finding ways to mitigate their impact we need to understand their structure and dynamics. Here we propose a novel network-based influence spreading…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
We study the spread of information on multi-type directed random graphs. In such graphs the vertices are partitioned into distinct types (communities) that have different transmission rates between themselves and with other types. We…
Researchers, policy makers, and engineers need to make sense of data on spreading processes as diverse as viral infections, water contamination, and misinformation in social networks. Classical questions include predicting infection…
One of the hot topics in machine learning is the field of GNN. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph…
Given a network and a set of vertices called seeds to initially inject information, influence spread is the expected number of vertices that eventually receive the information under a certain stochastic model of information propagation.…
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…
Graph learning plays a pivotal role and has gained significant attention in various application scenarios, from social network analysis to recommendation systems, for its effectiveness in modeling complex data relations represented by graph…
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…
A Burling graph is an induced subgraph of some graph in Burling's construction of triangle-free high-chromatic graphs. Equivalently, a Burling graph is a graph that admits a so-called strict frame representation. We provide a…
We propose an exact algorithm for the Graph Burning Problem ($\texttt{GBP}$), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph $G$ with vertex set $V$, the objective is to find a sequence…
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…