Shortest Path Between All Network Nodes and Average Network Shortest Path

This text describes an algorithm - Dijkstra's Algorithm - used to calculate the shortest paths between all nodes in a network and the average shortest path of the entire network. This algorithm employs a greedy approach, iteratively determining the shortest paths from a starting node to all other vertices. The implementation typically involves maintaining a priority queue to efficiently select the next closest node, with key operations including distance initialization, neighbor relaxation, and path updates.

The algorithm's time complexity is O(N²), where N represents the number of nodes in the network. In practical implementations, this can be optimized to O((N+E) log N) using min-heap data structures, where E denotes the number of edges. Alternative algorithms for computing network shortest paths include Floyd-Warshall Algorithm (using dynamic programming for all-pairs shortest paths with O(N³) complexity) and Bellman-Ford Algorithm (handling negative-weight edges with O(NE) complexity).

Code implementation typically involves: 1. Initializing distance arrays with Infinity values 2. Setting the source node distance to 0 3. Iterating through nodes while updating neighboring node distances 4. Calculating path averages after processing all node pairs