The NetLogo NW Extension for Network Analysis

This extension provides a large set of network analysis tools for use in NetLogo.

Usage

The first thing that one needs to understand in order to work with the network extension is how to tell the extension which network to work with. Consider the following example situation:

breed [ bankers banker ]
breed [ clients client ]

undirected-link-breed [ friendships friendship ]
directed-link-breed [ accounts account ]

Basically, you have bankers and clients. Clients can have accounts with bankers. Bankers can probably have account with other bankers, and anyone can be friends with anyone.

Now we might want to consider this whole thing as one big network. If that is the case, there is nothing special to do: by default, the NW extension primitives consider all turtles and all links to be part of the current network.

We could also, however, be only interested in a subset of the network. Maybe we want to consider only friendship relations. Furthermore, maybe we want to consider only the friendships between bankers. After all, having a very high centrality in a network of banker friendships is very different from having a high centrality in a network of client friendships.

To specify such networks, we need to tell the extension both which turtles and which links we are interested in. All the turtles from the specified set of turtles will be included in the network, and only the links from the specified set of links that are between turtles of the specified set will be included. For example, if you ask for bankers and friendships, even the lonely bankers with no friends will be included, but friendship links between bankers and clients will not be included. The way to tell the extension about this is with the nw:set-context primitive, which you must call prior to doing any operations on a network.

Some examples:

nw:set-context turtles links will give you everything: bankers and clients, friendships and accounts, as one big network.
nw:set-context turtles friendships will give you all the bankers and clients and friendships between any of them.
nw:set-context bankers friendships will give you all the bankers, and only friendships between bankers.
nw:set-context bankers links will give you all the bankers, and any links between them, whether these links are friendships or accounts.
nw:set-context clients accounts will give you all the clients, and accounts between each other, but since in our fictional example clients can only have accounts with bankers, this will be a completely disconnected network.

Special agentsets vs normal agentsets

It must be noted that NetLogo has two types of agentsets that behave slightly differently, and that this has an impact on the way nw:set-context works. We will say a few words about these concepts here but, for a thorough understanding, it is highly recommended that you read the section on agentsets in the NetLogo programming guide.

The "special" agentsets in NetLogo are turtles, links and the different "breed" agentsets. What is special about them is that they can grow: if you create a new turtle, it will be added to the turtles agentset. If you have a bankers breed and you create a new banker, it will be added to the bankers agentset and to the turtles agentset. Same goes for links. Other agentsets, such as those created with the with primitive (e.g., turtles with [ color = red ]) or the turtle-set and link-set primitives) are never added to. The content of normal agentsets will only change if the agents that they contain die.

To show how different types of agentsets interact with nw:set-context, let's create a very simple network:

clear-all
create-turtles 3 [ create-links-with other turtles ]

Let's set the context to turtles and links (which is the default anyway) and use nw:get-context to see what we have:

nw:set-context turtles links
show map sort nw:get-context

We get all three turtles and all three links:

[[(turtle 0) (turtle 1) (turtle 2)] [(link 0 1) (link 0 2) (link 1 2)]]

Now let's kill one turtle:

ask one-of turtles [ die ]
show map sort nw:get-context

As expected, the context is updated to reflect the death of the turtle and of the two links that died with it:

[[(turtle 0) (turtle 1)] [(link 0 1)]]

What if we now create a new turtle?

create-turtles 1
show map sort nw:get-context

Since our context is using the special turtles agentset, the new turtle is automatically added:

[[(turtle 0) (turtle 1) (turtle 3)] [(link 0 1)]]

Now let's demonstrate how it works with normal agentsets. We start over with a new network of red turtles:

clear-all
create-turtles 3 [
  create-links-with other turtles
  set color red
]

And we set the context to turtles with [ color = red ]) and links

nw:set-context (turtles with [ color = red ]) links
show map sort nw:get-context

Since all turtles are red, we get everything in our context:

[[(turtle 0) (turtle 1) (turtle 2)] [(link 0 1) (link 0 2) (link 1 2)]]

But what if we ask one of them to turn blue?

ask one-of turtles [ set color blue ]
show map sort nw:get-context

No change. The agentset used in our context remains unaffected:

[[(turtle 0) (turtle 1) (turtle 2)] [(link 0 1) (link 0 2) (link 1 2)]]

If we kill one of them, however...

ask one-of turtles [ die ]
show map sort nw:get-context

It gets removed from the set:

[[(turtle 0) (turtle 2)] [(link 0 2)]]

What if we add a new red turtle?

create-turtles 1 [ set color red ]
show map sort nw:get-context

Nope:

[[(turtle 0) (turtle 2)] [(link 0 2)]]

A note regarding floating point calculations

Neither JGraphT nor Jung, the two network libraries that we use internally, use strictfp floating point calculations. This does mean that exact reproducibility of results involving floating point calculations between different hardware architectures is not fully guaranteed. (NetLogo itself always uses strict math so this only applies to some primitives of the NW extension.)

Performance

In order to be fast in as many circumstances as possible, the NW extension tries hard to never calculate things twice. It remembers all paths, distances, and centralities that it calculates. So, while the first time you ask for the distance between turtle 0 and turtle 3782 may take some time, after that, it should be almost instantaneous. Furthermore, it keeps track of values it just happened to calculate along the way. For example, if turtle 297 is closer to turtle 0 than turtle 3782 is, it may just happen to figure out the distance between turtle 0 and turtle 297 while it figures out the distance between turtle 0 and turtle 3782. It will remember this value, so that if you ask it for the distance between turtle 0 and turtle 297, it doesn't have to do all that work again.

