Q:

Can people in Heaven communicate with each other?

Can they communicate with each other?
For example, in Islam they believe that people in Heaven cannot talk or communicate to each other, because they are in some kind of "nirvana" (this is the wrong word, but I am not native EN speaker) or a happy-hybernated-statis state, and they can talk to each other. Something like in the movie The Matrix where the bodies are connected to a computer and they cannot move, but feel happy.
What does the Bible say about people in Heaven communicating with each other?

A:

They can, it seems. The clearest example is from Luke 16:22-25:

22 When the poor man died, he was carried away by angels to the bosom of Abraham. The rich man also died and was buried, 23 and from the netherworld, where he was in torment, he raised his eyes and saw Abraham far off and Lazarus at his side. 
  24 And he cried out, ‘Father Abraham, have pity on me. Send Lazarus to dip the tip of his finger in water and cool my tongue, for I am suffering torment in these flames.’
  25 Abraham replied, ‘My child, remember that [...]

The rich man is in hell, suffering, and he cries out to Abraham. Abraham is dead and in a far-off and elevated place. 
If even this person in hell can speak with Abraham, then surely Lazarus, who is right beside Abraham (and not secluded and separated from him like in the "Matrix" description you give), must be able to speak to Abraham.

A:

As the commenters have already pointed out in response to other answers, the various points in the Bible which might be seen as answering this question are ambiguous.  The only passage that I've seen that claims to answer it definitively comes from outside of mainstream Christianity.  In the book of Doctrine and Covenants--a collection of revelations and teachings accepted as canonical by the Latter-Day saints, and held to be authoritative along with the Bible and the Book of Mormon--we read:

And that same sociality which exists among us here will exist among us
  there, only it will be coupled with eternal glory, which glory we do
  not now enjoy.
  -- Doctrine and Covenants 130: 2

While these revelations are not accepted in mainstream Christianity, to the Latter-Day Saints this passage provides comfort and reassurance that those we count as friends and family and loved ones in this life will be able to maintain such interpersonal relationships with us throughout eternity.

A:

Sure they can.

Matthew 17 (NIV) 1 After six days Jesus took with him
  Peter, James and John the brother of James, and led them up a high
  mountain by themselves. 2 There he was transfigured before
  them. His face shone like the sun, and his clothes became as white as
  the light. 3 Just then there appeared before them Moses and
  Elijah, talking with Jesus.

In this story, the spirit of Moses was talking with Jesus who was in the flesh. Elijah was also in flesh because he was taken to heaven alive. Although the place was on Earth, if they can communicate on earth, I don't see any reason why they would not do the same in Heaven.

