# Additive Mechanisms for Interorganizational Hyperlink Networks

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## WHAT IS IT?

This model combines three additive network mechanisms: preferential attachment, resource dependence effects, and homophily. This can be used to model interorganizational hyperlink networks, collaboration networks, and citation networks etc.

Homophily describes the tendency for actors to search and select similar actors to oneself to create connections (Monge & Contractor, 2003). Resource dependence theory suggests that the more resources an actor has, the more likely it is to attract relationships (Pfeffer & Salancik, 1978). Preferential attachment refers to actorsâ€™ preference to select and form relationships with actors that are already popular network connection receivers.

## HOW IT WORKS

At each round, a user can determine the probability of an agent's probability for preferential attachment, resource dependence, and homophily when deciding which other agent to have a link with. The totol probability of the three mechanisms is 100. For preferential attachment, an agent links with another agent that is very popular, that is, one of the most popular agents in the network with three highest degree centrality. For resource dependence effects, each agent links with another agent that has more wealth than the agent's. As such, the more resources an agent has, the more likely it will have more connections. Finally, for homophily, an agent selects an agent that has similar wealth with the agent's. Similarity can be either lower or higher within a range for this continous variable.

## HOW TO USE IT

Before running the model, a user can select the number of nodes and links in the network by using the two sliders. A user can then determine his/her preferred probability for preferential attachment, resource dependence effects, and homophily effects respectively. Note that the total probability of the three is equal to 100 percent. After the model is done, a user need to resize the nodes and redo the layout to make it more visually appealing. There are a bunch of monitors and plots to demonstrate network descriptive statistics, including betweenness centrality, closeness centrality, degree centrality, clustering coefficient, and average path length. Please note that in rare cases the mean path length is shown as "false", indicating that not every node in the network is connected. In addition, the number of links from preferential attachment mechanism, resource dependence mechanism, and homophily mechanism is shown respectively.

## THINGS TO NOTICE

For a comparison of how each network mechanism works, the user need to adjust the probability for homophily and resource dependence. By default, the probability for preferential attachment is 100 - pr(homophily) - pr(resource dependence). There are several measures for network descriptives and structures, such as average degree centrality, betweenness centrality, closeness, path length, clustering coefficient. Please note that sometimes average path length is not available because some nodes are not connected with every pair of other nodes.

The distribution of betweenness centrality in the model is highly skewed and the distribution of closeness centrality is similar to a normal curve irrespective of the probability of resource dependence effect, homophily effect, and preferential attachment effect in the model.

If the probability of homophily is the highest among the three network mechanisms, agents of similar colors are observed to be clustered together. This is because homophily effect leads to segregation (Monge & Contractor, 2003). If the probability of resource dependence is the highest among the three network mechanisms, agents with higher level of wealth (indicated by lighter green) are positioned in the center. Further, if the probability of preferential attachment is the highest among the three network mechanisms, the network is a star-shaped centralized network and the biggest agent with the highest degree centrality is placed in the center of the network.

## THINGS TO TRY

Before running the model, a user can select the number of nodes and links in the network by using the two sliders. A user can then determine his/her preferred probability for preferential attachment, resource dependence effects, and homophily effects respectively. In addition, for the preferential attachment effect, a user can determine the number of top agents with the highest degree centrality. For example, 3 means an agent will choose among one of the three top agents to link with.

## EXTENDING THE MODEL

In the future extentions, several features can be added to this model. Previous scholarship has explored interorganizational hyperlink networks from two perspectives: organizational attribute and structural embeddedness. This model largely deals with the attribute perspective. Thus, in the future extentions, feedback processes should be added for some structural signatures, such as reciprocity and transitivity. Second, from the socio-evolutionary point of review, ties could be resolved in situations such as lack of reciprocity.

## NETLOGO FEATURES

Using nw network extensions from GitHub to calculate some network descriptive statistics.

## RELATED MODELS

Preferential attachment; resource dependence; homophily; and contagion. Users can explore some other network models in the Models Library such as preferential attachment and giant component.

## CREDITS AND REFERENCES

Credit to Prof. Uri Wilensky and his team for the preferential attachment model.

Pfeffer, J., & Salancik, G. R. (1978). The External control of organizations: A resource dependence perspective. New York: Harper Row.

Monge, P. R., & Contractor, N. S. (2003). Theories of communication networks. Oxford: Oxford University Press.

