Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes t...Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.展开更多
This paper derives the distribution of the deviation distance to visit an alternative fuel station. Distance is measured as the Euclidean distance on a continuous plane. The distribution explicitly considers the vehic...This paper derives the distribution of the deviation distance to visit an alternative fuel station. Distance is measured as the Euclidean distance on a continuous plane. The distribution explicitly considers the vehicle range and whether the round trip between origin and destination can be made. Three cases are examined: fuel is available at both origin and destination, fuel is available at either origin or destination, and fuel is available at neither origin nor destination. The analytical expressions for the distribution demonstrate how the vehicle range, the shortest distance, and the refueling availability at origin and destination affect the deviation distance. The distribution will thus be useful to estimate the number of vehicles refueled at a station.展开更多
文摘Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.
文摘This paper derives the distribution of the deviation distance to visit an alternative fuel station. Distance is measured as the Euclidean distance on a continuous plane. The distribution explicitly considers the vehicle range and whether the round trip between origin and destination can be made. Three cases are examined: fuel is available at both origin and destination, fuel is available at either origin or destination, and fuel is available at neither origin nor destination. The analytical expressions for the distribution demonstrate how the vehicle range, the shortest distance, and the refueling availability at origin and destination affect the deviation distance. The distribution will thus be useful to estimate the number of vehicles refueled at a station.
