The best shortest path algorithm
Dijkstra's algorithm finds the shortest path between a node and every other node in the graph. You'd run it once for every node. Weights must be non-negative, so if necessary you have to normalise the values in the graph first.
Floyd-Warshall calculates the shortest routes between all pairs of nodes in a single run! Cycle weights must be non-negative, and the graph must be directed (your diagram is not).
Johnson's algorithm is using Dijkstra's algorithm to find all pairs in a single pass, and is faster for sparse trees (see the link for analysis).
Floyd Warshall find the paths between all pairs of vertices, but Dijkstra only finds the path from one vertex to all others.
Floyd Warshall is O(|V|3) and Dikstra is O(|E| + |V| log |V|) but you'll have to run it V times to find all pairs which gives a complexity of O(|E * V| + |V2| log |V|) I guess. This means it's possibly faster to use Dijsktra repeatedly than the FW algorithm, I would try both approaches and see which one is fastest in the actual case.