## Comments and Questions

turtles-own [wealth] globals[number-links number-homophily number-RDT number-PA p] extensions[nw] to setup clear-all nw:set-context turtles links ask patches [set pcolor violet + 1] create-turtles number-of-nodes [ ;; users can choose the number of nodes and number of links in the network that they want using a slider set wealth random 30 ;; each node has a random wealth set shape "circle" set color scale-color green wealth -10 30 ;; the color is used to represent the wealth of the turtle; with darker color representing smaller wealth set size 1 setxy random-xcor random-ycor] reset-ticks end to go ask links [set color gray] ;; links formed in previous ticks turn gray ask one-of turtles [ ;; at each tick, based on a random probability, a random turtle either chooses to link to another turtle make-node find-partner wealth] ;; based on the principle of homophily, resource dependence, or preferential attchment, the sum of probabilities is 1 if number-links >= number-of-links [ask links [set color gray] stop] ;; if the number of links exceeds the number of links that the user wants, the model stops tick if layout? [layout] end to make-node [node] if node != nobody [ create-link-with node [set color red] move-to node fd 8 ] set number-links number-links + 1 end to-report find-partner [W] set p random 100 ;; random probability of RD, PA, and homophily, totaling 100 percent ifelse p < probability-of-homophily ;; based on users' preferred probability of homophily, an agent chooses another agent that has similar wealth with itself [set number-homophily number-homophily + 1 report one-of other turtles with [wealth = W or wealth = W - 1 or wealth = W + 1] ] [ifelse p > 100 - probability-of-RDT [set number-RDT number-RDT + 1 report one-of other turtles with [wealth > W] ] ;; otherwise, if the probability is about 100 - probability of resource dependence effect [set number-PA number-PA + 1 report one-of max-n-of max-number other turtles [count link-neighbors] ;; a user can determine the number of the top agents with the highest degree centrality ] ] ;; resource dependence: an agent chooses another agent that has wealth larger than its own end ;; prefential attachment: an agent chooses another agent to link based on its degree. The agent is among the top XX in terms of degree ;;Layout ;; resize-nodes to resize-nodes ifelse all? turtles [size <= 1] [ ;; a node is a circle with diameter determined by ;; the SIZE variable; using SQRT makes the circle's ;; area proportional to its degree ask turtles [ set size sqrt sqrt count link-neighbors ] ;; sqrt sqrt makes the agents visually attractive instead of too large ] [ ask turtles [ set size 1 ] ] end to layout ;; this is based on the preferential attachment model in the model lirbaility ;; the number 3 here is arbitrary; more repetitions slows down the ;; model, but too few gives poor layouts repeat 3 [ ;; the more turtles we have to fit into the same amount of space, ;; the smaller the inputs to layout-spring we'll need to use let factor sqrt count turtles ;; numbers here are arbitrarily chosen for pleasing appearance layout-spring turtles links (1 / factor) (10 / factor) (10 / factor) display ;; for smooth animation ] ;; don't bump the edges of the world let x-offset max [xcor] of turtles + min [xcor] of turtles let y-offset max [ycor] of turtles + min [ycor] of turtles ;; big jumps look funny, so only adjust a little each time set x-offset limit-magnitude x-offset 0.1 set y-offset limit-magnitude y-offset 0.1 ask turtles [ setxy (xcor - x-offset / 2) (ycor - y-offset / 2) ] end to-report limit-magnitude [number limit] if number > limit [ report limit ] if number < (- limit) [ report (- limit) ] report number end

There is only one version of this model, created almost 3 years ago by Jiawei Fu.

## Attached files

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

Additive Mechanisms for Interorganizational Hyperlink Networks.png | preview | Preview for 'Additive Mechanisms for Interorganizational Hyperlink Networks' | almost 3 years ago, by Jiawei Fu | Download |

Contagion.nlogo | extension | Preferential Attachment and Contagion model | almost 3 years ago, by Jiawei Fu | Download |

EECS 472 Poster- Jiawei Fu.pdf | Poster Slide | almost 3 years ago, by Jiawei Fu | Download | |

Final Project Proposal - Fu.pdf | Project Proposal | almost 3 years ago, by Jiawei Fu | Download | |

Final Project Report - Fu.pdf | Final Project Report and Analyses | almost 3 years ago, by Jiawei Fu | Download | |

Fu_Jiawei_Slam.pdf | Slam Slides | almost 3 years ago, by Jiawei Fu | Download | |

Homophily.nlogo | extension | Homophily model | almost 3 years ago, by Jiawei Fu | Download |

JiaweiFu_ June1.pdf | Progress Report 3 | almost 3 years ago, by Jiawei Fu | Download | |

JiaweiFu_ May18.pdf | Progress Report 1 | almost 3 years ago, by Jiawei Fu | Download | |

JiaweiFu_ May25.pdf | Progress Report 2 | almost 3 years ago, by Jiawei Fu | Download | |

Resource Dependence.nlogo | extension | Resource dependence model | almost 3 years ago, by Jiawei Fu | Download |

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