Completed some details about Pregel's Label Propagation.

arangodb · ansoboleva · Jun 23, 2022 · Jun 21, 2022 · Jun 22, 2022 · Jun 23, 2022
commit 0cea3f1c24bccbd30c7d4d37f0cbf2d4c4432bfc
diff --git a/3.10/graphs-pregel.md b/3.10/graphs-pregel.md
@@ -409,17 +409,33 @@ based on common location, interests, occupation, etc.
 #### Label Propagation
 
 *Label Propagation* can be used to implement community detection on large
-graphs. The idea is that each vertex should be in the community that most of
-his neighbors are in. We iteratively determine this by first assigning random
-Community ID's. Then each iteration, a vertex will send it's current community
-ID to all its neighbor vertices. Then each vertex adopts the community ID it
-received most frequently during the iteration.
+graphs. The algorithm assigns a community, more precisely, a Community ID 
+(a natural number), to every vertex in the graph. 
+The idea is that each vertex should be in the community that most of
+its neighbors are in. 
+
+The algorithm, first, assigns unique initial Community ID's to the vertices. 
+There is no guarantee that a vertex obtains the same initial 
+ID in two different runs of the algorithm even if the graph does not change
+(although, it may often happen). Moreover, there is no guarantee on a particular
+distribution of the initial ID's over the vertices.
+
+Then, in each iteration, a vertex sends its current Community
+ID to all its neighbor vertices. Then each vertex adopts the Community ID it
+received most frequently in the last step. If a vertex obtains more than one
+most frequent ID's, it chooses the least one. Moreover, if no ID arrived more 
+than once and the ID of the vertex from the previous step is less than the
+least obtained ID, the old ID is kept. 
 
 The algorithm runs until it converges, which likely never really happens on
-large graphs. Therefore you need to specify a maximum iteration bound which
-suits you. The default bound is 500 iterations, which is likely too large for
-your application. It should work best on undirected graphs, results on directed
-graphs might vary depending on the density of your graph.
+large graphs. Therefore you need to specify a maximum iteration bound.
+The default bound is 500 iterations, which is too large for
+common applications. 
+
+The algorithm should work best on undirected graphs. On directed
+graphs, the resulting partition into communities might change if the number 
+of performed steps changes. How strong the dependence is
+may be influenced by the density of the graph.
 
 ```js
 const pregel = require("@arangodb/pregel");