There are a few circumstances where the NW extension has to forget things. If the network changes at all (you add turtles or links, or remove turtles or links), it has to forget everything. For weighted primitives, if the value of the weight variable changes for any of the links in the network, it will forget the values associated with that weight variable.

If you're working on a network that can change regularly, try to do all your network calculations at once, then all your network changes at once. The more your interweave network calculations and network changes, the more the NW extension will have to recalculate things. For example, if you have a traffic model, and cars need to figure out the shortest path to their destination based on the traffic each tick, have all the cars find their shortest paths, then change the network weights to account for how traffic has changed.

There may be rare occasions in which you don't want the NW extension to remember values. For example, if you're working on an extremely large network, remembering all those values may take more memory than you have. In that case, you can just call nw:set-context (first nw:get-context) (last nw:get-context) to force the NW extension to immediately forget everything.

Primitives

`nw:set-context`

nw:set-context turtleset linkset

Specifies the set of turtles and the set of links that the extension will consider to be the current graph. All the turtles from turtleset and all the links from linkset that connect two turtles from turtleset will be included.

This context is used by all other primitives (unless specified otherwise) until a new context is specified. (At the moment, only the generator primitives and the file input primitives are exceptions to this rule.)

See the usage section for a much more detailed explanation of nw:set-context.

`nw:get-context`

nw:get-context

Reports the content of the current graph context as a list containing two agentsets: the agentset of turtles that are part of the context and the agentset of links that are part of the context.

Let's say we start with a blank slate and the default context consisting of turtles and links, nw:get-context will report a list the special turtles and links breed agentsets:

observer> clear-all
observer> show nw:get-context
observer: [turtles links]

If we add some turtles and links to our context, we'll still see the same thing, even though turtles and links have internally grown:

observer> crt 2 [ create-links-with other turtles ]
observer> show nw:get-context
observer: [turtles links]

If you had set your context to normal agentsets instead (built with turtle-set, link-set or with) here is what you would see:

observer> clear-all
observer> nw:set-context turtle-set turtles link-set links
observer> show nw:get-context
observer: [(agentset, 0 turtles) (agentset, 0 links)]

If you then create new turtles and links, they are not added to the context because normal agentsets don't grow (see Special agentsets vs normal agentsets):

observer> crt 2 [ create-links-with other turtles ]
observer> show nw:get-context
observer: [(agentset, 0 turtles) (agentset, 0 links)]

But if you construct new agentsets and set the context to them, your new agents will be there:

observer> nw:set-context turtle-set turtles link-set links
observer> show nw:get-context
observer: [(agentset, 2 turtles) (agentset, 1 link)]

If you want to see the actual content of your context, it is easy to turn your agentsets into lists that can be nicely displayed. Just use a combination of map and sort:

observer> show map sort nw:get-context
observer: [[(turtle 0) (turtle 1)] [(link 0 1)]]

Finally, you can use nw:get-context to store a context that you eventually want to restore:

extensions [ nw ]
to store-and-restore-context
  clear-all
  crt 2 [
    set color red
    create-links-with other turtles with [ color = red ] [
      set color yellow
    ]
  ]
  crt 2 [
    set color blue
    create-links-with other turtles with [ color = blue ] [
      set color green
    ]
  ]
  nw:set-context turtles with [ color = red ] links with [ color = yellow ]
  show map sort nw:get-context
  let old-turtles item 0 nw:get-context
  let old-links item 1 nw:get-context
  nw:set-context turtles with [ color = blue ] links with [ color = green ]
  show map sort nw:get-context
  nw:set-context old-turtles old-links
  show map sort nw:get-context
end

Here is the result:

observer> store-and-restore-context
observer: [[(turtle 0) (turtle 1)] [(link 0 1)]]
observer: [[(turtle 2) (turtle 3)] [(link 2 3)]]
observer: [[(turtle 0) (turtle 1)] [(link 0 1)]]

`nw:with-context`

nw:with-context turtleset linkset command-block

Executes the command-block with the context temporarily set to turtleset and linkset. After command-block finishes running, the previous context will be restored.

For example:

observer> create-turtles 3 [ create-links-with other turtles ]
observer> nw:with-context (turtle-set turtle 0 turtle 1) (link-set link 0 1) [ show nw:get-context ]
observer: [(agentset, 2 turtles) (agentset, 1 link)
observer> show nw:get-context
observer: [turtles links]

If you have NW extension code running in two forever buttons or loop blocks that each need to use different contexts, you should use nw:with-context in each to make sure they are operating in the correct context.

`nw:turtles-in-radius`

nw:turtles-in-radius radius

Returns the set of turtles within the given distance (number of links followed) of the calling turtle in the current context, including the calling turtle.

nw:turtles-in-radius form will follow both undirected links and directed out links. You can think of turtles-in-radius as "turtles who I can get to in radius steps".

If you want the primitive to follow only undirected links or only directed links, you can do it by setting the context appropriately. For example: nw:set-context turtles undir-links (assuming undir-links is an undirected link breed) or nw:set-context turtles dir-links (assuming dir-links is a directed link breed).

