weighted graphs
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2022 ◽  
Vol 13 (1) ◽  
pp. 1-25
Yuandong Wang ◽  
Hongzhi Yin ◽  
Tong Chen ◽  
Chunyang Liu ◽  
Ben Wang ◽  

In recent years, ride-hailing services have been increasingly prevalent, as they provide huge convenience for passengers. As a fundamental problem, the timely prediction of passenger demands in different regions is vital for effective traffic flow control and route planning. As both spatial and temporal patterns are indispensable passenger demand prediction, relevant research has evolved from pure time series to graph-structured data for modeling historical passenger demand data, where a snapshot graph is constructed for each time slot by connecting region nodes via different relational edges (origin-destination relationship, geographical distance, etc.). Consequently, the spatiotemporal passenger demand records naturally carry dynamic patterns in the constructed graphs, where the edges also encode important information about the directions and volume (i.e., weights) of passenger demands between two connected regions. aspects in the graph-structure data. representation for DDW is the key to solve the prediction problem. However, existing graph-based solutions fail to simultaneously consider those three crucial aspects of dynamic, directed, and weighted graphs, leading to limited expressiveness when learning graph representations for passenger demand prediction. Therefore, we propose a novel spatiotemporal graph attention network, namely Gallat ( G raph prediction with all at tention) as a solution. In Gallat, by comprehensively incorporating those three intrinsic properties of dynamic directed and weighted graphs, we build three attention layers to fully capture the spatiotemporal dependencies among different regions across all historical time slots. Moreover, the model employs a subtask to conduct pretraining so that it can obtain accurate results more quickly. We evaluate the proposed model on real-world datasets, and our experimental results demonstrate that Gallat outperforms the state-of-the-art approaches.

2022 ◽  
Vol 309 ◽  
pp. 68-74
Alan Frieze ◽  
Wesley Pegden

2022 ◽  
Vol 27 (2) ◽  
pp. 1-25
Somesh Singh ◽  
Tejas Shah ◽  
Rupesh Nasre

Betweenness centrality (BC) is a popular centrality measure, based on shortest paths, used to quantify the importance of vertices in networks. It is used in a wide array of applications including social network analysis, community detection, clustering, biological network analysis, and several others. The state-of-the-art Brandes’ algorithm for computing BC has time complexities of and for unweighted and weighted graphs, respectively. Brandes’ algorithm has been successfully parallelized on multicore and manycore platforms. However, the computation of vertex BC continues to be time-consuming for large real-world graphs. Often, in practical applications, it suffices to identify the most important vertices in a network; that is, those having the highest BC values. Such applications demand only the top vertices in the network as per their BC values but do not demand their actual BC values. In such scenarios, not only is computing the BC of all the vertices unnecessary but also exact BC values need not be computed. In this work, we attempt to marry controlled approximations with parallelization to estimate the k -highest BC vertices faster, without having to compute the exact BC scores of the vertices. We present a host of techniques to determine the top- k vertices faster , with a small inaccuracy, by computing approximate BC scores of the vertices. Aiding our techniques is a novel vertex-renumbering scheme to make the graph layout more structured , which results in faster execution of parallel Brandes’ algorithm on GPU. Our experimental results, on a suite of real-world and synthetic graphs, show that our best performing technique computes the top- k vertices with an average speedup of 2.5× compared to the exact parallel Brandes’ algorithm on GPU, with an error of less than 6%. Our techniques also exhibit high precision and recall, both in excess of 94%.

2022 ◽  
Guillaume Peron

The graph transitivity measures the probability that adjacent vertices in a network are interconnected, thus revealing the existence of tightly connected neighborhoods playing a role in information and pathogen circulation. The graph transitivity is usually computed for dichotomized networks, therefore focusing on whether triangular relationships are closed or open. But when the connections vary in strength, focusing on whether the closing ties exist or not can be reductive. I score the weighted transitivity according to the similarity between the weights of the three possible links in each triad. In a simulation, that new technique correctly diagnosed excesses of balanced or imbalanced triangles, for example, strong triplets closed by weak links. I illustrate the biological relevance of that information with two reanalyses of animal contact networks. In the rhesus macaque Macaca mulatta, a species in which kin relationships strongly predict social relationships, the new metrics revealed striking similarities in the configuration of grooming networks in captive and free-ranging groups, but only as long as the matrilines were preserved. In the barnacle goose Branta leucopsis, in an experiment designed to test the long-term effect of the goslings' social environment, the new metrics uncovered an excess of weak triplets closed by strong links, particularly pronounced in males, and consistent with the triadic process underlying goose dominance relationships.

