Sink Propagation Values on Network v4.1

System Log

System ready.

Selection

Element Properties

Select a node or link to edit its properties.

SPV Configuration (Local Rules)

Target Object
Decision Mode
Param A
Param α

Agent Simulation & Strategies

Decision Strategy
Max Steps
Sequence Editor

Optimal: Selects the absolute best option.
Sub-Optimal: Selects the second-best option. It simulates minor human errors.
Reverse: Selects the worst option. It models adverse decisions.
Satisficing: Chooses the first option that improves the current state. It models bounded rationality.
Proportional: Selects probabilistically. Better options have higher chances. It uses the discrete Logit model.
Random: Selects any available option with equal probability. Sequence: Follows user-defined state steps before switching to the next state.

The agent optimizes based on the Target (Node/Link) and Mode (Min/Max) established in the SPV Configuration panel.

Select "Set Origin". Click a node on the canvas. Click "Step Node" or "Play". Pause and Step Back to scrutinize routing choices. Click "Restart Agent" to restart from the same origin.

Network Generators

1. Preset Examples

2. Random Graph

Nodes: Links:

Make Coplanar

3. Text-Based Generator

Links (Origin, Dest, Cost) - Required: Nodes (ID, X, Y) - Optional:

Network Connectivity Analysis

Network Statistics & Matrices

Trajectories & Flow

Agent Group Parameters

Max Speed (m/s)
Max Density
Model Type

Export Network Image

Import Background Image

Advanced Configuration

Global Options

Snap to Grid

Grid Size: px

Auto Link Length

Documentation

SPV-NET Virtual Laboratory

We present the SPV-NET Virtual Laboratory. This platform disseminates research on Sink Propagation Value (SPV). Kardi Teknomo discovered SPV and coined the term in 2008. The framework unifies shortest-path potentials as local information. This unification applies over network graphs, lattice grids, and continuous eikonal space. We assure local-to-global optimization invertibility. We use this local information for decision navigation processes. This reduces computational costs to reach global optimization for multi-sink multi-values shortest-paths. The individual components and algorithms are known. The explicit unification and the invertibility result are new discoveries.

The purpose of SPVNET is to build a model for network theory and sink propagation value (SPV).

1. Network Building

A network consists of interconnected nodes and links. Nodes represent discrete states or spatial coordinates. Links represent directional connections between nodes. You can build a network by adding nodes and connect them with links.

Pointer Mode: Select, move, and edit individual elements. Click on an empty canvas space to unselect everything.
Add Nodes: Switch to "Node" mode. Click anywhere on the canvas to add a new node.
Make Links: Switch to "Link" mode. Drag from an origin node to a destination node to create a directional edge. The system enforces strict directional segments. We permit only simple networks. No self-loop or multiple edges between identical nodes are permitted.
Move Nodes: Switch "Pointer" mode. Drag node across the canvas to reposition it. Any movement will always snap to the grid if the snapping constraint is enabled in Advanced Configuration.
Set Sink Basin: In Pointer mode, select a node to open it's "Element Properties" inspector. Set the "Is Basin" property to True. This designates the node as an absorption sink. Sink basins absorb flow. They turn red upon assignment.

2. Selections & Collective Editing

Select ROI: Switch to "Select ROI" mode. Draw a rectangle on canvas to select a Region of Interest (ROI) containing multiple nodes simultaneously. When a node is selected, it turns into red color.
Context Menu: Right-click a node to delete it. Right-click a link to cycle through directional states: One way from origin to destination, Two ways, and One way from destination to origin. Two ways link is represented by a no-arrow link.
Property Editor: Modify selected elements. The "Element Properties" grid allows you to change parameters (like 'Is Basin' or 'Direction') for all selected items simultaneously. Edits apply collectively to all active selections. Click "Apply Changes".

3. Element Properties Inspector

Node Rows: ID (System identifier), Tag (Custom name), X/Y Coordinate (Spatial position), SPV (Calculated gradient value), Component (Sub-graph group number), Is Basin (Designates the node as an absorption sink).
Link Rows: ID (System identifier), Tag (Custom name), Origin/Dest ID (Connected nodes), Length (Spatial or weighted length), Flow (Trajectory usage density), Direction (0: Two-way, 1: Start-to-End, 2: End-to-Start).

The properties panel acts as a mathematical inspector.

