Network model

The network models include the traditional applications of finding the most efficient way to link a number of locations directly or indirectly, finding the shortest route between two cities, determining the maximum flow in a pipeline network, determining the minimum-cost flow in a network that satisfies supply and demand requirements at different locations, and scheduling the activities of a project.Network Definitions: A network consists of a set of nodes linked by arcs (or branches). The notation for describing a network is (N, A), where N is the set of nodes and A is the set of arcs.An arc is said to be directed or oriented if it allows positive flow in one direction and zero flow in the opposite direction. A directed network has all directed arcs. A path is a sequence of distinct arcs that join two nodes through other nodes regardless of the direction of flow in each arc. A path forms a cycle or a loop if it connects a node to itself through other nodes.A connected network is such that every two distinct nodes are linked by at least one path. The network in Figure above demonstrates this type of network. A trce is a cycle-free connected network comprised of a subset of all the nodes.