Information_Diffusion_Model.nlogo

extensions [ nw ]
turtles-own [ adopted? ] ;; has the agent adopted the product
globals [avg_path_length]
to setup
  ca
  if network = "random" [
    nw:generate-random turtles links num-agents density [
    set adopted? false
    setxy random-xcor random-ycor
    ;; appearance
    set color white
    set shape "person"
    ]
  ]
  if network = "preferential-attachment" [
    nw:generate-preferential-attachment turtles links num-agents 1 [
    ;; adoption property is initialized
    set adopted? false
    setxy random-xcor random-ycor
    set color white
    set shape "person"
    ]
  ]
  repeat 30 [ layout-spring turtles links 0.2 5 1]

  if network = "Watts-Strogatz"[
    nw:generate-watts-strogatz turtles links num-agents 2 0 [ fd 10 set adopted? false set color white set shape "circle"]
  ]
  if (not is_broadcast) [seed_one_turtle]     ;; For Q4, removing the broadcast using the switch and seeding one turtle
  path_length
  reset-ticks
end

to rewire
  ca
  nw:generate-watts-strogatz turtles links num-agents 2 rewiring-probability  [ fd 10 set adopted? false set color white set shape "circle"]
  if (not is_broadcast) [seed_one_turtle]
  path_length
  reset-ticks
  update-plots
end

to go
  ;; diffuse information
  ask turtles with [ not adopted?] [
  adopt
  ]
  ;; stop the model if no one is left to adopt
  if ( not any? turtles with [ not adopted?])[
    stop
  ]
  tick
end

;; reset the diffusion of information
to reset-diffusion
  ask turtles [
    set adopted? false
    ifelse ( not is_broadcast and color = red ) [ set adopted? true] [ set color white ]
  ]
  clear-all-plots
  update-plots
end

to adopt
  ;; adoption based on broadcast influence
  if is_broadcast and random-float 1.0 < broadcast-influence [
    set adopted? true
    set color red
  ]
  let neighbors-adopted count link-neighbors with [ adopted? ]
  let total-neighbors count link-neighbors
  if total-neighbors > 0 [
    if not adopted? and random-float 1.0 <
    (social-influence * ( neighbors-adopted / total-neighbors )) [
      set adopted? true
      set color blue
    ]
  ]
end

to seed_one_turtle
  ask one-of turtles [
    set adopted? true
    set color red
  ]
end

to path_length
  nw:set-context turtles links
  set avg_path_length nw:mean-path-length
end
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## Can you justify with the aid of the monitors the logic of the Watts-Strogatz method for building small world networks?

The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering.The  randomly rewired links dramatically reduce the average path lengths.

From the degree distribution monitor it can be infered that the degree distribution of Whatts-Strogatz model converges to a Poisson distribution, rather than a power law as observed in preferential-attachment model. There is a spike around the mean degree of the graph (which is 4 in this case) and the distribution decays on the other sides. 
The mean degree is always constant, and is very small, just 4. 

The most astonishing fact is that when we set up cluster with large number of nodes, we can see that the mean path length is quite large( around 13-14), but as soon as we perform a single rewiring operation, the mean path length is reduced a lot, and comes to be around 3-3.7. Even when the number of nodes are quite large, the mean path length is very small.  

The small world models says that, no matter how many people you are connected with, it will only take certain small number of people(approximately 6-8) to connect to the whole world. And it is quite evident from the Whatts-Strogatz model. In the set each node only have 2 neighbors on the left and 2 on the right. However just on one rewiring operation, the mean path length is reduced just to between 3-4. 


## Cancel broadcast-influence and seed one turtle with adoption. What happens
to the diffusion of information in the new network when you modify rewiring?
For this we are using 100 nodes, with social-influence 0.7, rewiring-probability 1.0 and density 0.2.

When we run this model on without rewiring, we can see that since the mean path length is large, therefore, it will take a lot more time for the information to diffuse. Hence the total time taken for adoption is around 72 ticks. Also, since we have a uniform pattern for neighbors, only immediate left 2 and right 2 neighbors, we see the adoption curve to be an approximate straight line. 

However, when rewiring operation is run, the mean path length is reduced to around 3-3.5. And thus the total time taken for information is reduced drastically. Now it takes only 16 ticks for complete adoption. And the adoption curve comes like an exponetial in its starting phase. 

Therefore, in conclusion, the diffusion rate increases much more in case of rewiring with respect to the case of no rewiring. And this is also supported by the fact that the mean path length in the rewired case is much less than in the non - rewired original model. 

## Which of the three types of network has a degree distribution closer to a power law?

The preferential-attachment network model has degree distribution is very close to the power law. There is a lot of complex mathematics behind it, but it might be because the probabilty is proportional to some number k raised to some power and therefore, we can see the degree distribution very close to the power law. 
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