If the path names were of the same set of paths then '+' symbol is used to denote them
The "path sum" represents paths in parallel between nodes
From the below image, links a and b are in parallel paths and are denoted by 'a+b'
Similarly, between the next two nodes links c and d are in parallel paths and are denoted by 'c+d'
The set of all paths between nodes 1 and 2 can be thought of as a set of parallel paths and denoted by 'eacf + eadf + ebdf'
If X and Y are sets of paths that lie between the same pair of nodes, then'X+Y' denotes the UNION of those set of paths
Example:
From the displayed image, the first set of parallel paths is denoted by 'X+Y+d' and the second set is denoted by 'U+V+W+h+i+j'. The set of all paths in this flow graph is 'f(X+Y+d)g(U+V+W+h+i+j+j)k'
The path is a set union operation, it is clearly commutative and associative
RULE 2: X+Y = Y+X
RULE 3: (X+Y)+Z = X+(Y+Z) = X+Y+Z
Example:
From the displayed image, the first set of parallel paths is denoted by 'X+Y+d' and the second set is denoted by 'U+V+W+h+i+j'. The set of all paths in this flow graph is 'f(X+Y+d)g(U+V+W+h+i+j+j)k'
The path is a set union operation, it is clearly commutative and associative
RULE 2: X+Y = Y+X
RULE 3: (X+Y)+Z = X+(Y+Z) = X+Y+Z
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