2 - marks * conditions involved in floyd's algorithm * residual network in flow of network * characterisitics of transportation network

Conditions involved in Floyd's Algorithm:

• Floyd's algorithm is used for finding the shortest paths between all pairs of vertices in a weighted graph with positive or negative edge weights.
• The graph must be directed and connected.
• The algorithm works by repeatedly improving an estimate on the shortest path between two vertices, until ultimately obtaining the shortest path.
• It uses a matrix to store the shortest distances between every pair of vertices.

Residual Network in Flow of Network:

• A residual network is derived from a given flow network and a flow.
• It consists of edges with capacities equal to the remaining capacity (original capacity - flow) of the corresponding edges in the flow network.
• The residual network can have an edge not in the original graph, if there is a positive flow on the edge in the original graph.
• It is used in algorithms like Ford-Fulkerson to find the maximum flow in a network.

Characteristics of Transportation Network:

• A transportation network is a network where nodes represent locations and edges represent routes between locations.
• Each edge has a weight, which could represent distance, cost, time, or any other relevant factor.
• The network is typically directed, meaning that travel from location A to location B does not necessarily imply that travel from B to A is possible.
• The goal in a transportation network is often to find the shortest or least expensive route from one location to another.