Dynamic Agent-based Network Generation

Audren Bouadjio-Boulic, Frederic Amblard and Benoit Gaudou

IRIT - Smac team, Universit

e de Toulouse, 2 rue du doyen Gabriel Marty, 31042, Toulouse, France

Keywords:

Synthetic Network Generation, Agent-based Modeling, Network Dynamic.

Abstract:

Networks are a very convenient and tractable way to model and represent interactions among entities. For

example, they are often used in agent-based models to describe agents’ acquaintances. Yet, data on real-world

networks are missing or difﬁcult to gather. Being able to generate synthetic but realistic social networks is

thus an important challenge in social simulation. In this article, we provide a very comprehensive and modular

agent-based process of network creation. We believe that the complexity of ABM (Agent-Based Models)

comes from the overall interactions of entities, but they could be kept very simple for better control over the

outcome. The idea is to use an agent-based simulation to generate networks: agent behaviors are rules for

the network construction. Because we want the process to be dynamic and resilient to nodes perturbation,

we provide a way for behaviors to spread among agents, following the meme basic principle - spreading by

imitation. Resulting generated networks are compared to a target network; the system automatically looks at

the best behavior distribution to generate this speciﬁc target network.

1 INTRODUCTION

The human society is composed of people in inter-

action. One of the most convenient way to represent

those interactions is to capture the corresponding re-

lations as a social network, i.e. mathematically by us-

ing a graph. The analysis of such networks allows to

compute some properties (density, centralities, ...) for

qualifying with precision the observed interactions.

Online networks are very well documented because

every interactions are consigned, but this is not the

case for those resulting of real-life interactions. Those

kind of networks are useful for simulating propaga-

tion of disease or opinion, for example. Data can be

missing or hidden, so it is often rather too difﬁcult

or too long to gather enough information to describe

a complete network (Barrett et al., 2009). As a con-

sequence, tools are often used to generate synthetic

network with properties close to the real ones. Even

with successful data gathering, synthetic network can

be used for scalability matter to enlarge coherently a

real network while keeping the same overall proper-

ties.

They are two main approaches for this generation:

(1) by reproducing the process of creation or (2) by

reproducing network properties. For (1), the Agent-

Based Modeling (ABM) paradigm is frequently used.

The network generation process is based on simpliﬁed

but still realistic actor actions. For (2), in contrary, the

generation by-pass the real network formation pro-

cess. (2) can also be subdivided into two branches:

(2.a) stylized models – having few properties match-

ing the real network – or (2.b) precise models. Sty-

lized models are simple, like Small-World (Watts and

Strogatz, 1998) or Preferential-Attachment (Small

et al., 2008), focusing on matching few properties,

without a good precision; we can categorize them

as qualitative approaches. Besides, precise models

of (2.b) are more complex processes, using statisti-

cal models, such as Exponential Random Generator

Models (ERGM) (Robins, 2011) or stochastic model

as K-Graph Generator (Leskovec et al., 2010), for a

quantitative correspondence on far more properties.

With (2.a), results can be too far from the reality for

a realistic use of the network to execute even the sim-

plest process on it (Menezes and Roth, 2014). Using

(2.b), the network generation process can be too ab-

stract or too hard to conﬁgure.

Our goal in this article is to provide a dynamic net-

work generator, based on agent behaviors, coupling

agent actions and behaviors transmission. Our hy-

pothesis is to keep the model simple in order to re-

duce the probability of adding false assumptions and

to increase the control on its dynamic.

Our network creation process is led by an input

network used as target. Agents are characterized by

Bouadjio-Boulic A., Amblard F. and Gaudou B.

Dynamic Agent-based Network Generation.

DOI: 10.5220/0006202705990606

In Proceedings of the 9th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2017), pages 599-606

ISBN: 978-989-758-220-2

599

their behaviors that build and shape a network in

which they are the nodes. Their only two available

actions are the creation and destruction of links. Be-

sides, behaviors are spread through the network. We

are looking for a set of agents’ behaviors – among a

preset of existing ones – that will lead the simulation

to generate a network similar to the target one. Our

aim is to have an adaptive system, that is resilient, in

terms of properties, to addition and removal of nodes.

For these new nodes to be actors in the process of

network evolution, it is necessary for them to learn a

social behavior. A way to do that is to make behavior

spreadable among nodes. That is why we choose to

integrate a spreading mechanism.

