To understand graphs better, here are some simple methods you can use:

1. How to Show a Graph:

   • Adjacency Matrix: Think of this as a chart. It’s a square that shows every node, or point, in the graph. The spot where row $i$ meets column $j$ tells us if there is a connection between node $i$ and node $j$. If a graph has $n$ nodes, this chart takes up a lot of space—about $n \times n$ spaces.
   • Adjacency List: This is more like a list of friends. Each node has its own list showing which other nodes it connects to. This way uses less space and is more efficient. It takes up space based on the total number of nodes plus the number of connections.

2. Tools to Visualize Graphs:

   • Gephi: This tool is great for handling big graphs. You can work with thousands of nodes without a problem.
   • Graphviz: This tool makes pictures of graphs based on simple text descriptions. It’s better for straightforward graphs.

3. Important Techniques:

   • Breadth-First Search (BFS): This method looks at all the nodes that are closest to the starting node first. It goes out layer by layer.
   • Depth-First Search (DFS): This technique goes deep into the graph, exploring as far as possible before coming back.

By learning about these ways to show graphs and these techniques, we can understand more about how graphs work, including their characteristics, patterns, and connections.