# Use Network

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## WHAT IS IT?

This model explores **how network structure and agent choice of routing influence the observed average steps between a message origin and target**. In terms of network structure, the model produces two types of networks:

a random network (default), and

a small-world network.

Speaking of agent rounting choice, the model has four different choice heuristics (See details on HOW TO USE IT):

random (default)

local search

homophilious search and

preferential attachment search.

The "actual" average path length (observed) means how many steps take until messages are reached, while the average path length (expected) can be conceptually calculated as the average possible shortest path between pairs of agents. However, research shows the actual paths are longer than computed expected shortest paths in real human practice due to the fact that people choose not shortest path once in two choices (Killworth et al., 2006). This model shows this phenomenon and the mechanisms of why this is the case.

## HOW IT WORKS

In the model, two agents are set up: (1) nodes who circulate a message and (2) a message who is circulated by nodes. Also, nodes have links, which create paths to other nodes.

When you press the SETUP button (See also the Choose Network Model):

- Create NUMBER nodes and NUMBER of directed links for each nodes - either randomly or in a small-world way (the SMALL-WORLD switch)
- Default is a circle layout
- One message is randomly set up on a node
- One target is randomly set up on another node
- Calculate the number of paths unavailable between pairs of nodes as NUMBER-OF-UNCONNECTED

Each tick (GO or GO ONCE):

- The message moves to a new location via a link
- A link becomes thicker as a mark of usage of the route
- Repeat the aforementioned processes until the message reaches or becoming one of the two conditions: (1) INCOMPLETES: When the ROUTE-LIMITS switch is on, nodes often exhaust their paths as a result that the message comes back them again and again. When nodes have no usable paths, STOP. (2) DEADEND: When not all nodes have avaiable access to every other node (i.e., NUMBER-OF-UNCONNECTED is not 0), the message can suddenly go a DEADEND path and can't get out to reach to the target. If so, it adds NUMBER-OF-DEADEND and STOP.

Once the message is reached:

- It counts as one session and adds NUMBER OF SESSIONS
- Re-setup a message and target at a random node, respecively
- If there is no path available between a randomly setup message and target, the case is recorded as UNREACHABLE-PAIRS

## HOW TO USE IT

This models provides a experimental setting for a small-world experiment. Changing the switches and sliders helps you understand how observed path lengths are emerged.

ROUTE-LIMITS: This gives constrains on use of links (paths). If the switch is on, agents can't use the same path twice.

SMALL-WORLD: This switch changes the network setting from a random to a small-world network (shorter path length and high clustering coefficient). Using REWIRING PROBABILITY, change the likelihood of rewiring links to create a small-world network.

NUMBER-OF-NODES: This gives you a control for creating how many nodes are in a network.

NUMBER-OF-LINKS: This determines how many links each node can hold.

SEARCH-STRATEGY: This chooser allows you to test how different cognitive strategies work in message delivery: (1)

**random search**: All links agents hold have a equal chance to be chose, (2)**local search**: First, agents look at their local neighbors. If no neighbors are the target, they pass a message to furthest link-neighbor or one of local neighbors if they don't have further link-neighbor, (3)**homophilious search**: Based on target's gender, agents determine which contact they will send. If the target is female, agents are more likely to choose female contact than male one, and (4)**preferential attachment**: Agents prefer to send a message to the highest in-link neighbors)

## THINGS TO NOTICE

You see a similarity and difference in terms of observed and expected average path length and the freqency distribution of path lengths. In particular, look at an observed line or bar (red) and an expected line or bar (gray) in the plots. How do their shapes differ?

Also, if you turn ROUTE-LIMITS on, what is the NUMBER-OF-INCOMPLETES? What is the successful chain rate? What is the incomplete rate? You can calculate the imcomplete rate as follows: (NUMBER-OF-INCOMPLETES + NUMBER-OF-DEADEND) / (SESSIONS - UNREACHABLE PAIRS).

## THINGS TO TRY

First, you should try to switch between a random network and small-world network, and see how observed path lengths change.

Second, use the SEARCH-STRATEGY chooser. The different search strategies return different results of observed path lengths.

