Sample dataset/04 Graph/Graph_Structure_README.md

Graph Structure Documentation

Overview

The MMS-VPR dataset conceptualizes the pedestrian network as a spatial graph G = (V, E) where nodes represent street intersections and edges represent street segments. This graph-based organization provides:

1. Structural clarity for dataset navigation
2. Foundation for GNN applications (Graph Neural Networks)
3. Spatial relationship modeling for context-aware VPR
4. Integration with urban science through space syntax theory

The graph comprises 208 locations organized into four spatial types:

• 81 Nodes: Street intersections
• 125 Edges: Pedestrian street segments (61 horizontal + 64 vertical)
• 2 Squares: Large open spaces

File Descriptions

00 Street Network Graph.pdf

Visualization of the complete pedestrian network showing:

• Geographic layout of all 208 locations
• Node positions (street intersections)
• Edge connections (street segments)
• Square boundaries
• Real-world mapping to Chengdu Taikoo Li

This map provides an intuitive understanding of:

• Spatial relationships between locations
• Network topology and connectivity
• Physical layout in the commercial district

Use this visualization to understand the overall dataset structure before diving into detailed data files.

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01 Node Features.xlsx

Contains: Attributes for all 81 street intersection nodes (+ 2 squares)

Column Descriptions

Column	Description	Example Values
Code	Node identifier	N-1-1, N-2-3, S-1
Node Type	Classification (1-4)	1, 2, 3, 4
Location Coordinates	Grid position (row, column)	1, 1 → Row 1, Column 1
J-graph Depth	Shortest path distance to public roads	0, 1, 2, 3, 4, 5
Longitude	GPS longitude coordinate	+104.081061
Latitude	GPS latitude coordinate	+30.658052

Node Type Classification

Nodes are classified based on accessibility depth (distance to public roads):

Type 1: Gateway Nodes (Depth 0-1)

• Located at or immediately adjacent to public roads
• Highest accessibility and visibility
• Serve as primary entry/exit points
• Characteristics: High pedestrian flow, easy wayfinding

Type 2: Intermediate Nodes (Depth 2-3)

• Moderately interior positions
• Balance between exposure and seclusion
• Act as conduits between entrances and deep zones
• Characteristics: Moderate flow, mixed accessibility

Type 3: Deep Interior Nodes (Depth 4-5)

• Deep interior locations
• Low visibility from public roads
• Lower pedestrian flow
• Higher wayfinding challenge
• Characteristics: Requires navigation through multiple turns

Type 4: Open Squares

• Large open spaces (S-1, S-2)
• Bounded by multiple edges and nodes
• Central gathering spaces
• Characteristics: High visibility within district, social hub

J-graph Depth Explanation

Definition: Shortest path distance (in number of street segments) from a node to the nearest public road.

• Depth 0: Node is ON a public road
• Depth 1: One street segment away from public road
• Depth 2-3: Interior positions requiring 2-3 turns from entrance
• Depth 4-5: Deep interior requiring complex navigation

This metric indicates:

• Ease of discovery by visitors
• Expected pedestrian traffic volume
• Wayfinding complexity

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02 Edge Features.xlsx

Contains: Attributes for all 125 street segments (edges)

Column Descriptions

Column	Description	Example Values
SegmentID	Edge identifier	Eh-1-1, Ev-2-3
NodeA	Starting node	N-1-1
NodeB	Ending node	N-1-2
Edge Type	Street width classification (1-3)	1, 2, 3
Location Coordinates	Grid position	1, 1
Orientation	Street angle in degrees	0 (horizontal), 90 (vertical)
Length	Physical length in meters	53.05
Width	Physical width in meters	4.0
Urban Roads	Public road indicator	1 (public), 0 (private)
Longitude	GPS longitude of street center	+104.082376
Latitude	GPS latitude of street center	+30.657317
e_loc_x	First coordinate component	1
e_loc_y	Second coordinate component	1
integration	Space syntax integration (angular)	0.015
betweenness	Space syntax betweenness (angular)	0.012
weighted_integration	Weighted integration (angular + Euclidean)	0.023
weighted_betweenness	Weighted betweenness (angular + Euclidean)	0.037

Edge Naming Convention

Horizontal Edges (East-West streets): Eh-i-j

• Example: Eh-1-1 = Row 1, Column 1 of horizontal edges
• Orientation: 0°

Vertical Edges (North-South streets): Ev-j-i

• Example: Ev-1-1 = Column 1, Row 1 of vertical edges
• Orientation: 90°

Edge Type Classification

Streets are classified by width following urban design principles:

