ENGM 732 Formalization of Network Flows Network Flow Models
Terminology Loop 5 Graph
Terminology Graph Multigraph
Terminology Directed Network Graph
Terminology Walk – alternating sequence of nodes and lines beginning and ending with nodes Closed walk – same node begins and ends walk Open walk – ends at node other than beginning node Trail – walk with no line repeated Path - a walk with no node repeated
Terminology Walk – alternating sequence of nodes and lines beginning and ending with nodes Open walk – ends at node other than beginning node 45
Terminology Closed walk – same node begins and ends walk Trail – walk with no line repeated 1 4 2
Terminology Path - a walk with no node repeated 1 4 2
Terminology - Trees [ b i ] (c k, h k ) [3] [-5] (1,2) (2,-1) (3,5) (2,1) (5,3) [0] (1,-1) (2,1) 5 Root = 5 N T = {5} M T =
Terminology - Trees [ b i ] (c k, h k ) [3] [-5] (1,2) (2,-1) (3,5) (2,1) (5,3) [0] (1,-1) (2,1) Root = 5 N T = {1,2,3,4,5} M T = {1,2,5,7} Spanning Tree
Terminology - Trees [ b i ] (c k, h k ) [3] [-5] (1,2) (2,-1) (3,5) (2,1) (5,3) [0] (1,-1) (2,1) Root = 5 N T = {1,2, 5} M T = {1,7} Spanning Forest Root = 3 N T = {3, 4} M T = {5}
Expanded Network Directed Network Expanded Network o(-k) = t(k) t(-k) = o(k)
Expanded Network Marginal Network Consists of a subset that are admissible arcs (2,2,-1) (f k, c k, h k ) Network with flow