The meme theory can be used as a propagation

mechanism. The main idea of memetic is that cultural

traits can be viewed as genes, sharing the reproduc-

tion, spread and mutation mechanisms. Memes are

also subject to selection by the environmental pres-

sure (Dawkins, 1976). It is convenient inter alia be-

cause memes ”leap” from man to man, depending on

the host compatibility, without their consent (Alvarez,

2004). Nevertheless, we only use memetic as a root

for our transmission process, because we do not take

into account the personalization phase of a behavior.

As a ﬁtness function for guiding our system, we

compute a distance to the target network. This dis-

tance is based on the difference between properties of

the two networks (e.g. density, degree distribution)

and the result of processes run on both networks (e.g.

speed of information diffusion). Our postulate is: if

we can reproduce the properties of a network, the gen-

eration process becomes an acceptable way to explain

the whole network, even if it is in a stylized way (a bit

like the preferential attachment process being a plau-

sible explanation for the power law property (Small

et al., 2008)).

In the section 2, we present the related works in

networks generation, to introduce our contribution.

The details of our model is in the development sec-

tion. The section 4, Implementation and results, will

illustrate the model imitating a Scale-Free network.

The ﬁth section will offer some discussions on postu-

lates taken by the model, along with the work to come.

The last part will be the occasion to draw a conclusion

on the system.

2 STATE OF THE ART

2.1 Social Network

A network is deﬁned by a set of nodes and a set of

edges linking those nodes. The degree of a node is

deﬁned by the number of edges it has. From a math-

ematical point of view, networks are thus graphs. So-

cial networks (SN) have some properties that differ-

entiate them from a random network; therefore those

properties can be used as a formal characterization of

a SN. They are often consequences of a speciﬁc pro-

cess of formation.

• For various reasons, people tend to become friend

with their friends’ acquaintances. From a graph

point of view, this is a triangle closure (or tran-

sitivity): if A is friend with B and C, B and C

meet each other and become friends as well. It

is possible to capture such tendency through the

clustering coefﬁcient. For an undirected graph,

the clustering coefﬁcient of a node n is:

− 1)

(1)

with k

the number of neighbours of n and e

the

number of connected nodes among them. The

higher the clustering is, the more interconnected

the nodes are.

• The Small World effect has been introduced by

Milgram (Milgram, 1967) as the ”six degrees of

separation” between person: anyone can reach

anyone within 6 hops of relatives on average. In

terms of network properties, it is a matter of av-

erage (shortest) path length between the nodes in

the network.

• SN among other kinds of networks have a scale

free property: few people are very famous, i.e.

well connected, while many other ones are poorly

served. The formal deﬁnition is that the degree

distribution of the nodes follows a power law, i.e.

a large number of nodes have few edges and a few

have many.

Those properties often come together while work-

ing in social networks.

2.2 Social Network Generation

For the generation of synthetic social networks, sev-

eral approaches have been proposed.

The Agent-Based Approach. The goal of using an

agent simulation for generating the network is to use

a realistic bottom up approach. Such models focus on

agent behaviors, based on some extend on real human

action. Morover, these methods facilitate the use of

real-world data as input and validation (Parunak et al.,

1998). It greatly simplify the test of what-if scenarii.

This kind of methods are most often ad hoc.

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Abstract Processes. It is possible to apply an ab-

stract process of network generation. The proposed

methods are often very simple but provide often only

good results on few properties at a time. These prop-

erties have been observed enough times on different

social networks to be considered as fundamental.

• Random network (RN) (Erdos and Renyi, 1959).

The only parameter is the probability for a node

to create an edge with another node. This process

assures a direct control on the density of the re-

sulting network.

• The Preferential Attachment (PA) algorithm

(Barabasi and Albert-L

aszl

o, 1999) provides a

network with the scale free property, i.e. a power

law distribution of degrees. The construction in-

volves an iterative process in which an incoming

node will be linked with a stronger probability to

an high degree network node.

• Small World (SW) (Watts and Strogatz, 1998)

generates networks with a correct clustering and

a small average path length, known as the small

world effect. The most cited model corresponds

to the construction from a regular lattice, rewiring

at random edges with a certain probability to an-

other random node.

Although these processes are very simple, they are

the most used, at least by the JASSS community (Am-

blard et al., 2015), mainly because their use is very

simple. They also allow modelers to test their sim-

ulation results based on a single but easy to control

network property.

Statistical or Stochastic Models. In those ap-

proaches, the existence of an edge between two given

nodes of the network is considered as a probability,

and the model will determine them. Those methods

have often a network as target, like it is the case for

the following items.