Example:

clear-all
create-turtles 5
ask turtle 0 [ create-link-with turtle 1 ]
ask turtle 0 [ create-link-with turtle 2 ]
ask turtle 1 [ create-link-with turtle 3 ]
ask turtle 2 [ create-link-with turtle 4 ]
ask turtle 0 [
  show sort nw:turtles-in-radius 1
]

Will output:

(turtle 0): [(turtle 0) (turtle 1) (turtle 2)]

As you may have noticed, the result includes the calling turtle. This mimics the behavior of the regular NetLogo in-radius primitive.

`nw:turtles-in-reverse-radius`

nw:turtles-in-reverse-radius radius

Like nw:turtles-in-radius, but follows in-links instead of out-links. Also follow undirected links. You can think of turtles-in-reverse-radius as "turtles who can get to me in radius steps".

`nw:distance-to`

nw:distance-to target-turtle

Finds the shortest path to the target turtle and reports the total distance for this path, or false if no path exists in the current context. Each link counts for a distance of one.

Example:

to go
  clear-all
  create-turtles 5
  ask turtle 0 [ create-link-with turtle 1 ]
  ask turtle 1 [ create-link-with turtle 2 ]
  ask turtle 0 [ create-link-with turtle 3 ]
  ask turtle 3 [ create-link-with turtle 4 ]
  ask turtle 4 [ create-link-with turtle 2 ]
  ask turtle 0 [ show nw:distance-to turtle 2 ]
end

Will output:

(turtle 0): 2

`nw:weighted-distance-to`

nw:weighted-distance-to target-turtle weight-variable

Like nw:distance-to, but takes link weight into account. The weights cannot be negative numbers.

Example:

links-own [ weight ]
to go
  clear-all
  create-turtles 5
  ask turtle 0 [ create-link-with turtle 1 [ set weight 2.0 ] ]
  ask turtle 1 [ create-link-with turtle 2 [ set weight 2.0 ] ]
  ask turtle 0 [ create-link-with turtle 3 [ set weight 0.5 ] ]
  ask turtle 3 [ create-link-with turtle 4 [ set weight 0.5 ] ]
  ask turtle 4 [ create-link-with turtle 2 [ set weight 0.5 ] ]
  ask turtle 0 [ show nw:weighted-distance-to turtle 2 weight ]
end

Will output:

(turtle 0): 1.5

`nw:path-to`

nw:path-to target-turtle

Finds the shortest path to the target turtle and reports the actual path between the source and the target turtle. The path is reported as the list of links that constitute the path.

If no path exist between the source and the target turtles, false will be reported instead.

Note that the NW-Extension remembers paths that its calculated previously unless the network changes. Thus, you don't need to store paths to efficiently move across the network; you can just keep re-calling one of the path primitives. If the network changes, however, the stored answers are forgotten. Example:

links-own [ weight ]
to go
  clear-all
  create-turtles 5
  ask turtle 0 [ create-link-with turtle 1 ]
  ask turtle 1 [ create-link-with turtle 2 ]
  ask turtle 0 [ create-link-with turtle 3 ]
  ask turtle 3 [ create-link-with turtle 4 ]
  ask turtle 4 [ create-link-with turtle 2 ]
  ask turtle 0 [ show nw:path-to turtle 2 ]
end

Will output:

(turtle 0): [(link 0 1) (link 1 2)]

`nw:turtles-on-path-to`

nw:turtles-on-path-to target-turtle

Like nw:path-to, but the turtles on the path are reported, instead of the links, including the source turtle and target turtle.

Example:

to go
  clear-all
  create-turtles 5
  ask turtle 0 [ create-link-with turtle 1 ]
  ask turtle 1 [ create-link-with turtle 2 ]
  ask turtle 0 [ create-link-with turtle 3 ]
  ask turtle 3 [ create-link-with turtle 4 ]
  ask turtle 4 [ create-link-with turtle 2 ]
  ask turtle 0 [ show nw:turtles-on-path-to turtle 2 ]
end

Will output:

(turtle 0): [(turtle 0) (turtle 1) (turtle 2)]

`nw:weighted-path-to`

nw:weighted-path-to target-turtle weight-variable

Like nw:path-to, but takes link weight into account.

Example:

links-own [ weight ]
to go
  clear-all
  create-turtles 5
  ask turtle 0 [ create-link-with turtle 1 [ set weight 2.0 ] ]
  ask turtle 1 [ create-link-with turtle 2 [ set weight 2.0 ] ]
  ask turtle 0 [ create-link-with turtle 3 [ set weight 0.5 ] ]
  ask turtle 3 [ create-link-with turtle 4 [ set weight 0.5 ] ]
  ask turtle 4 [ create-link-with turtle 2 [ set weight 0.5 ] ]
  ask turtle 0 [ show nw:weighted-path-to turtle 2 weight ]
end

Will output:

(turtle 0): [(link 0 3) (link 3 4) (link 2 4)]

`nw:turtles-on-weighted-path-to`

nw:turtles-on-weighted-path-to target-turtle weight-variable

Like nw:turtles-on-path-to, but takes link weight into account.

Example:

links-own [ weight ]
to go
  clear-all
  create-turtles 5
  ask turtle 0 [ create-link-with turtle 1 [ set weight 2.0 ] ]
  ask turtle 1 [ create-link-with turtle 2 [ set weight 2.0 ] ]
  ask turtle 0 [ create-link-with turtle 3 [ set weight 0.5 ] ]
  ask turtle 3 [ create-link-with turtle 4 [ set weight 0.5 ] ]
  ask turtle 4 [ create-link-with turtle 2 [ set weight 0.5 ] ]
  ask turtle 0 [ show nw:weighted-path-to turtle 2 weight ]
end

Will output:

(turtle 0): [(turtle 0) (turtle 3) (turtle 4) (turtle 2)]

`nw:mean-path-length`

nw:mean-path-length

Reports the average shortest-path length between all distinct pairs of nodes in the current context.

