Advanced Graph Theory Tools

Explore powerful graph algorithms with stunning visualizations. Optimize campus infrastructure, sensor placement, and energy networks using cutting-edge mathematical models and extreme color schemes.

Graph Types

Graph Operations

Algorithm Parameters

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Algorithm Results

Minimum Spanning Tree

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No MST calculated yet. Run the algorithm to see results.

Dominating Set

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No dominating set calculated yet. Run the algorithm to see results.

Shortest Path

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No path calculated yet. Select start and end nodes.

Cluster Analysis

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No clusters identified yet. Run the algorithm to see results.

Mathematical Foundation

Our advanced graph analysis tools are built on proven mathematical algorithms that form the intelligence behind campus optimization and infrastructure planning.

Minimum Spanning Tree

Find the minimum cost tree connecting all nodes using Prim's or Kruskal's algorithm. Essential for optimizing wiring and network costs.

MST = argminT⊆G Σe∈T w(e)

Dominating Set

Find the smallest set of nodes where every node is either in the set or adjacent to it. Perfect for optimal sensor placement.

D ⊆ V such that ∀v∈V: v∈D ∨ ∃u∈D: (u,v)∈E

Shortest Path

Find the minimum cost path between two nodes using Dijkstra's algorithm. Critical for routing and navigation systems.

dist(s,t) = minp∈paths(s,t) Σe∈p w(e)

Cluster Analysis

Partition nodes into clusters based on connectivity and usage patterns. Ideal for grouping similar campus areas.

C = {C1, C2, ..., Ck} where Ci ⊆ V
Graph algorithm executed successfully!