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In flow networks, the source s is deficient, and the sink t is active. Pseudo-flows, feasible flows, and pre-flows are all examples of flow functions. A pseudo-flow is a function f of each edge in the network that satisfies the following two constraints for all nodes u and v:
A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. [1] Examples include but are not limited to road networks , railways , air routes , pipelines , aqueducts , and power lines .
An active flow network is a graph with edges and nodes, where particles inside this graph are propelled by an active mechanism. [1] [2] This type of network is used to study the motion of molecules in biological medium. Examples are organelles, including the Endoplasmic Reticulum (ER). [3]
An example pipe flow network. The Hardy Cross method can be used to calculate the flow distribution in a pipe network. Consider the example of a simple pipe flow network shown at the right. For this example, the in and out flows will be 10 liters per second.
The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network.It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified [1] or it is specified in several implementations with different running times. [2]
In fluid dynamics, pipe network analysis is the analysis of the fluid flow through a hydraulics network, containing several or many interconnected branches. The aim is to determine the flow rates and pressure drops in the individual sections of the network. This is a common problem in hydraulic design.
The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from source s to sink t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem.
In packet switches, the flow may be identified by IEEE 802.1Q Virtual LAN tagging in Ethernet networks, or by a label-switched path in MPLS tag switching. Packet flow can be represented as a path in a network to model network performance. For example, a water flow network can be used to conceptualize packet flow.