Identify the vertices and edges of the graph
Determine the dependency or precedence relationships between vertices
Choose a traversal or ordering method
Perform a topological sort if the graph is directed and acyclic
Use depth-first search to generate a linear order if applicable
Use breadth-first search when level-based ordering is needed
Resolve cycles before linearization
Remove or contract edges as required by the application
Preserve the required constraints while ordering the vertices
Output the vertices in the resulting linear sequence