Reports false unless paths exist between all pairs.

Example:

links-own [ weight ]
to go
  clear-all
  create-turtles 3
  ask turtle 0 [ create-link-with turtle 1 [ set weight 2.0 ] ]
  ask turtle 1 [ create-link-with turtle 2 [ set weight 2.0 ] ]
  show nw:mean-path-length
  create-turtles 1 ; create a new, disconnected turtle
  show nw:mean-path-length
end

Will ouput:

observer: 1.3333333333333333
observer: false

`nw:mean-weighted-path-length`

nw:mean-weighted-path-length weight-variable

Like nw:mean-path-length, but takes into account link weights.

Example:

links-own [ weight ]
to go
  clear-all
  create-turtles 3
  ask turtle 0 [ create-link-with turtle 1 [ set weight 2.0 ] ]
  ask turtle 1 [ create-link-with turtle 2 [ set weight 2.0 ] ]
  show nw:mean-path-length
  show nw:mean-weighted-path-length weight
  create-turtles 1 ; create a new, disconnected turtle
  show nw:mean-path-length
  show nw:mean-weighted-path-length weight
end

Will ouput:

observer: 2.6666666666666665
observer: false

`nw:betweenness-centrality`

nw:betweenness-centrality

To calculate the betweenness centrality of a turtle, you take every other possible pairs of turtles and, for each pair, you calculate the proportion of shortest paths between members of the pair that passes through the current turtle. The betweenness centrality of a turtle is the sum of these.

As of now, link weights are not taken into account.

`nw:eigenvector-centrality`

nw:eigenvector-centrality

The Eigenvector centrality of a node can be thought of as the amount of influence a node has on a network. In practice, turtles that are connected to a lot of other turtles that are themselves well-connected (and so on) get a higher Eigenvector centrality score.

In this implementation, the eigenvector centrality is normalized such that the highest eigenvector centrality a node can have is 1. This implementation is designed to agree with Gephi's implementation out to at least 3 decimal places. If you discover that it disagrees with Gephi on a particular network, please report it.

The primitive respects link direction, even in mixed-directed networks. This is the one place where it should disagree with Gephi; Gephi refuses to treat directed links as directed in mixed-networks.

As of now, link weights are not taken into account.

`nw:page-rank`

nw:page-rank

The page rank of a node can be thought of as the proportion of time that an agent walking forever at random on the network would spend at this node. The agent has an equal chance of taking any of a nodes edges, and will jump around the network completely randomly 15% of the time. In practice, like with eigenvector centrality, turtles that are connected to a lot of other turtles that are themselves well-connected (and so on) get a higher page rank.

Page rank is one of the several algorithms that search engines use to determine the importance of a website.

The sum of all page rank values should be approximately one. Unlike eigenvector centrality, page rank is defined for all networks, no matter the connectivity. Currently, it treats all links as undirected links.

As of now, link weights are not taken into account.

`nw:closeness-centrality`

nw:closeness-centrality

The closeness centrality of a turtle is defined as the inverse of the average of it's distances to all other turtles. (Some people use the sum of distances instead of the average, but the extension uses the average.)

Note that this primitive reports the intra-component closeness of a turtle, that is, it takes into account only the distances to the turtles that are part of the same component as the current turtle, since distance to turtles in other components is undefined. The closeness centrality of an isolated turtle is defined to be zero.

`nw:weighted-closeness-centrality`

nw:weighted-closeness-centrality link-weight-variable

This is identical to nw:closeness-centrality, except that weights provided by the given variable are treated as the distances of links.

`nw:clustering-coefficient`

nw:clustering-coefficient

Reports the local clustering coefficient of the turtle. The clustering coefficient of a node measures how connected its neighbors are. It is defined as the number of links between the node's neighbors divided by the total number of possible links between its neighbors.

nw:clustering-coefficient takes the directedness of links into account. A directed link counts as a single link whereas an undirected link counts as two links (one going one-way, one going the other).

The global clustering coefficient measures how much nodes tend to cluster together in the network in general. It is defined based on the types of triplets in the network. A triplet consists of a central node and two of its neighbors. If its neighbors are also connected, it's a closed triplet. If its neighbors are not connected, it's an open triplet. The global clustering coefficient is simply the number of closed triplets in a network divided by the total number of triplets. It can be calculated from the local clustering coefficient quite easily with the following code

to-report global-clustering-coefficient
  let closed-triplets sum [ nw:clustering-coefficient * count my-links * (count my-links - 1) ] of turtles
  let triplets sum [ count my-links * (count my-links - 1) ] of turtles
  report closed-triplets / triplets
end

Note that the above will only work with the default context, and may need to tweaked if you've set the turtles or links in the network to something other than turtles and links.

The average local clustering coefficient is another popular method for measuring the amount of clustering in the network as a whole. It may be calculated with

mean [ nw:clustering-coefficient ] of turtles

`nw:modularity`

nw:modularity

Modularity is a measurement of community structure in the network. It is defined based on the number of in-community links versus the number of between-community links. This primitive takes as input a list of agentsets, where each of the agentsets is one the communities that you're separating the network into.

This measurement works on undirected, directed, and mixed-directedness networks. In the case of mixed-directedness, undirected links are treated essentially the same as two opposing directed links. It does not take weight into account.