Type 1: Alley (1-3 meters)

• Narrow passages
• Constrained flow corridors
• Primarily for connectivity
• Characteristics: Intimate scale, limited dwell potential

Type 2: Intermediate Street (4-7 meters)

• Comfortable circulation width
• Moderate dwell potential
• Supports walking + browsing
• Characteristics: Balanced flow and activity

Type 3: Primary Broad Street (8-13 meters)

• Wide open corridors
• Supports high pedestrian flow
• Suitable for events and gatherings
• Characteristics: High capacity, visual prominence

Urban Roads Indicator

• 1: Public city road (district perimeter)
• 0: Private interior street (within shopping district)

This distinguishes between:

• External connections to city street network
• Internal pedestrian-only circulation

Space Syntax Metrics

Integration (Global Accessibility)

• Measures how easily a street can be reached from all other streets
• Higher values → Centrally located, easily accessible streets
• Lower values → Peripheral or isolated streets

Betweenness (Through-Movement Potential)

• Measures how often a street lies on shortest paths between other streets
• Higher values → Primary routes with heavier pedestrian flow
• Lower values → Secondary streets with local traffic only

Metric Variants:

1. integration / betweenness: Based on angular distance only

   • Angular distance = sum of turn angles / 90°
   • Represents cognitive wayfinding effort

2. weighted_integration / weighted_betweenness: Based on weighted distance

   • Weighted distance = 50% normalized Euclidean + 50% normalized angular
   • Balances physical distance and turning complexity
   • More comprehensive spatial measure

Why Two Variants?

• Angular metrics better predict pedestrian movement (people minimize turns)
• Weighted metrics balance physical distance with cognitive ease
• Different research questions may require different metrics

Normalization: All metrics are normalized to [0, 1] range for comparability.

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03 Edge Connections.xlsx

Contains: Pairwise relationships between all connected street segments

Column Descriptions

Column	Description	Example Values
Segment_X	First street identifier	Eh-1-1
Segment_Y	Second street identifier	Ev-1-1
SharedNode	Intersection connecting X and Y	N-1-1
Angle_X	Orientation of street X	0°
Angle_Y	Orientation of street Y	90°
TurnAngle	Turn angle from X to Y	90°
Angular Distance	Normalized angular distance	1.0
Euclidean Distance	Physical distance (m)	65.46
Weighted Distance	Combined distance metric	1.2

Distance Metrics Explained

Turn Angle

• Range: 0° to 180°
• Angle required to turn from street X to street Y
• Example: 90° = perpendicular turn, 180° = reverse direction

Angular Distance

• Formula: TurnAngle / 90°
• Range: 0.0 to 2.0
• Normalized cognitive cost of turning
• Example: 90° turn = 1.0, 45° turn = 0.5

Euclidean Distance

• Physical distance = Length(X) + Length(Y)
• Actual walking distance between street centers
• Unit: meters

Weighted Distance

• Combines angular and Euclidean distances
• Both components normalized to [0, 1] via min-max scaling
• Formula: 0.5 × norm(Euclidean) + 0.5 × norm(Angular)
• Balances physical distance and turning difficulty

Use Cases

This file enables:

1. Graph Construction:

   • Segment_X and Segment_Y define edge connectivity
   • Build adjacency matrices for GNN input

2. Pathfinding:

   • Use Angular Distance for cognitively easy routes
   • Use Euclidean Distance for shortest physical paths
   • Use Weighted Distance for balanced optimization

3. Network Analysis:

   • Identify critical junctions (high-degree nodes)
   • Analyze route options between locations
   • Compute centrality measures

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04 Square Features.xlsx

Contains: Attributes for the 2 large open square spaces

Column Descriptions

Column	Description	Example Values
Square Code	Square identifier	S-1, S-2
Node Type	Always 4 (open square)	4
List of Adjacent Edges	Boundary streets	Eh-8-3, Ev-6-1, Eh-10-4
List of Adjacent Nodes	Boundary intersections	N-8-3, N-10-3, N-10-4
Size Rank	Area ranking	1 (largest), 2
J-graph Depth	Minimum depth of adjacent nodes	2
Longitude	GPS longitude of square center	+104.081061
Latitude	GPS latitude of square center	+30.658052
Perimeter	Boundary length (m)	198
Area	Total area (m²)	2347

