Relationship information describes how entities connect. A graph makes it usable: nodes represent entities, and edges represent their relationships. This differs from an ordinary database table or spreadsheet, whose rows and columns do not by themselves express a graph of connections. section 1.2.1 section 1.0
An adjacency matrix records those connections in a table: a value of 1 marks a link, while 0 marks its absence. For an undirected graph, the matrix is symmetric because a connection appears in both directions. A larger value can represent a more heavily weighted relationship. section 1.2.1
Table 1.1 The adjacency matrix for the simple graph in figure 1.1
|
A
|
B
|
C
|
D
|
E
|
|
|---|---|---|---|---|---|
|
A
|
0
|
1
|
0
|
0
|
1
|
|
B
|
1
|
0
|
1
|
1
|
1
|
|
C
|
0
|
1
|
0
|
1
|
0
|
|
D
|
0
|
1
|
1
|
0
|
1
|
|
E
|
1
|
1
|
0
|
1
|
0
|
The matrix shows which of five nodes connect. Compare entries on opposite sides of the diagonal to see the symmetry of an undirected graph. section 1.2.1
When connections matter to a prediction, a graph neural network can use message passing to turn node and edge features into embeddings. For example, a mechanical graph can represent connected body parts or forces between objects to help predict future states. This approach is less suitable when entries stand alone and relationships add little information; model choice should also account for training speed and computational resources. section 1.2.4 section 1.3.3 section 1.6 section 4.4.3