Example:

nw:modularity (list (turtles with [ color = blue ]) (turtles with [ color = red ]))

`nw:bicomponent-clusters`

nw:bicomponent-clusters

Reports the list of bicomponent clusters in the current network context. A bicomponent (also known as a maximal biconnected subgraph) is a part of a network that cannot be disconnected by removing only one node (i.e. you need to remove at least two to disconnect it). The result is reported as a list of agentsets, in random order. Note that one turtle can be a member of more than one bicomponent at once.

`nw:weak-component-clusters`

nw:weak-component-clusters

Reports the list of "weakly" connected components in the current network context. A weakly connected component is simply a group of nodes where there is a path from each node to every other node. A "strongly" connected component would be one where there is a directed path from each node to every other. The extension does not support the identification of strongly connected components at the moment.

The result is reported as a list of agentsets, in random order. Note that one turtle cannot be a member of more than one weakly connected component at once.

`nw:louvain-communities`

nw:louvain-communities

Detects community structure present in the network. It does this by maximizing modularity using the Louvain method. The communities are reported as a list of turtle-sets.

Often you'll want to tell turtles about the community that they are in. You can do this like so:

turtles-own [ community ]

...

foreach nw:louvain-communities [ [comm] ->
  ask comm [ set community comm ]
]

You can give each community its own color with something like this:

let communities nw:louvain-communities
let colors sublist 0 (length communities) base-colors
(foreach communities colors [ [community col] ->
  ask community [ set color col ]
])

`nw:maximal-cliques`

nw:maximal-cliques

A clique is a subset of a network in which every node has a direct link to every other node. A maximal clique is a clique that is not, itself, contained in a bigger clique.

The result is reported as a list of agentsets, in random order. Note that one turtle can be a member of more than one maximal clique at once.

The primitive uses the Bron–Kerbosch algorithm and only works with undirected links.

`nw:biggest-maximal-cliques`

nw:biggest-maximal-cliques

The biggest maximal cliques are, as the name implies, the biggest cliques in the current context. Often, more than one clique are tied for the title of biggest clique, so the result is reported as a list of agentsets, in random order. If you want only one clique, use one-of nw:biggest-maximal-cliques.

The primitive uses the Bron–Kerbosch algorithm and only works with undirected links.

`nw:generate-preferential-attachment`

nw:generate-preferential-attachment turtle-breed link-breed num-nodes min-degree optional-command-block

Generates a new network using a version of the Barabási–Albert algorithm. This network will have the property of being "scale free": the distribution of degrees (i.e. the number of links for each turtle) should follow a power law.

Generation works as follows turtles are added, one by one, each forming min-degree links to a previously added turtles, until num-nodes is reached. The more links a turtle already has, the greater the probability that new turtles form links with it when they are added.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-preferential-attachment turtles links 100 1 [ set color red ]

`nw:generate-random`

nw:generate-random turtle-breed link-breed num-nodes connection-probability optional-command-block

Generates a new random network of num-nodes turtles in which each one has a connection-probability (between 0 and 1) of being connected to each other turtles. The algorithm uses the G(n, p) variant of the Erdős–Rényi model.

The algorithm is O(n²) for directed networks and O(n²/2) for undirected networks, so generating more than a couple thousand nodes will likely take a very long time.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-random turtles links 100 0.5 [ set color red ]

`nw:generate-watts-strogatz`

nw:generate-watts-strogatz turtle-breed link-breed num-nodes neighborhood-size rewire-probability optional-command-block

Generates a new Watts-Strogatz small-world network.

The algorithm begins by creating a ring of nodes, where each node is connected to neighborhood-size nodes on either side. Then, each link is rewired with probability rewire-prob.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. Furthermore, the turtles are generated in the order they appear as in create-ordered-turtles. So, in order to lay the ring out as a ring, you can do something like:

nw:generate-watts-strogatz turtles links 50 2 0.1 [ fd 10 ]

`nw:generate-small-world`

nw:generate-small-world turtle-breed link-breed row-count column-count clustering-exponent is-toroidal optional-command-block

Generates a new small-world network using the Kleinberg Model. Note that nw:generate-watts-strogatz generates a more traditional small-world network.

The algorithm proceeds by generating a lattice of the given number of rows and columns (the lattice will wrap around itself if is-toroidal is true). The "small world effect" is created by adding additional links between the nodes in the lattice. The higher the clustering-exponent, the more the algorithm will favor already close-by nodes when adding new links. A clustering exponent of 2.0 is typically used.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-small-world turtles links 10 10 2.0 false [ set color red ]

The turtles are generated in the order that they appear in the lattice. So, for instance, to generate a kleinberg lattice accross the entire world, and lay it out accordingly, try the following:

nw:generate-small-world turtles links world-width world-height 2.0 false
(foreach (sort turtles) (sort patches) [ [t p] -> ask t [ move-to p ] ])

`nw:generate-lattice-2d`

nw:generate-lattice-2d turtle-breed link-breed row-count column-count is-toroidal optional-command-block

Generates a new 2D lattice network (basically, a grid) of row-count rows and column-count columns. The grid will wrap around itself if is-toroidal is true.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-lattice-2d turtles links 10 10 false [ set color red ]

The turtles are generated in the order that they appear in the lattice. So, for instance, to generate a lattice accross the entire world, and lay it out accordingly, try the following:

nw:generate-lattice-2d turtles links world-width world-height false
(foreach (sort turtles) (sort patches) [ [t p] -> ask t [ move-to p ] ])

`nw:generate-ring`

nw:generate-ring turtle-breed link-breed num-nodes optional-command-block

Generates a ring network of num-nodes turtles, in which each turtle is connected to exactly two other turtles.