Third, using the ROUTE-LIMITS switch, see how a message is circulated within a network. Particularly, no route limit condition is barely able to be observed in the reality. Compared to no route limit condition, see how much the route limit condition chages observed path lengths.

## EXTENDING THE MODEL

Try to change the number of message propagation. The current model is set one message at a time. However, circulating multiple messages is a reasonable scenario in the reality. For doing so, you may require to change some other procedures.

It is also possible to implement a memory for each agents, for instance, using the LevelSpace extension. This extension may enable to test how agents become better or worse at routing over time.

## NETLOGO FEATURES

This model uses the NW extension to calculate path length, clustering coefficient and in-degree centrality for each node. However, for the average path length, it doesn't use the NW extension, but it returns the same result as a command of nw:mean-path-length in the NW extension.

## RELATED MODELS

This model is based on Stanley Milgram's small-world experiment:

Milgram, S. (1967). The Small World Problem, Psychology Today, 2: 60-67.

Travers, J., & Milgram, S. (1969). An experimental study of the small world problem. Sociometry, 425-443.

In terms of the expected emergence patterns for this model:

- Killworth, P. D., McCarty, C., Bernard, H. R., & House, M. (2006). The accuracy of small world chains in social networks. Social networks, 28(1), 85-96.

Also, this model extensively refers to in Models Library:

Small Worlds: Wilensky, U. (2005). NetLogo Small Worlds model. http://ccl.northwestern.edu/netlogo/models/SmallWorlds. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Link-Walking Turtle Example

## CREDITS AND REFERENCES

This model is developed by Kyosuke Tanaka at Northwestern University. If you have any questions or want to use this model not in your own use, please email at kyosuke [at] u.northwestern.edu.