Understanding Squares

Squares are sub-graphs defined as:

• S_k = (E_k, V_k) where:
  • E_k ⊂ E: Subset of edges forming the boundary
  • V_k ⊂ V: Subset of nodes at corners

S-1: Central Square

• Area: 2,347 m²
• Primary gathering space
• Highest visibility within district
• Multiple access points (edges)

S-2: Secondary Square

• Smaller auxiliary open space
• Complementary function to S-1

Adjacent Elements

Adjacent Edges: Streets forming the square's perimeter

• Define the boundary of the open space
• Connect the square to the rest of the network

Adjacent Nodes: Intersections at square corners

• Entry/exit points to the square
• Connection hubs to surrounding streets

J-graph Depth for Squares

• Calculated as the minimum depth among all adjacent nodes
• Represents the easiest path to reach the square from public roads
• Example: If adjacent nodes have depths [2, 3, 3, 4], square depth = 2

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Using Graph Structure in Research

For GNN Applications

Step 1: Build Adjacency Matrix

# Use 03 Edge Connections.xlsx
adjacency_matrix[Segment_X][Segment_Y] = 1  # Or use weighted distance

Step 2: Extract Node Features

# Use 01 Node Features.xlsx and 02 Edge Features.xlsx
node_features = [depth, coordinates, integration, betweenness, ...]

Step 3: Define Graph

G = (V, E, X)
V = all nodes (from 01)
E = all connections (from 03)  
X = node/edge features (from 01, 02)

For Spatial Analysis

Accessibility Studies:

• Use integration to identify most accessible streets
• Compare gateway nodes vs. deep interior nodes
• Analyze pedestrian flow distribution

Route Planning:

• Use Angular Distance for intuitive routes
• Use Weighted Distance for balanced optimization
• Consider Edge Type for comfort (prefer wider streets)

Urban Design Insights:

• Correlate betweenness with observed pedestrian counts
• Identify under-utilized spaces (low integration + low betweenness)
• Suggest interventions to improve connectivity

For VPR Research

Context-Aware Retrieval:

• Use graph structure to constrain search space
• Prioritize neighbors in graph when matching queries
• Weight matches by spatial proximity in network

Hierarchical Search:

• First: Identify region using Node Type and J-graph Depth
• Then: Refine within local graph neighborhood
• Finally: Match specific location

Flow-Aware Methods:

• Weight locations by integration (high-traffic areas)
• Account for betweenness in query distribution
• Model expected pedestrian paths

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Space Syntax Theory Integration

Background

Space Syntax is an established theory in urban science and architecture that quantifies spatial configuration's impact on human movement and social behavior.

Key Insight: The way spaces are connected (topology) influences how people move through them, independent of function or aesthetics.

Integration Metric

Mathematical Definition:

$${\text{Integration}}_i=\frac{k-2}{2(\frac{1}{k-1}\sum _{j\mathrm{\ne }i}d(i,j)-1)}\backslash text\{Integration\}\_i\; =\; \backslash frac\{k-2\}\{2\; \backslash left(\; \backslash frac\{1\}\{k-1\}\; \backslash sum\_\{j\; \backslash neq\; i\}\; d(i,j)\; -\; 1\; \backslash right)\}$$

Where:

• k = total number of streets
• d(i,j) = shortest path distance from street i to street j

Interpretation:

• High integration → Street is central, easily reached from everywhere
• Low integration → Street is peripheral, requires many turns to access

Practical Meaning:

• Predicts pedestrian flow volume
• Indicates commercial potential
• Guides wayfinding difficulty

Betweenness Metric

Mathematical Definition:

$${\text{Betweenness}}_i=\sum _{\begin{array}{c}j\mathrm{\ne }i\\ k\mathrm{\ne }i,k\mathrm{\ne }j\end{array}}\frac{{\sigma }_{jk}(i)}{{\sigma }_{jk}}\backslash text\{Betweenness\}\_i\; =\; \backslash sum\_\{\backslash substack\{j\; \backslash neq\; i\; \backslash \backslash \; k\; \backslash neq\; i,\; k\; \backslash neq\; j\}\}\; \backslash frac\{\backslash sigma\_\{jk\}(i)\}\{\backslash sigma\_\{jk\}\}$$

Where:

• σ_jk = total number of shortest paths from j to k
• σ_jk(i) = number of those paths passing through i

Interpretation:

• High betweenness → Street is on many shortest paths (through-route)
• Low betweenness → Street is rarely on shortest paths (destination only)

Practical Meaning:

• Identifies primary circulation routes
• Predicts encounter probability
• Indicates strategic retail locations

Why This Matters for VPR

Traditional VPR datasets provide only:

• Visual appearance
• GPS coordinates

MMS-VPR adds:

• Topological context: How is this place connected?
• Movement potential: How much traffic does it get?
• Accessibility hierarchy: How easy is it to find?

