Hi, I'm trying to understand the main concepts of graph theory and the algorithms within it. Most algorithms seem to contain a "Relaxation Condition" I'm unsure about what this is.

Could some one explain it to me please.

An example of this is dijkstras algorithm, here is the pseudo-code.

 1  function Dijkstra(Graph, source):
 2      for each vertex v in Graph:           // Initializations
 3          dist[v] := infinity               // Unknown distance function from source to v
 4          previous[v] := undefined          // Previous node in optimal path from source
 5      dist[source] := 0                     // Distance from source to source
 6      Q := the set of all nodes in Graph
    // All nodes in the graph are unoptimized - thus are in Q
 7      while Q is not empty:                 // The main loop
 8          u := vertex in Q with smallest dist[]
 9          if dist[u] = infinity:
 10              break                         // all remaining vertices are inaccessible from source
 11          remove u from Q
 12          for each neighbor v of u:         // where v has not yet been removed from Q.
 13              alt := dist[u] + dist_between(u, v)
 14              if alt < dist[v]:             // Relax (u,v,a)
 15                  dist[v] := alt
 16                  previous[v] := u
 17      return dist[]

Thanks