The number of nodes must be at least three.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-ring turtles links 100 [ set color red ]

`nw:generate-star`

nw:generate-star turtle-breed link-breed num-nodes optional-command-block

Generates a star network in which there is one central turtle and every other turtle is connected only to this central node. The number of turtles can be as low as one, but it won't look much like a star.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-star turtles links 100 [ set color red ]

`nw:generate-wheel`

nw:generate-wheel turtle-breed link-breed num-nodes optional-command-block

Variants:

nw:generate-wheel-inward
nw:generate-wheel-outward

Generates a wheel network, which is basically a ring network with an additional "central" turtle that is connected to every other turtle.

The number of nodes must be at least four.

The nw:generate-wheel only works with undirected link breeds. The nw:generate-wheel-inward and nw:generate-wheel-outward versions only work with directed link-breed. The inward and outward part of the primitive names refer to the direction that the "spokes" of the wheel point to relative to the central turtle.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:generate-wheel turtles links 100 [ set color red ]

`nw:save-matrix`

nw:save-matrix file-name

Saves the current network, as defined by nw:set-context, to file-name, as a text file, in the form of a simple connection matrix.

Here is, for example, a undirected ring network with four nodes:

0.00 1.00 0.00 1.00
1.00 0.00 1.00 0.00
0.00 1.00 0.00 1.00
1.00 0.00 1.00 0.00

And here is the directed version:

0.00 1.00 0.00 0.00
0.00 0.00 1.00 0.00
0.00 0.00 0.00 1.00
1.00 0.00 0.00 0.00

At the moment, nw:save-matrix does not support link weights. Every link is represented as a "1.00" in the connection matrix. This will change in a future version of the extension.

`nw:load-matrix`

nw:load-matrix file-name turtle-breed link-breed optional-command-block

Generates a new network according to the connection matrix saved in file-name, using turtle-breed and link-breed to create the new turtles and links.

At the moment, nw:load-matrix does not support link weights.

Please be aware that the breeds used to load the matrix may be different from those that you used when you saved it.

For example:

extensions [ nw ]
directed-link-breed [ dirlinks dirlink ]
to go
  clear-all
  crt 5 [ create-dirlinks-to other turtles ]
  nw:set-context turtles dirlinks
  nw:save-matrix "matrix.txt"
  clear-all
  nw:load-matrix "matrix.txt" turtles links
  layout-circle turtles 10
end

...will give you back undirected links, even if you saved directed links into the matrix.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:load-matrix "matrix.txt" turtles links [ set color red ]

`nw:save-graphml`

nw:save-graphml file-name

You can save the current graph to GraphML. The following NetLogo code:

extensions [ nw ]

breed [ bankers banker ]
bankers-own [ bank-name ]
breed [ clients client ]
clients-own [ hometown ]

undirected-link-breed [ friendships friendship ]

directed-link-breed [ accounts account ]
accounts-own [ amount ]

to go
  clear-all
  create-bankers 1 [
    set bank-name "The Bank"
  ]
  create-clients 1 [
    set hometown "Turtle City"
    create-friendship-with banker 0
    create-account-to banker 0 [
      set amount 9999.99
    ]
  ]
  nw:set-context turtles links
  nw:save-graphml "example.graphml"
end

Will produce the following GraphML file:

<?xml version="1.0" encoding="UTF-8"?>
<graphml xmlns="http://graphml.graphdrawing.org/xmlns/graphml"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns/graphml">
<key id="PEN-MODE" for="node" attr.name="PEN-MODE" attr.type="string"/>
<key id="YCOR" for="node" attr.name="YCOR" attr.type="double"/>
<key id="PEN-SIZE" for="node" attr.name="PEN-SIZE" attr.type="double"/>
<key id="LABEL" for="node" attr.name="LABEL" attr.type="string"/>
<key id="SHAPE" for="node" attr.name="SHAPE" attr.type="string"/>
<key id="BREED" for="node" attr.name="BREED" attr.type="string"/>
<key id="WHO" for="node" attr.name="WHO" attr.type="double"/>
<key id="HIDDEN?" for="node" attr.name="HIDDEN?" attr.type="boolean"/>
<key id="LABEL-COLOR" for="node" attr.name="LABEL-COLOR" attr.type="double"/>
<key id="HEADING" for="node" attr.name="HEADING" attr.type="double"/>
<key id="BANK-NAME" for="node" attr.name="BANK-NAME" attr.type="string"/>
<key id="HOMETOWN" for="node" attr.name="HOMETOWN" attr.type="string"/>
<key id="COLOR" for="node" attr.name="COLOR" attr.type="double"/>
<key id="XCOR" for="node" attr.name="XCOR" attr.type="double"/>
<key id="SIZE" for="node" attr.name="SIZE" attr.type="double"/>
<key id="END1" for="edge" attr.name="END1" attr.type="string"/>
<key id="TIE-MODE" for="edge" attr.name="TIE-MODE" attr.type="string"/>
<key id="END2" for="edge" attr.name="END2" attr.type="string"/>
<key id="LABEL-COLOR" for="edge" attr.name="LABEL-COLOR" attr.type="double"/>
<key id="THICKNESS" for="edge" attr.name="THICKNESS" attr.type="double"/>
<key id="LABEL" for="edge" attr.name="LABEL" attr.type="string"/>
<key id="SHAPE" for="edge" attr.name="SHAPE" attr.type="string"/>
<key id="BREED" for="edge" attr.name="BREED" attr.type="string"/>
<key id="COLOR" for="edge" attr.name="COLOR" attr.type="double"/>
<key id="AMOUNT" for="edge" attr.name="AMOUNT" attr.type="double"/>
<key id="HIDDEN?" for="edge" attr.name="HIDDEN?" attr.type="boolean"/>
<graph edgedefault="undirected">
<node id="client 1">
<data key="PEN-MODE">up</data>
<data key="YCOR">0</data>
<data key="PEN-SIZE">1</data>
<data key="LABEL"></data>
<data key="SHAPE">default</data>
<data key="BREED">clients</data>
<data key="WHO">1</data>
<data key="HIDDEN?">false</data>
<data key="LABEL-COLOR">9.9</data>
<data key="HEADING">356</data>
<data key="HOMETOWN">Turtle City</data>
<data key="COLOR">115</data>
<data key="XCOR">0</data>
<data key="SIZE">1</data>
</node>
<node id="banker 0">
<data key="PEN-MODE">up</data>
<data key="YCOR">0</data>
<data key="PEN-SIZE">1</data>
<data key="LABEL"></data>
<data key="SHAPE">default</data>
<data key="BREED">bankers</data>
<data key="WHO">0</data>
<data key="HIDDEN?">false</data>
<data key="LABEL-COLOR">9.9</data>
<data key="HEADING">32</data>
<data key="BANK-NAME">The Bank</data>
<data key="COLOR">85</data>
<data key="XCOR">0</data>
<data key="SIZE">1</data>
</node>
<edge source="client 1" target="banker 0">
<data key="END1">(client 1)</data>
<data key="TIE-MODE">none</data>
<data key="END2">(banker 0)</data>
<data key="LABEL-COLOR">9.9</data>
<data key="THICKNESS">0</data>
<data key="LABEL"></data>
<data key="SHAPE">default</data>
<data key="BREED">accounts</data>
<data key="COLOR">5</data>
<data key="AMOUNT">9999.99</data>
<data key="HIDDEN?">false</data>
</edge>
<edge source="banker 0" target="client 1">
<data key="END1">(banker 0)</data>
<data key="TIE-MODE">none</data>
<data key="END2">(client 1)</data>
<data key="LABEL-COLOR">9.9</data>
<data key="THICKNESS">0</data>
<data key="LABEL"></data>
<data key="SHAPE">default</data>
<data key="BREED">friendships</data>
<data key="COLOR">5</data>
<data key="HIDDEN?">false</data>
</edge>
</graph>
</graphml>

A few things to notice:

The breed is stored as data field, both for nodes and edges. Note that the breed is stored in its plural form.
The data includes both NetLogo's internal variables and the variables that were defined as either breeds-own, turtles-own, linkbreeds-own or links-own.
Each key gets an attr.type based on the actual types of the values contained in the agent variables. The three possible types are "string", "double" and "boolean". To determine the attribute type of a particular agent variable, the extension will look at the first agent in the graph. To see which agent is first, you can look at the result of nw:get-context. Note that variables containing other types of values, such as turtles, patches, lists, etc., will be stored as strings.
This example only has a directed link, and you will notice the <graph edgedefault="directed"> element. If we had only undirected links, we would have <graph edgedefault="undirected">. What if we try to mix both kinds of link? At the moment, the extension will save such a "mixed" graph as if it were an undirected graph (see this issue for more details). The order of the source and target will be respected, however, so if you know which breeds represent directed links, you can figure it out a posteriori.

`nw:load-graphml`

nw:load-graphml file-name optional-command-block

Loading a GraphML file into NetLogo with the network extension should be as simple as calling nw:load-graphml "example.graphml", but there is a bit of preparation involved.

The key idea is that nw:load-graphml will try to assign the attribute values defined in the GraphML file to NetLogo agent variables of the same names (this is not case sensitive). The first one it tries to set is breed if it is there, so the turtle or link will get the right breed and, hence, the right breed variables. The load expects the plural form of the breed for a turtle or link, it will not recognize the singular form.

One special case is the who number, which is ignored by the importer if it is present as a GraphML attribute: NetLogo does not allow you to modify this number once a turtle is created and, besides, there could already be an existing turtle with that number.

The simplest case to handle is when the original GraphML file has been saved from NetLogo by using nw:save-graphml. In this case, all you should have to do is to make sure that you have the same breed and variables definition as when you saved the file and you should get back your original graph. For example, if you want to load the file from the nw:save-graphml example above, you should have the following definitions:

breed [ bankers banker ]
bankers-own [ bank-name ]
breed [ clients client ]
clients-own [ hometown ]

undirected-link-breed [ friendships friendship ]

directed-link-breed [ accounts account ]
accounts-own [ amount ]

Loading a graph that was saved from a different program than NetLogo is quite possible as well, but it may take a bit of tinkering to get all the attribute-variable match up right. If you encounter major problems, please do not hesitate to open an issue.

The extension will try to assign the type defined by attr.type to each variable that it loads. If it's unable to convert it to that type, it will load it as a string. If attr.type is not defined, or is set to an unknown value, the extension will first try to load the value as a double, then try it as a boolean, and finally fall back on a string.

