Modeling the Public Transport Networks: A Study of Their Efficiency

Abstract

The public transportation network (PTN) provides mobility and access to community resources, employment, medical care, infrastructures, and other resources in the city. This research studies the process of the formation of links among nodes in different real-world PTNs. We have found that this process may be appropriately explained by a generalized linear model (GLM) using local, global, and quasilocal similarity indexes as explanatory variables. In modeling, the response variable was described by a binomial probability density function, and the logit function was used as a link function. In the crossvalidation process, utilising a downsampling approach, both average accuracy and area under the receiver operating characteristic curve (AUC) metrics presented higher values than 0.99. The kappa parameter had magnitudes larger than 0.93 for most of the PTNs. In the final validation stage, recall and specificity metrics took the value 1. Accuracy and precision parameters were larger than 0.99 and 0.87, respectively, for the majority of PTNs. Only one of the PTNs required utilising a smoothed bootstrap approach in order to achieve better results. The similarity measures with the greatest influence on the model were determined. We also assessed the impact of link removal on the global efficiency of PTNs, considering several similarity indexes. Additionally, we find that most of the networks show low local and global efficiencies (≤0.20), as well as travel times with a relevant variability, exhibiting standard deviations larger than 790 seconds. Significant similarities exist between the cumulative probability distributions of the local efficiency in all PTNs. With respect to the centrality measures, the eigenvector centrality presented a strong correlation with the hub/authority centralities (>0.80), while the pagerank showed a moderate, high, or very high correlation with the degree in all PTNs, >0.50.

Exploring the mobility in the Madrid Community

“…A low betweenness was identified in all types of networks (< 0.06), except for T15 (Passenger in company car), T18 (Public motorbike/moped) and T19 (Motorcycle/motorcycle company). Networks exhibiting a low betweenness are more robust to failures than those with a high value 39 , 40 , which is particularly relevant in the public transport mobility networks.…”

Modeling the Interaction Networks about the Climate Change on Twitter: A Characterization of its Network Structure

“…(ii) e second procedure uses certain similarity indexes. In this method, analogously to [28], we calculated local, quasi-local, and global similarity metrics between nodes. Specifically, the local measures were resource allocation [29], Leicht-Holme-Newman [30], common neighbors, cosine [31], cosine similarity on L+ [25], hub promoted [32], Jaccard [33], hub depressed [32], preferential attachment [8], and Sørensen [34].…”

“…(ii) Accuracy, in binary classification, as the one we are dealing with, symbolizes the proportion of correct predictions (both true positives (TP) and true negatives (TN)) among the total number of cases examined. It is computed as follows [28]:…”

“…(iii) Sensitivity or Recall, which represents the ability of the classifier to correctly identify the positive samples (1: a link between a pair of nodes exists), can be defined as [28] Sensitivity…”

“…(iv) Specificity or Selectivity, which symbolizes the ability of the classifier to identify a negative sample (there is any link between nodes), is defined as [28] Specificity…”