A flow network is a directed graph where each edge has a capacity and each flow must not exceed the capacity, typically used to model the flow of resources through a system. The goal is often to find the maximum flow from a source node to a sink node, which can be efficiently computed using algorithms like the Ford-Fulkerson method.

Flow Network

flow network

A directed graph, or digraph, is a set of vertices connected by edges, where the edges have a direction associated with them, indicating a one-way relationship between the vertices. This structure is widely used in computer science and mathematics to model relationships like web page links, social media networks, and dependency graphs in software projects.

directed graph

Edge capacity refers to the maximum amount of flow that can pass through an edge in a flow network, often used in network flow problems to determine optimal routing and resource allocation. It is a crucial parameter in algorithms like the Ford-Fulkerson method, which computes the maximum flow in a flow network by repeatedly finding augmenting paths until no more can be found.

Edge Capacity

Maximum Flow refers to the greatest possible rate of flow from a source to a sink in a flow network, subject to capacity constraints on the edges. It is a fundamental problem in network theory with applications in transportation, telecommunications, and supply chain optimization.

maximum flow

A source node is the starting point in a network or graph from which data or signals originate and propagate through the system. It plays a crucial role in network analysis, influencing the flow and distribution of information across the network structure.

source node

A sink node is a type of node in a directed graph that has no outgoing edges, meaning it cannot transfer data or influence other nodes. It often represents a terminal state or an endpoint in network flow models, data structures, and algorithmic processes.

sink node

The Ford-Fulkerson Method is an algorithm used to compute the maximum flow in a flow network. It operates by iteratively finding augmenting paths in the residual graph and increasing the flow until no more augmenting paths are found.

Ford-Fulkerson method

flow of resources

Flow algorithms

Resource modeling is like making a map of all the things we have and how we can use them to build or make something. It helps us plan better by showing what we need, what we have, and how to use everything wisely.

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