Zagreb Graph Library

This demo showcases the Zagreb Graph Library running in WebAssembly. Create different types of graphs, visualize them, and analyze their properties using the First Zagreb Index.

Graph Visualization

Low Degree

High Degree

Minimum Degree

Maximum Degree

Create Graph

Graph Type:

Number of Vertices:

Connection Probability (0-1): Higher values create more connected gossip networks

Set A Size (m): Set B Size (n): Complete bipartite graph Km,n will have m+n vertices

Number of Shards: Intra-Shard Connectivity: Inter-Shard Connectivity: Controls how densely connected shards are internally and between each other

Add Edges

From:

To:

Analyze Graph

Calculate the Zagreb index and determine Hamiltonian properties.

Create a graph and click "Analyze Graph" to see the results.

About the Zagreb Index

The First Zagreb Index of a graph G is defined as:

Z₁(G) = ∑(d²(u)) for all vertices u in G

Where d(u) is the degree of vertex u (the number of edges connected to it).

This index is used to analyze graph properties, including Hamiltonicity, which is important for network design and optimization.

Graph Types Explanation

Cube Graph (Q3): A 3-regular graph with 8 vertices arranged in a cube structure. Every vertex has exactly 3 neighbors.
Platonic Solids: Regular, convex polyhedra with faces of identical regular polygons meeting at each vertex the same number of times.
- Tetrahedron: 4 vertices, each connected to all others (K4).
- Octahedron: 6 vertices arranged as two antipodal points connected to a square.
- Icosahedron: 12 vertices with 20 triangular faces.
Bipartite Graph (Km,n): A complete bipartite graph with two disjoint sets of vertices (m and n), where every vertex in the first set is connected to every vertex in the second set.
Scale-Free Graph: Network with power-law degree distribution, where a small number of nodes have many connections while most nodes have only a few. Common in natural and human-made systems including the internet and blockchain networks.
Gossip Network: Models blockchain validators with a baseline connectivity (cycle) and probabilistic additional connections. Some nodes serve as high-degree coordinators to simulate validator roles.
Sharded Network: Represents a blockchain system with multiple shards (subgraphs), where connections within shards are dense but connections between shards are sparse. Models the topology of sharded blockchain architectures.

Key Properties

Hamiltonian Graph: Contains a cycle that visits every vertex exactly once
Traceable Graph: Contains a path that visits every vertex exactly once
k-Connected Graph: Remains connected even after removing any k-1 vertices