This enables:

1. Context-aware matching: Use spatial configuration to improve accuracy
2. Query distribution modeling: Account for non-uniform real-world usage
3. Cross-city transfer: Spatial patterns generalize across urban contexts
4. Interpretable models: Explain predictions using urban design theory

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Data Quality and Validation

Topology Validation

✅ Verified Properties:

• All edges connect exactly two nodes
• No isolated components (graph is connected)
• Coordinates match real-world positions
• Angular distances computed correctly

Metric Computation

✅ Computation Tools:

• Space syntax metrics: Computed using DepthmapX/UCL software
• Angular distance: Based on street centerline geometry
• Euclidean distance: Direct calculation from GPS + street length

✅ Normalization:

• All spatial metrics: Min-max normalized to [0, 1]
• Enables fair comparison across different distance types

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Frequently Asked Questions

Q: Why use graph structure for VPR?

A: Graph structure captures spatial relationships that pure visual matching misses. It enables context-aware retrieval, handles ambiguous queries better, and improves performance in visually similar areas.

Q: What's the difference between angular and weighted distance?

A: Angular distance considers only turns (cognitive ease). Weighted distance balances turns and physical distance (50-50). Choose based on your application: navigation apps may prefer angular, while distance estimation needs weighted.

Q: How do I convert location codes to indices?

A: Each location has a unique index 0-207:

• Nodes: N-1-1 to N-9-9 → indices 0-80
• Squares: S-1, S-2 → indices 81-82
• Horizontal edges: Eh-1-1 to Eh-11-7 → indices 83-143
• Vertical edges: Ev-1-1 to Ev-7-11 → indices 144-207

See Texts/Annotations.xlsx for complete mapping.

Q: Can I use only visual data without graphs?

A: Yes! The dataset works perfectly for standard image-based VPR. Graph structure is an additional resource for advanced methods, not a requirement.

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Recommended Workflow

For First-Time Users

1. Start with 00 Street Network Graph.pdf → Understand spatial layout
2. Read Texts/Annotations.xlsx → Learn location codes
3. Explore one location folder in Images/ → See actual data
4. Review 01 Node Features.xlsx → Understand location attributes
5. Try basic image retrieval → Validate setup

For GNN Researchers

1. Load 03 Edge Connections.xlsx → Build adjacency matrix
2. Extract features from 01 and 02 → Create feature vectors
3. Align with visual features from Images/ → Multimodal embedding
4. Train GNN model → Leverage graph structure
5. Evaluate on graph-aware metrics → Consider topological accuracy

For Urban Analytics

1. Analyze integration and betweenness → Identify key streets
2. Correlate with image counts → Validate with actual activity
3. Compare J-graph Depth across locations → Accessibility patterns
4. Visualize using 00 Street Network Graph.pdf → Present findings

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Version History

v1.0 (February 2026)

• Initial release
• 208 locations (81 nodes + 125 edges + 2 squares)
• Complete space syntax metrics
• Validated graph topology

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Citation

When using graph structure data, please cite:

@article{ou2025mmsvpr,
  title     = {MMS-VPR: Multimodal Street-Level Visual Place Recognition Dataset and Benchmark},
  author    = {Ou, Yiwei and Ren, Xiaobin and Sun, Ronggui and Gao, Guansong and 
               Jiang, Ziyi and Zhao, Kaiqi and Manfredini, Manfredo},
  journal   = {arXiv preprint arXiv:2505.12254},
  year      = {2025},
  url       = {https://arxiv.org/abs/2505.12254}
}

References

For more on space syntax theory:

• Hillier, B., & Hanson, J. (1984). The Social Logic of Space
• Turner, A. (2001). Angular analysis. 3rd International Symposium on Space Syntax
• Peponis, J., et al. (1997). The spatial core of urban culture

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For questions about graph structure, please open an issue on GitHub or contact the authors.