LECTURE 28:GRAPH ADT

CSC 213 – Large Scale Programming

Today’s Goals

Discuss what is NOT meant by term “Graph” Why no bar charts, scatter plots, & pie charts

mentioned How term is used for mathematical graph

Review terminology of mathematical graphs Why do we care about edges & vertices Directed vs. undirected more than types of

plays Which 1 of these made up: incident, adjacent,

feeder Cycles & paths not related to Queen songs

Examine GRAPH ADT’s method & what they do

Graphs

Mathematically, graph is pair (V, E) where V is collection of nodes, called vertices Two nodes can be connected by an edge in

E Position implemented by Vertex & Edge

classes ORD PVD

MIADFW

SFO

LAX

LGAHNL

849

802

13871743

1843

10991120

1233337

2555

142

Edge Types

Edge connects two vertices in the graph Image we have edge connecting u & v (u,v) is name given to this edge

Edges can be directed One-way street is directed edge u is origin or source v is destination

Undirected edge is alternative Vertices listed in any order Subway lines normally undirected

Life Death

Best Canisius

John

DavidPaul

brown.edu

cox.net

cs.brown.edu

att.netqwest.net

math.brown.edu

cslab1bcslab1a

Undirected Graph Applications Electronic circuits Transportation networks Databases Packing suitcases Finding terrorists Assigning classes to rooms Coloring countries on a map Playing minesweeper

Directed Graph Problems

Used to solve many problems in real-world Not always obvious: directedness used in

many ways Examples:

Diagnose cause of injury Schedule tasks to perform Garbage collection Track progress of disease Compiling a program

Graph Types

Graph is directed if all edges directed All edges in graph must be directed Examples include trees & Java object

hierarchy Any edge allowed in undirected graphs

Can have only undirected or mix of both edges

Roadways & CSC major are examples of this

Weighted Graphs

Edge’s weight is cost of using edge Distance, cost, travel time, &c. usable as

the weight Weights below are distance in miles

Edges undirected; but directed weighted Graph legal ORD PVD

MIADFW

SFO

LAX

LGAHNL

849

802

13871743

1843

10991120

1233337

2555

142

Terminology

Edge incident on its endpoints U & V endpoints of a

Vertices adjacent when joined by edge U adjacent to V V adjacent to U Directedness unimportant

determining adjacency

XU

V

W

Z

Y

a

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Terminology

Degree of vertex is number incident edges X has degree of 5 Does not matter if

edges directed or not What the edges’ other

endvertices unimportant (Self-edges only count once)

XU

V

W

Z

Y

a

c

b

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h

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Path Terminology

Path is set of vertices in Graph where All of the consecutive vertices adjacent May or may not have edge from last to first

vertices

(U, W, X, Y, W, V) is pathXU

V

W

Z

Y

a

c

b

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Path Terminology

Simple path is a path which: Is named by alternating vertices & edges 0 or 1 appearance for each vertex & edge

(V, b, X, h, Z) is simple path XU

V

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a

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b

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Cycle Terminology

Cycle is path with several additional properties Each cycle must begin & end at same

vertex No edge required from this vertex to itself

Simple cycle is special cycle But is also simple path

(V, X, Y, W, U, V) is simple cycle

XU

V

W

Z

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a

c

b

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Graph ADT

Accessor methods vertices(): iterable for

vertices edges(): iterable for

edges endVertices(e): array

with end points of edge e

opposite(v,e): e’s end point that is not v

areAdjacent(v,w): check 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(x):

create vertex storing element x

insertEdge(v,w,x): add edge (v,w) with element x

removeVertex(v): remove v (& incident edges)

removeEdge(e): remove e

Retrieval methods incidentEdges(v): get

edges incident to v

For Next Lecture

No weekly assignment this week or next

Get cracking on coding up your program #2 Due on Wednesday, so better start working

on it How were designs & test? What could you

do better? Reading on implementing Graph for

Friday What are simplest implementations of

Graph? When would each be good to use is

program?