1. CSC 213 – Large Scale Programming Lecture 27: Graph ADT

2. Graphs Graph is a pair (V, E), where V is collection of nodes, called vertices E is collection of edges, where an edge connects 2 nodes Vertex and Edge each implement Position ORD PVD MIA DFW SFO LAX LGA HNL 849 802 1387 1743 1843 1099 1120 1233 337 2555 142

3. Edge Types Each edge links two vertices Imagine edge connecting u & v Edge written as (u,v) Directed edge Ordered pair of vertices u is origin or source v is destination Like a one-way street Undirected edge -- (u,v) Un ordered pair of vertices Similar to subway line ORDPVD ORDPVD

4. Graphs Types Directed graph Also called a digraph All edges in graph must be directed Examples include Java object hierarchy Undirected graph Edges are mix of directed & undirected Examples include American highways

5. Applications Electronic circuits Transportation networks Computer networks Databases Packing suitcases Finding terrorists Scheduling college’s exams Assigning classes to rooms Garbage collection Coloring countries on a map Playing minesweeper

6. Terminology Edge incident on its endpoints U & V endpoints of a Vertices adjacent when joined by edge U & V are adjacent Degree of vertex is number incident edges X has degree 5 XU V W Z Y a c b e d f g h i j

7. More Terminology Path Alternates vertices & edges Begins & ends at vertices Edge preceded & followed by endpoints ( U, c, W, e, X, g, Y, f, W, d, V ) is a path Simple path Visits vertices & edges at most once ( V, b, X, h, Z ) is a simple path XU V W Z Y a c b e d f g h

8. Even More Terminology Cycle Path that begins & ends at same vertex Simple cycle Cycle that is also simple path ( V, b, X, g, Y, f, W, c, U, a,  ) is simple cycle C1C1 XU V W Z Y a c b e d f g h

9. Graph ADT Accessor methods vertices(): iterable collection of vertices edges(): iterable collection of edges endVertices(e): array with endvertices of e opposite(v,e): e’s endvertex that is not v areAdjacent(v,w): tests if v and w are adjacent replace(v,x): make x new element at vertex v replace(e,x): make x new element at edge e Update methods insertVertex(o): add vertex storing element o insertEdge(v,w,o): add edge (v,w) with element o removeVertex(v): kill v (& its incident edges) removeEdge(e): remove e Retrieval methods incidentEdges(v): edges incident to v

10. For Next Lecture Discuss first Graph ADT implementation How should we store edge & vertex collections How do we implement the different methods? Is this approach efficient?