Calculating average shortest path length using Compute Unified Design Architecture (CUDA)

2019 ◽  
Author(s):  
Stefan Petrushevski ◽  
Marjan Gusev ◽  
Vladimir Zdraveski
Keyword(s):  
Shortest Path ◽  
Path Length ◽  
Unified Design

scholarly journals Topological measures for identifying and predicting the spread of complex contagions

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Douglas Guilbeault ◽  
Damon Centola
Keyword(s):  
Social Networks ◽  
Shortest Path ◽  
Empirical Data ◽  
Path Length ◽  
Centrality Measures ◽  
Social Phenomena ◽  
Node Centrality ◽  
Network Connectedness ◽  
Topological Measures ◽  
Definition Of

AbstractThe standard measure of distance in social networks – average shortest path length – assumes a model of “simple” contagion, in which people only need exposure to influence from one peer to adopt the contagion. However, many social phenomena are “complex” contagions, for which people need exposure to multiple peers before they adopt. Here, we show that the classical measure of path length fails to define network connectedness and node centrality for complex contagions. Centrality measures and seeding strategies based on the classical definition of path length frequently misidentify the network features that are most effective for spreading complex contagions. To address these issues, we derive measures of complex path length and complex centrality, which significantly improve the capacity to identify the network structures and central individuals best suited for spreading complex contagions. We validate our theory using empirical data on the spread of a microfinance program in 43 rural Indian villages.

A Different Approach for Solving the Shortest Path Problem Under Mixed Fuzzy Environment

2020 ◽  
Vol 9 (2) ◽  
pp. 132-161 ◽  
Author(s):  
Ranjan Kumar ◽  
Sripati Jha ◽  
Ramayan Singh
Keyword(s):  
Linear Programming ◽  
Shortest Path ◽  
Path Length ◽  
Real Life ◽  
Shortest Path Problem ◽  
Fuzzy Linear Programming ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Membership Functions ◽  
Fuzzy Environment

The authors present a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the authors can solve the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions. Moreover, the authors can solve the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated. Furthermore, the shortcomings of some existing methods are discussed and compared with the algorithm. The objective of the proposed method is to find the fuzzy shortest path (FSP) for the given network; however, this is also capable of predicting the fuzzy shortest path length (FSPL) and crisp shortest path length (CSPL). Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical results show that this method is superior to the existing methods.

A Genetic Algorithms Approach for Inverse Shortest Path Length Problems

2014 ◽  
Vol 4 (4) ◽  
pp. 36-54 ◽  
Author(s):  
António Leitão ◽  
Adriano Vinhas ◽  
Penousal Machado ◽  
Francisco Câmara Pereira
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Path Length ◽  
Shortest Paths ◽  
Research Subject ◽  
Relevant Research ◽  
Real Cost ◽  
Shortest Path Problems ◽  
The Past ◽  
Specific Outcome

Inverse Combinatorial Optimization has become a relevant research subject over the past decades. In graph theory, the Inverse Shortest Path Length problem becomes relevant when people don't have access to the real cost of the arcs and want to infer their value so that the system has a specific outcome, such as one or more shortest paths between nodes. Several approaches have been proposed to tackle this problem, relying on different methods, and several applications have been suggested. This study explores an innovative evolutionary approach relying on a genetic algorithm. Two scenarios and corresponding representations are presented and experiments are conducted to test how they react to different graph characteristics and parameters. Their behaviour and differences are thoroughly discussed. The outcome supports that evolutionary algorithms may be a viable venue to tackle Inverse Shortest Path problems.

Scaling of average weighted shortest path and average receiving time on weighted expanded Koch networks

2014 ◽  
Vol 28 (17) ◽  
pp. 1450111 ◽  
Author(s):  
Zikai Wu ◽  
Baoyu Hou ◽  
Hongjuan Zhang ◽  
Feng Jin
Keyword(s):  
Shortest Path ◽  
Linear Dependence ◽  
Path Length ◽  
Network Models ◽  
Structural Features ◽  
The Other ◽  
Large Network ◽  
Dynamical Processes ◽  
Current Generation ◽  
Evolutionary Step

Deterministic network models have been attractive media for discussing dynamical processes' dependence on network structural features. On the other hand, the heterogeneity of weights affect dynamical processes taking place on networks. In this paper, we present a family of weighted expanded Koch networks based on Koch networks. They originate from a r-polygon, and each node of current generation produces m r-polygons including the node and whose weighted edges are scaled by factor w in subsequent evolutionary step. We derive closed-form expressions for average weighted shortest path length (AWSP). In large network, AWSP stays bounded with network order growing (0 < w < 1). Then, we focus on a special random walks and trapping issue on the networks. In more detail, we calculate exactly the average receiving time (ART). ART exhibits a sub-linear dependence on network order (0 < w < 1), which implies that nontrivial weighted expanded Koch networks are more efficient than un-weighted expanded Koch networks in receiving information. Besides, efficiency of receiving information at hub nodes is also dependent on parameters m and r. These findings may pave the way for controlling information transportation on general weighted networks.

scholarly journals A Multilevel Simplification Algorithm for Computing the Average Shortest-Path Length of Scale-Free Complex Network

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guoyong Mao ◽  
Ning Zhang
Keyword(s):  
Complex Network ◽  
Shortest Path ◽  
Path Length ◽  
Large Scale ◽  
Computation Time ◽  
Scale Free Network ◽  
Original Network ◽  
Memory Space ◽  
Scale Free ◽  
Free Network

Computing the average shortest-path length (ASPL) of a large scale-free network needs much memory space and computation time. Based on the feature of scale-free network, we present a simplification algorithm by cutting the suspension points and the connected edges; the ASPL of the original network can be computed through that of the simplified network. We also present a multilevel simplification algorithm to get ASPL of the original network directly from that of the multisimplified network. Our experiment shows that these algorithms require less memory space and time in computing the ASPL of scale-free network, which makes it possible to analyze large networks that were previously impossible due to memory limitations.

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