Submitted:
06 November 2025
Posted:
07 November 2025
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Abstract
This paper presents an automated GIS-based procedure for the analysis and optimization of hiking trails. A preliminary analysis of the topological and environmental features of a trail network is performed by evaluating a set of connection metrics describing both the local and global connectivity of its graph. Subsequently, the evaluation of optimal hiking trails has been implemented in an automatic procedure, which can use walking time, distance or upward slope as costs to be minimized. The evaluation of the hiking times for trail sections has been implemented in a GIS as a function of terrain slope. A Python script has been used to automate this process in GRASS GIS. The process was tested on the network of mountain trails in Trentino, an alpine region of Italy, where a digital map of the routes is accessible online. Empirical times and estimated trip times agree fairly well. The optimal paths vary based on the cost choice, i.e., whether the distance, trip time, or total height difference is minimized. It is therefore possible to integrate the determination of optimal hiking paths in a GIS, allowing the integration of this tool with all the other spatial analysis available in this environment.
Keywords:
1. Introduction
1.1. Trail Network in the Trentino Region
1.2. Network Analysis for Trail Networks
1.3. Path Optimization for Hiking Trail Networks
2. Materials and Methods
2.1. Study Area
2.2. Topological Analysis of the Trail Network
2.3. Global Connectivity Evaluation
- number of cycles
- which compares a graph’s number of cycles with the maximum number of cycles that could exist. A network with great redundancy and connectivity is indicated by high index values;
- which measures a graph’s degree of connectedness by dividing its number of edges (e) by its number of nodes (n). For simple networks and trees, the value of β is less than 1, for a linked network with a single cycle, it is 1, and for complex networks with many alternative paths, it is greater than 1;
- which uses the correlation between the number of observed and potential links to calculate connectedness. Its value ranges between 0 and 1, with γ=1 for completely connected networks.
2.4. Local Connectivity Evaluation
- degree centrality, which is the number of edges connecting a node;
- closeness centrality, defined as the average length of the shortest path between a node and all the other nodes in the network; the more central a node is, the closer it is to all other nodes;
- betweenness centrality, measuring the average length of shortest paths between two any other nodes passing through the node; the value is 0 if no shortest path passes through the node;
- eigenvector centrality, which assesses the influence of a node on a network by its connections to other nodes with high eigenvector centrality, i. e. a node is important if it is connected to important nodes; it is evaluated by a linear combination of the eigenvectors of the adjacency matrix.
2.5. Route Optimization and Hiking Time Evaluation
3. Results
3.1. Global Connectivity Evaluation
3.2. Local Connectivity Evaluation
3.3. Paths Optimization
| Point of interest | Elev. [m] | Point of interest | Elev. [m] |
|---|---|---|---|
| Rifugio Croz dell’Altissimo | 1,441 | Baita Ciclamino | 927 |
| Rifugio Montanara | 1,507 | Baito Brenta Alta | 1,668 |
| Rifugio Pedrotti | 2,500 | Malga Cavedago | 1,852 |
| Rifugio Pradél | 1,364 | Malga Spora | 1,857 |
| Rifugio Sella | 2,282 | Rifugio Alberto e Maria ai Brentei | 2,179 |
| Rifugio Selvata | 1,656 | Rifugio Alimonta | 2,589 |
| Rifugio Tosa | 2,449 | Rifugio Brenta | 1,357 |
| Rifugio Tuckett | 2,270 | Rifugio Cacciatori di Spora | 1,868 |
| Rifugio XII Apostoli |
2,490 | Rifugio Casinei | 1,825 |



4. Discussion
5. Conclusions
Author Contributions
Data Availability Statement
Conflicts of Interest
Abbreviations
| ATVs | All-Terrain Vehicles |
| CES | Cultural Ecosystem Services |
| DGLib | Directed Graph Library |
| DTM | Digital Terrain Model |
| EPSG | European Petroleum Survey Group |
| ETRS | European Terrestrial Reference System |
| GIS | Geographic Information System |
| GNU | GNU’s Not Unix |
| GPS | Global Position System |
| GRASS | Geographic Resources Analysis Support System |
| MCDM | Multi-Criteria Decision-Making |
| PAT | Provincia Autonoma di Trento (Autonomous Province of Trento) |
| SAT | Società degli Alpinisti Tridentini (Society of the Tridentine Mountaineers) |
| SHP | Shape file |
| SIAT | Sistema Informativo Ambiente e Territorio (Provincial Environment and Territory Information System) |
| TSP | Traveling Salesman Problem |
| UTM | Universal Transverse Mercator |
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| Type of trail | Number | Length [m] | Equipment length [m] |
|---|---|---|---|
| Alpine trails | 866 | 4,365,995 | 345 |
| Equipped alpine trails | 144 | 974,136 | 8,843 |
| Vie ferrate | 69 | 258,555 | 20,096 |
| Total | 1,079 | 5,598,680 | 29,284 |
| Slope interval [degrees] | Speed polynomial [Km/h] |
|---|---|
| [-90 ÷ -80] | 0.05 |
| (-80 ÷ -45] | 0.0002 p2 + 0.0285 p + 1.162 |
| (-45 ÷ -7] | 0.0005 p3 + 0.0067 p2 + 0.3169 p + 5.8524 |
| (-7 ÷ 4] | 0.0012 p3 − 0.0194 p2 − 0.1559 p + 4.2097 |
| (4 ÷ 25] | −0.00008 p3 + 0.0091 p2 − 0.3296 p + 4.5583 |
| (25 ÷ 80] | 0.0003 p2 − 0.0437 p + 1.6718 |
| (80÷ 90] | 0.05 |
| Degree | Closeness | Betweenness | Eigenvector | |
|---|---|---|---|---|
| Average | 2.39 | 28,209.08 | 3,015.33 | 0.001369 |
| Std dev. | 0.99 | 18,901.51 | 10,068.70 | 0.033921 |
| Max | 5.00 | 85,633.16 | 99,176.00 | 1.000000 |
| Min | 1.00 | 446.07 | 0.00 | 0.000000 |
| Median | 3.00 | 25,761.63 | 242.50 | 0.000000 |
| Id | Time forward [h] | Time backward [h] | Elev. change. forward [m] | Elev. change. backward [m] |
|---|---|---|---|---|
| 3 | 0.03 | 0.03 | 6.588 | 0 |
| 11 | 0.01 | 0.01 | 2.485 | 0 |
| 13 | 0.06 | 0.04 | 20.479 | 0 |
| 15 | 0.09 | 0.07 | 12.765 | 0 |
| 20 | 0.03 | 0.04 | 0 | 4.213 |
| 21 | 0.19 | 0.23 | 0 | 43.094 |
| Evaluated time | SAT tables times | |||
|---|---|---|---|---|
| Backward | Forward | Trail num. | Backward | Forward |
| 2:59h | 4:44h | 447 | 3:45h | 5:00h |
| 1:46h | 2:55h | 442 | 2:00h | 3:00h |
| 3:14h | 5:09h | 431 | 4:00h | 5:15h |
| 4:12h | 5:06h | 425 | 4:00h | 4:40h |
| Minimized cost | Distance [m] | % | Time [h] | % | Elev. change [m] | % |
|---|---|---|---|---|---|---|
| Distance | 34.797 | 100.00 | 25.24 | 100.52 | 2,626.74 | 102.79 |
| Time | 35.398 | 101.73 | 25.11 | 100.00 | 2,815.55 | 110.18 |
| Elevation change | 41.927 | 120.49 | 31.80 | 126.64 | 2,555.52 | 100.00 |
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