Zsombor Petho ◽  
Intiyaz Khan ◽  
Árpád Torok

AbstractThis article investigates cybersecurity issues related to in-vehicle communication networks. In-vehicle communication network security is evaluated based on the protection characteristics of the network components and the topology of the network. The automotive communication network topologies are represented as undirected weighted graphs, and their vulnerability is estimated based on the specific characteristics of the generated graph. Thirteen different vehicle models have been investigated to compare the vulnerability levels of the in-vehicle network using the Dijkstra's shortest route algorithm. An important advantage of the proposed method is that it is in accordance with the most relevant security evaluation models. On the other hand, the newly introduced approach considers the Secure-by-Design concept principles.

2021 ◽  
pp. 147387162110603
Gerd Kortemeyer

The paper describes a method for the immersive, dynamic visualization of undirected, weighted graphs. Using the Fruchterman-Reingold method, force-directed graphs are drawn in a Virtual-Reality system. The user can walk through the data, as well as move vertices using controllers, while the network display rearranges in realtime according to Newtonian physics. In addition to the physics behind the employed method, the paper explains the most pertinent computational mechanisms for its implementation, using Unity, SteamVR, and a Virtual-Reality system such as HTC Vive (the source package is made available for download). It was found that the method allows for intuitive exploration of graphs with on the order of [Formula: see text] vertices, and that dynamic extrusion of vertices and realtime readjustment of the network structure allows for developing an intuitive understanding of the relationship of a vertex to the remainder of the network. Based on this observation, possible future developments are suggested.

2021 ◽  
Vol vol. 23, no. 3 (Graph Theory) ◽  
Zhanar Berikkyzy ◽  
Axel Brandt ◽  
Sogol Jahanbekam ◽  
Victor Larsen ◽  
Danny Rorabaugh

A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and any list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that $f(e)\in L(e)$ for all $e\in E(G)$, labels of edges are pairwise distinct, and the sum of the labels on edges incident to a vertex plus the weight of that vertex is distinct from the sum at every other vertex. In this paper we prove that every graph on $n$ vertices having no $K_1$ or $K_2$ component is $\lfloor{\frac{4n}{3}}\rfloor$-weighted-list-antimagic. An oriented graph $G$ is $k$-$oriented-antimagic$ if there exists an injective edge labeling from $E(G)$ into $\{1,\dotsc,|E(G)|+k\}$ such that the sum of the labels on edges incident to and oriented toward a vertex minus the sum of the labels on edges incident to and oriented away from that vertex is distinct from the difference of sums at every other vertex. We prove that every graph on $n$ vertices with no $K_1$ component admits an orientation that is $\lfloor{\frac{2n}{3}}\rfloor$-oriented-antimagic.

2021 ◽  
Vol 630 ◽  
pp. 252-273
Jakob Hansen

2021 ◽  
Vol 2131 (3) ◽  
pp. 032101
V V Kostenko ◽  
V A Golubtsov ◽  
R V Pank ◽  
A O Shmidt

Abstract This article presents the results of developing a model for a regional passenger transport network aimed at solving the logistical problem of constructing rational intermodal routes in a defined closed loop. The tools of graph theory and linear mathematical programming have been applied to build the model algorithm, which allows finding solutions for weighted graphs, in the absence of negative weight links, while keeping information about the sequence of hub points on the selected paths. The proposed solutions are versatile enough to be scalable for regions with different network topologies. The model is adapted to dynamically changing and extensible systems, allowing it to be practically applied to justify options for the future development of infrastructure in different modes of transport.

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