Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Data
2.2.1. Inventory of Skiing Zones System
2.2.2. Mobility Data of Backcountry Skiers
2.3. Data Analysis
- GPS data pre-processing
- Creation of the structural network (undirected graph)
- Creation of the functional network (directed graph)
- Quantification of network connectivity indices
- Calculation of centrality measures of network nodes.
2.3.1. Pre-Processing of GPS Data
2.3.2. Creating the Structural Network
2.3.3. Creating the Functional Network
2.3.4. Calculating Network Connectivity Indices
- Kansky index where is the number of edges, is the number of vertices (the higher the value of , the more coherent the network);
- Kansky index , defining the ratio of the existing number of edges (e) to the maximum possible number of edges resulting from the number of vertices (v). The value ranges from 0 to 1, where the value of 1 indicates a completely connected network.
- Kansky index , where is a cyclomatic measure calculated as , where p is the number of isolated subgraphs. An value of 1 indicates a completely meshed network, and 0 indicates a very simple network.
2.3.5. Calculating Node Centrality Measures
3. Results
3.1. General Characteristics of the Structural and Functional Networks
3.2. Network Coherence (Connectivity Indices)
3.3. Relative Importance of Network Nodes (Centrality Measures)
4. Discussion and Conclusions
4.1. General Meaning of the Findings
4.2. Comparison of the Structural and Functional Networks in the Study Area
4.3. Limitations of the Proposed Methodology
4.4. Meaning of the Findings for Visitor Management in Protected Areas
Supplementary Materials
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Centrality Measure | Description | Mathematical Equation |
---|---|---|
Input degree | Number of edges entering to vertex i. | signal the position between node i and node j. |
Output degree | Number of edges leaving vertex i. | |
Degree (all) | Total number of edges connected to the vertex i. | |
Closeness | Inverse sum of distances from a given vertex to all other vertices in the graph. | where is a topological distance between vertices |
Betweenness | A number of times a vertex is crossed by shortest paths in the graph. | where is the number of geodesics connecting jk, and is the number that geodesics i is on. |
Proximity prestige | Expresses the influence domain of a vertex by the average distance from all vertices in the influence domain. Pp value of 0 indicates that node i is unreachable; whereas Pp = 1 if all nodes are directly connected to node i. |
Node Number | Degree | Closeness | Betweenness |
---|---|---|---|
79 | 6 | 0.14 | 0.14 |
24 | 5 | 0.15 | 0.08 |
48 | 5 | 0.18 | 0.43 |
61 | 5 | 0.17 | 0.30 |
69 | 5 | 0.14 | 0.02 |
16 | 4 | 0.11 | 0.12 |
18 | 4 | 0.12 | 0.17 |
27 | 4 | 0.15 | 0.09 |
44 | 4 | 0.17 | 0.09 |
45 | 4 | 0.15 | 0.14 |
Node Number | Weighted Input Degree | Weighted Output Degree | Weighted All Degree | Closeness | Betweenness | Proximity Prestige |
---|---|---|---|---|---|---|
45 | 350 | 532 | 882 | 0.19 | 0.08 | 0.19 |
49 | 351 | 149 | 500 | 0.20 | 0.13 | 0.20 |
48 | 197 | 194 | 391 | 0.19 | 0.06 | 0.19 |
44 | 152 | 149 | 301 | 0.18 | 0.01 | 0.17 |
61 | 109 | 90 | 199 | 0.17 | 0.10 | 0.17 |
62 | 93 | 100 | 193 | 0.15 | 0.05 | 0.15 |
41 | 86 | 84 | 170 | 0.17 | 0.04 | 0.17 |
54 | 82 | 88 | 170 | 0.17 | 0.06 | 0.17 |
7 | 79 | 78 | 157 | 0.12 | 0.07 | 0.12 |
51 | 56 | 83 | 139 | 0.17 | 0.02 | 0.17 |
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Taczanowska, K.; Bielański, M.; González, L.-M.; Garcia-Massó, X.; Toca-Herrera, J.L. Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory. Symmetry 2017, 9, 317. https://doi.org/10.3390/sym9120317
Taczanowska K, Bielański M, González L-M, Garcia-Massó X, Toca-Herrera JL. Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory. Symmetry. 2017; 9(12):317. https://doi.org/10.3390/sym9120317
Chicago/Turabian StyleTaczanowska, Karolina, Mikołaj Bielański, Luis-Millán González, Xavier Garcia-Massó, and José L. Toca-Herrera. 2017. "Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory" Symmetry 9, no. 12: 317. https://doi.org/10.3390/sym9120317