Invertibility Inspector: Select a link. The properties panel exposes the exact derivation of the edge score from global distances. We extract the destination node distance using local algebra.
Global to Local: Select a link. The panel exposes the exact derivation of the edge score from global distances.
Local to Global: Select a link. The system extracts the destination node distance using local algebra.

4. SPV Dualities and Local Decisions

The Sink Propagation (SPV) to maps shortest distances to the nearest sink basin. The system resolves optimal paths using dualized local edge rules.

The SPV metric maps the topological distance gradient from all nodes to the nearest sink. We compute four mathematically equivalent SPV forms.

Node Min (Standard): The absolute cost-to-go distance to the sink.
Node Max (Normalized): An inverted potential field. It uses parameters A and α.
Link Min (Feasible Potential): The edge-specific cost. It evaluates immediate cost plus destination distance.
Link Max: The normalized edge potential.

Agents utilize Link SPV exclusively to make greedy local decisions. The local edge score guarantees global Bellman optimality.

5. Graph Algorithms, Connectivity & Matrices

We provide tools for empirical verification and structural analysis.

Sink Propagation Value (SPV): Set at least one node's "Is Basin" property to True. Click "Show SPV" to calculate the topological distance gradient from all nodes to the nearest sink.
Connectivity Analysis: Use the dedicated panel to identify structural endpoints. Source Nodes have no incoming edges. Sink Nodes have no outgoing edges. Strongly Connected Components (SCC) identify cyclic sub-graphs using Kosaraju's algorithm.
Path to Sink (SPV): Click an origin node to highlight the optimal traversal path to the nearest basin based on current SPV gradients. It requires at least one sink node.
Point-to-Point Path: Clicking an origin then a destination calculates the absolute shortest traversal across the network using the Floyd-Warshall algorithm.
Matrices: Generates Adjacency and Distance matrices, as well as the Floyd-Warshall All-Pairs Shortest Path matrix. Distributions are visualized in bar charts.

6. Agent Simulation & Sequence Strategies

We provide a step-by-step proof of local decision validity and explore behavioral routing.

Initialization: Click 'Set Origin'. The canvas enters Agent Origin mode. Click any node on the canvas to instantiate the agent. The origin is saved in memory.
Decision Strategies: Select a behavioral model from the dropdown. We support Optimal (strict Bellman), Sub-Optimal, Reverse (worst choice), Satisficing (bounded rationality), Proportional (Logit), and Random paths.
Sequence Editor (Repentance): Selecting "Custom Sequence" reveals the Sequence Editor. Build a multi-stage behavioral plan (e.g., Reverse for 3 steps, then Optimal forever). This simulates human "repentance" or bounded memory.
Step Execution: Click 'Step Node'. The agent evaluates immediate edges based on the chosen strategy and target metric (Node SPV or Link SPV). The log records the mathematical evaluation.
Verification: The system executes a Floyd-Warshall benchmark upon reaching the sink. It compares the traversed path against the absolute global optimum.
Reset: Click 'Reset Agent' to clear the current traversal. The agent automatically snaps back to the memorized origin, ready for another simulation.

7. Trajectories & Flow

Recording: Click "Start" in "Trajectories and Flow" panel.Sequentially click connected nodes to record and map a traversal path. The system validates directions. Click "Finish" to save the trajectory.
Flow Pattern: Click "Show Flow Pattern" to aggregate all recorded trajectories. Link thickness and color will dynamically update to reflect usage density.

8. Advanced Tools & Configurations

Snap to Grid / Grid Size: Forces node positioning to align to a pixel grid constraint.
Auto Link Length: Automatically recalculates a link's length based on the Euclidean spatial distance between its connected nodes.
Agent Group: Defines macroscopic pedestrian behaviors. Parameters include Max Speed (m/s) and Max Density (peds/cell). The Model Type (Linear, Convex, Concave) dictates the probability-to-enter curves.
Random Graph: Generates a random network topology. Toggle "Make Coplanar" to prevent crossing edges using a geometric intersection algorithm.
Export: Save the visual canvas to high-definition PNG/JPEG, vector SVG, or LaTeX (TikZ) format for academic publishing.

System Testing

The app includes automated validation.

Unit Tests: Validates mathematical invertibility across all presets.
Topology Tests: Verifies structural mutations and cascades.
Algorithmic Tests: Benchmarks matrices and flow mapping.
Integration Tests: Validates UI binding and state transitions.
Agent Tests: Verifies simulation state machine and locks.
Stress Tests: Benchmarks calculation latency on massive random graphs.

Welcome to SPV-NET