## Comments and Questions

extensions [ nw ] breed [nodes node] breed [messages message] messages-own [ location ;;holds a node in which a message is ] nodes-own[ ;; Use Net target ;;target as a message destination ;; this RECEIVDED is not used well in this implementation ;; But this is useful to see which node is "actually used as a "hub" received ;;if a node received, add 1 ;; Choose Net distance-to-other-nodes ;; list of distances of this node to other turtles ;; Local Search localset ;; holds a local agentset ;; Homophily gender ;; gender to either 0 "male" or 1 "female" ] links-own [ used ;;if a message went through a link, add 1 ] globals [ ;; Use Net origin ;;holds a starting node current-location ;; holds a node where a message is currently next-location ;; owns a node where a message goes next target-node ;;holds a target node unreachable ;;holds true/false number-of-unreachable ;;counts unreachable cases steps ;;holds count of steps steps-record ;;holds a list of steps per session min-pl-record ;; holds a list of min path length per session min-pl ;; holds min distance between the origin and target number-of-sessions ;;owns the count of sessions incomplete ;;holds the number of imcomplete cases incomplete-case ;;holds true/false deadend ;;holds true/false number-of-deadend ;;counts deadend cases actual-average-pl ;; average path length of the network number-of-neighbors ;; holds [out-link-neighbors] of location ;; Choose Net average-path-length ;; average path length of the network pl-list ;; list of distances of this node to other turtles unconnected ;; holds the number of unconnected pairs connected ;; holds the number of connected pairs ] ;;;;;;;;;;;;;;;;;;;;; ;; Setup Procedure ;; ;;;;;;;;;;;;;;;;;;;;; to setup clear-all set-default-shape nodes "circle" create-nodes number-of-nodes [set color blue] ask nodes [ create-links-to n-of number-of-links other nodes set target one-of other nodes set received 0 set gender random 2 ;; set gender to either 0 "male" or 1 "female" ] layout message-setup ask target-node [ set color red ] ask nodes [ set localset (min-n-of 4 other nodes [distance myself]) ;; holds a turtles-own variable ] local-search link-setup ask origin [ ifelse nw:distance-to target = False [ set min-pl 0 ][ set min-pl nw:distance-to target] ] set number-of-sessions 0 set unreachable false set incomplete 0 unreachable-setup set steps-record [] set min-pl-record [] ;; Choose Net find-path-lengths find-connected-pairs path-length-list find-average reset-ticks end ;;circle layout to layout layout-circle (sort nodes) max-pxcor - 1 end to go if any? messages with [location = target-node][ set steps number-of-steps set steps-record lput number-of-steps steps-record set min-pl-record lput min-pl min-pl-record set number-of-sessions number-of-sessions + 1 target-resetup ] unreachable-setup if unreachable = true [ set unreachable false set number-of-unreachable number-of-unreachable + 1 set steps 0 set steps-record lput 0 steps-record ;; tentatively assign 0 but INF should be more appropriate... set min-pl-record lput 0 min-pl-record set number-of-sessions number-of-sessions + 1 target-resetup ] wrong-choice if deadend = true [ set deadend false set number-of-deadend number-of-deadend + 1 set steps 0 set steps-record lput 0 steps-record;; tentatively assign 0 but INF should be more appropriate... set min-pl-record lput 0 min-pl-record set number-of-sessions number-of-sessions + 1 target-resetup ] ask links [ set thickness 0 ask links with [used >= 1] [set thickness 0.3] ] message-procedure tick end ;;;;;;;;;;;;;;;;;;;;;;; ;; Use Net procedure ;; ;;;;;;;;;;;;;;;;;;;;;;; ;;mesasge procedure to message-procedure ask messages [ if not any? [out-link-neighbors] of location [ stop ] set current-location location ;set upper limits of passing messages through links ifelse route-limits? [ ;; 1 as an arbitrary limit let out-link-node [my-out-links with [(used < 1) and (self != myself)]] of current-location ifelse count out-link-node > 1 ;;count out-link-node = number-of-links [set number-of-neighbors turtle-set [end2] of out-link-node if search-strategy = "random-search" [set next-location one-of number-of-neighbors] ;[out-link-neighbors] of location] if search-strategy = "local-search" [ls-strategy] if search-strategy = "homophilious-search" [homophily] if search-strategy = "preferential-attachment" [preferential] ] ;; if running out of available links a node can use, end the session [ifelse count out-link-node = 0 [set incomplete incomplete + 1 set incomplete-case true stop] [set next-location one-of turtle-set [end2] of out-link-node] ] ][ set number-of-neighbors [out-link-neighbors] of current-location if search-strategy = "random-search" [set next-location one-of number-of-neighbors] ;[out-link-neighbors] of location] if search-strategy = "local-search" [ls-strategy] if search-strategy = "homophilious-search" [homophily] if search-strategy = "preferential-attachment" [preferential] ] let new-location next-location ;; change the thickness of the link as a message moves ask [out-link-to new-location] of location [set thickness 0.3 set used used + 1] face new-location ;; not strictly necessary, but improves the visuals a bit move-to new-location set location new-location ask location [ set received received + 1 ;; increase received ] ] if incomplete-case = true [ set number-of-sessions number-of-sessions + 1 set incomplete-case false target-resetup ] end ;;new round setup to target-resetup ask nodes [ set target one-of other nodes ;set received 0 set color blue ] ask messages [die] message-setup ask target-node [ set color red ] link-setup ;unreachable-setup ask origin [ ifelse nw:distance-to target = False [ set min-pl 0 ][ set min-pl nw:distance-to target] ] reset-ticks end ;;procedure for target to message-setup create-messages 1 [ ;; TO DO: replace 1 to a slider set color orange set location one-of nodes set origin location set target-node [target] of location move-to location ] end ;;link weight to link-setup ask links [ set used 0 set thickness 0 ;ask links with [used >= 1] ;[set thickness 0.3] ] end ;;detect an unreachable case to unreachable-setup ;;an empty means no path b/w the origin and target exists if empty? [nw:path-to target-node] of origin [ set unreachable true ] end ;;critical mistakes of route choices ;;where a path to the target becomes no longer avaiable to wrong-choice ask messages [ ask location [ if empty? nw:path-to target-node [ set deadend true ] ] ] end ;; average simulated path length to-report calculate-average let avg-pl filter [? != 0] steps-record set actual-average-pl (sum avg-pl) / (length avg-pl) report actual-average-pl end to-report unreachable-pairs report number-of-unreachable end to-report number-of-steps report ticks end to-report sessions report number-of-sessions end to-report incompletes report incomplete end ;;;;;;;;;;;;;;;;;;;;;;;;;; ;; Choose Net procedure ;; ;;;;;;;;;;;;;;;;;;;;;;;;;; to path-length-list set pl-list [] foreach sort nodes [ let x [distance-to-other-nodes] of ? set pl-list sentence pl-list x ] end ;; calculate the number of unconnected pairs and connected pairs to find-connected-pairs set connected 0 set unconnected 0 let i 0 ;;holds a target turtle number let node-count count nodes foreach sort nodes[ ask ? [ while [ i < node-count ] [ifelse ? = node i ;;if a turtle is the same as i, skip it [set i i + 1] [ifelse empty? nw:path-to node i ;;since if there is no path from a turtle to i, return an empty list [ set i i + 1 set unconnected unconnected + 1 ] [set i i + 1 set connected connected + 1] ] ] ] set i 0 ;;set the default again ] end ;; calculate distance from turtles to other turtles only if they are connected with each other to find-path-lengths ask nodes [ set distance-to-other-nodes filter [is-number? ?] [[nw:distance-to myself] of myself] of other nodes ] end ;; average path length to find-average set average-path-length (sum [sum distance-to-other-nodes] of nodes) / (connected) end to-report avg-path-length report average-path-length end to-report unreachable-path report unconnected end ;; calculate global clustering coefficient to-report clustering-coefficient let closed-triplets sum [ nw:clustering-coefficient * count my-links * (count my-links - 1) ] of nodes let triplets sum [ count my-links * (count my-links - 1) ] of nodes report closed-triplets / triplets end ;; local search implementation of small-world networks to local-search if small-world? [ ask links [die] ask nodes [ ;; if NUMBER of links are below 4, use n-of for localset since localset includes 4 neighbors ifelse number-of-links <= 4 [ create-links-to n-of number-of-links localset if (random-float 1) < rewiring-probability [ let rewire one-of other nodes with [ (self != myself) and (localset != myself) ] ask one-of links [ die ] create-link-to rewire ] ] [create-links-to localset create-links-to n-of (number-of-links - 4) other nodes with [ (self != myself) and (localset != myself) ] ] ] ] end ;;;;;;;;;;;;;;; ;; Cognition ;; ;;;;;;;;;;;;;;; ;; local search strategy to ls-strategy ;; this procedure gives local knowledge of who is the target to nodes ;; but nodes don't hold any knowledge of long nodes which are not in their local set ;; If nodes hold long nodes and they don't find the target in their localset, then they send a message to a long node ask nodes [ let l1 sort-on [who] [localset] of current-location let l2 sort-on [who] number-of-neighbors let long-node filter [? != l1] l2 ifelse member? [target] of origin number-of-neighbors [ ifelse member? [target] of origin [localset] of current-location [ set next-location [target] of origin][ ;; since some nodes don't rewire, make sure whether nodes have links with long-distant nodes ifelse empty? long-node[ set next-location one-of number-of-neighbors][ set next-location item random length long-node long-node ] ] ][ifelse empty? long-node[ set next-location one-of number-of-neighbors][ set next-location item random length long-node long-node ] ] ] end ;; homophily search to homophily ;; A node holding a message prefers to send the same gender neighbor as target's gender ;; if they don't have any neighbor's gender same as target's, then they randomly choose next destination in their link neighbors ask nodes [ ifelse any? number-of-neighbors with [gender = [gender] of target-node] [ ;; a 70 percent chance to choose a contact whose gender is the same as target ;; Otherwise, follow the random choice procedure ;; this random implementation is not parcilarly something I'm not proud of... ;; 70 is an abtraral number, but it works both with & without route limits ifelse random 99 < 70 [set next-location one-of number-of-neighbors with [gender = [gender] of target-node]][ set next-location one-of number-of-neighbors] ][set next-location one-of number-of-neighbors ] ] end ;; preferential attachment search to preferential ;; nodes look at maximum indegree neighbor as their next message destination ask nodes [ set next-location max-one-of number-of-neighbors [count [in-link-neighbors] of self ] ] end

There are 5 versions of this model.

## Attached files

File | Type | Description | Last updated | |
---|---|---|---|---|

Use Network.png | preview | preview image | over 2 years ago, by Kyosuke Tanaka | Download |

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