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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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
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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