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A Review of Graphs for TestingPowerPoint Presentation

A Review of Graphs for Testing

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Directed graphs

- A directed graph G(V,E)
- A finite V = {n1, n2, …, nm} of nodes
- A finite set E = {e1, e2, …, ep} of edges
- Each edge ek = {ni, nj} is an ordered pair (start and end nodes)
- V = {n1, n2, n3}
- E = {e1, e2, e3} = {(n1,2), (n2,n3), (n2,n4)}

e1

e2

n1

n2

n3

e3

n4

Graph terminology

- Indegree (ni): the number of distinct edges that have ni as a terminal node
- Outdegree (ni): the number of distinct edges that have ni as starting node
- Source node: a node with indegree={}
- Sink node: a node with outdegree = {}
- Transfer node: a node with indegree !={} and outdegree != {}

Graph terminology

- Directed path: a sequence of edges such that for any adjacent pairs of ei, ej, the terminal node of ei is the start node of ej
- Connectedness: for two odes ni, nj
- 0-connected: iff there is no path between ni, nj
- 2-connected: iff there is a path between ni, nj
- 3-connected: iff there is a path from ni to nj and a path from nj to ni

- Strongly connected graph: all pairs of nodes are 3-connected

Program graphs

- Given a program in an imperative language, its graph is a directed graph in which noes are either entire statements or fragments of a statement and edges represent flow of control

Program graphs

- Given a program in an imperative language, its graph is a directed graph in which noes are either entire statements or fragments of a statement and edges represent flow of control

Program flowgraph: an example

Program flowgraph: another example

Cyclomatic complexity

- The cyclomatic number of a graph G is given by
- V(G) = e – n + 2, where
- e is the number of edges in G
- n is the number of nodes in G

- Cyclomatic complexity pertains to both ordinary and directed graphs
- V(G) is sometimes called McCabe Complexity after Thomas McCabe

Cyclomatic complexity

- Used for testing (identifying the number of independent paths) and design (reduce complexity)
- It gives the number of independent paths from in a program (also called the basis path)
- It provides the degree of complexity

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