If you specify an optional-command-block, it is executed for each turtle in the newly created network. For example:

nw:load-graphml "example.graphml" [ set color red ]

Note that this command block can be used to build a list or an agentset containing the newly created nodes:

let node-list []
nw:load-graphml "example.graphml" [
  set node-list lput self node-list
]
let node-set turtle-set node-list

`nw:load`

nw:load file-name default-turtle-breed default-link-breed optional-command-block

Filetype specific variants:

nw:load
nw:load-dl
nw:load-gdf
nw:load-gexf
nw:load-gml
nw:load-vna

Import the given file into NetLogo. Like nw:load-graphml, the importer will do its best to match node and edge attributes in the file with turtle and link variables in NetLogo. If breed is specified for nodes and edges in the file and exists in NetLogo, it will be used. Otherwise, the default turtle and link breeds are used.

Limitations:

Multigraphs are not supported in importing. Even if the file format supports it (and many don't), only the first link will be used on import. This is due to a limitation in the parsing libraries NW uses. nw:load-graphml does support multigraphs with the normal NetLogo limitation that two turtles can share more than one link only if all the links are of different breeds.

nw:load determines the file-type of given file based on the extension and calls the corresponding load-* primitive on it. Note that GraphML must be imported with nw:load-graphml.

`nw:save`

nw:save file-name

Filetype specific variants:

nw:save-dl
nw:save-gdf
nw:save-gexf
nw:save-gml
nw:save-vna

Export the network context in the given format to the given file. Turtle and link attributes will be exported to formats that support node and edge properties.

Limitations:

x and y (not xcor and ycor) can only be numbers. x and y are commonly used in formats pertaining to position and behind the scenes NW uses Gephi's libraries for exporting. Furthermore, x and y will be added even if they didn't exist in the model. Again, this is because NW uses Gephi's libraries which assume that nodes have positions stored in x and y. If you wish to export to Gephi specifically, we recommend creating x and y turtles variables and setting them to xcor and ycor before export.
Color will be exported in a standard RGB format. This should hopefully increase compatibility with other programs.
Turtle and link variables that contain values of different types will be stored as strings. Unfortunately, most network formats require that node and attributes have a single type.
Many programs use label to store the id of nodes. Thus, if you're having trouble importing data exported from NetLogo into another program, you might try setting turtles' labels to their who number.
Multigraphs are not supported. Thus, two turtles can share at most one link. nw:save-graphml does support multigraphs, so use that if turtles can have more than one type of link connecting them.

nw:save determines the file-type of the given file based on the extension and calls the corresponding save-* primitive on it. Note that GraphML must be exported with nw:save-graphml.

Building

The extension is written in Scala (version 2.9.2).

Run ./sbt package to build the extension.

Unless they are already present, sbt will download the needed Jung and JGraphT jar files from the Internet.

If the build succeeds, nw.jar will be created. To use the extension, this file and all the other jars will need to be in the extensions/nw folder under your NetLogo installation.

Terms of Use

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

Jung is licensed under the BSD license and JGraphT is licensed under the LGPL license.

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The NetLogo NW Extension for Network Analysis

Usage

Special agentsets vs normal agentsets

A note regarding floating point calculations

Performance

Primitives

Generators

Path and Distance

Clusterer/Community Detection

Context Management

Import and Export

Centrality Measures

Clustering Measures

nw:set-context

nw:get-context

nw:with-context

nw:turtles-in-radius

nw:turtles-in-reverse-radius

nw:distance-to

nw:weighted-distance-to

nw:path-to

nw:turtles-on-path-to

nw:weighted-path-to

nw:turtles-on-weighted-path-to

nw:mean-path-length

nw:mean-weighted-path-length

nw:betweenness-centrality

nw:eigenvector-centrality

nw:page-rank

nw:closeness-centrality

nw:weighted-closeness-centrality

nw:clustering-coefficient

nw:modularity

nw:bicomponent-clusters

nw:weak-component-clusters

nw:louvain-communities

nw:maximal-cliques

nw:biggest-maximal-cliques

nw:generate-preferential-attachment

nw:generate-random

nw:generate-watts-strogatz

nw:generate-small-world

nw:generate-lattice-2d

nw:generate-ring

nw:generate-star

nw:generate-wheel

nw:save-matrix

nw:load-matrix

nw:save-graphml

nw:load-graphml

nw:load

nw:save

Building

Terms of Use

`nw:set-context`

`nw:get-context`

`nw:with-context`

`nw:turtles-in-radius`

`nw:turtles-in-reverse-radius`

`nw:distance-to`

`nw:weighted-distance-to`

`nw:path-to`

`nw:turtles-on-path-to`

`nw:weighted-path-to`

`nw:turtles-on-weighted-path-to`

`nw:mean-path-length`

`nw:mean-weighted-path-length`

`nw:betweenness-centrality`

`nw:eigenvector-centrality`

`nw:page-rank`

`nw:closeness-centrality`

`nw:weighted-closeness-centrality`

`nw:clustering-coefficient`

`nw:modularity`

`nw:bicomponent-clusters`

`nw:weak-component-clusters`

`nw:louvain-communities`

`nw:maximal-cliques`

`nw:biggest-maximal-cliques`

`nw:generate-preferential-attachment`

`nw:generate-random`

`nw:generate-watts-strogatz`

`nw:generate-small-world`

`nw:generate-lattice-2d`

`nw:generate-ring`

`nw:generate-star`

`nw:generate-wheel`

`nw:save-matrix`

`nw:load-matrix`

`nw:save-graphml`

`nw:load-graphml`

`nw:load`

`nw:save`