A review of graphs for testing
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A Review of Graphs for Testing. Directed graphs. A directed graph G(V,E) A finite V = {n 1 , n 2 , …, n m } of nodes A finite set E = {e 1 , e 2 , …, e p } of edges Each edge e k = { n i , n j } is an ordered pair (start and end nodes) V = {n1, n2, n3}

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A Review of Graphs for Testing

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A review of graphs for testing

A Review of Graphs for Testing


Directed graphs

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

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 terminology1

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

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 graphs1

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 graphs2

Program graphs


Program flowgraph an example

Program flowgraph: an example


Program flowgraph another example

Program flowgraph: another example


C yclomatic complexity

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


C yclomatic complexity1

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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