• p*/ERGM Exponential Random Generative Mod-

els (Robins, 2011) is a family of statistical mod-

els in which modelers has to choose a set of net-

work patterns (called terms or factors) that may

describe to a certain level of precision a given net-

work. A model ﬁtting process allows to determine

the relative importance (factor value) of terms in

the observed network structure. Each factor value

expresses how likely the feature is to be found,

compared to a random network of the same size.

ERGM allows to generate networks with respect

to any valid combination of terms (e.g. degree

distribution, substructures, edges and nodes vari-

ables, etc.).

• For Kronecker Graphs (Leskovec et al., 2010),

the idea is to start from a 2x2 or 3x3 stochastic ad-

jacency matrix that will be enlarged by a recursive

method. Correct starting parameters will then be

searched by comparison with the target network.

This model is good at generating graphs with an

appropriate degree distribution and network diam-

eter. Also, properties on the adjacency matrix as-

sociated with the graph have good eigenvalues and

vectors.

• Menezes and Roth method (MR-method)

(Menezes and Roth, 2014) is searching for a good

formula deﬁning p(i,j), the probability of having

a link between two nodes of a target network.

Generating a synthetic network with p(i,j) and

using a distance to a target network as the ﬁtness,

the model uses a genetic algorithm in order to

make evolve p(i,i), trying to ﬁnd the closest

synthetic network possible.

2.3 Contribution

Concerning the agent-based generation, while behav-

iors incorporated in agents are realistic, it is difﬁcult

to get a network with good properties. Real phenom-

ena are more or less stylized and the results can be, in

the best case, correct in a qualitative way.

Concerning the abstract processes – SW, PA, RN

–, one can argue that resulting networks can be used

for qualitative results. In fact, far more network topol-

ogy properties inﬂuence the speed of propagation, as

Cointet and Roth (Cointet and Roth, 2007) pointed

out. They advise to use any real world network, even

from others ﬁeld, to get better results. Classic stylized

networks give incoherent results mainly because these

networks do not take into account properties that do

matter for processes like propagation, e.g. the dia-

mond clustering that will slow down speed (a triangle

closure extended to four nodes). For the qualitative

approaches, network generation processes can be too

abstract or too hard to conﬁgure. Parameters cannot

be interpreted easily, and in the case of ERGM there

are some real difﬁculties using it without the required

knowledge.

Besides, our method is fundamentally different in

the approach while we hope being able to give close

quality of results, with a conﬁguration-free method

and in a dynamic way.

3 MODEL DESCRIPTION

Our model need to be usable in several cases of appli-

cation, that is why available behaviors for the agents

Dynamic Agent-based Network Generation

601

Figure 1: Overall process: example of executing the behav-

ior ”Add a link to more connected agent”. [Action]: Add

link. [Attribute]: degree [Filter]: has a higher degree than

mine.

a. Selection of the acting agent and of the behavior to apply

b. Selection of candidate after a ﬁrst pass of ﬁltering c. Se-

lection of a single target d. Spreading of the behavior, end

of turn.

are generic. We don’t reproduce a speciﬁc process of

network creation. Instead, we want to ﬁnd an abstract

and general model that can get us to the targeted net-

work. Many choices in the mechanisms of the model

have been made for having:

• a restrictive enough context for two distinct simu-

lations to give approximately the same result. We

will refer to this goal as (A - Restrain).

• a loose enough context to enable a large space of

networks that can be generated (B - Widen)

Going deeper in complexity has many drawbacks

such as increasing the number of parameters, while

we want to keep them at a reasonable number. More-

over, they have to be readable, understandable, and

easily searchable.

The evolution of the network is driven by two dy-

namics:

• Behaviors application by agents, that add and re-

move edges and thus shape the network

• Behaviors spreading among agents using the net-

work structure

3.1 Agent

The agents are the nodes of the network. They are

caracterized by their degree and by their behaviors,

for which they have two slots. One of these slots can

only contain a behavior embedding an add action, the

other slot receives a remove action. Agents have per-

fect informations about others attributes.

3.2 Behavior

3.2.1 Behavior Composition

A behavior is composed of three elements: (1) one

action, (2) ﬁlters and (3) attributes. An attribute can

be every kind of information characterizing an agent.

Then ﬁlter is applied in regard to those attributes, re-

straining the list of available agents on which the ac-

tion can be done. For example, the behavior: (1)[Ad-

dLink] on one agent having his (3)[degree] (2)[>] the

acting agent (3)[degree] (cf. Figure 2). If more than

one agent is available in the ﬁnal set, the ﬁlter [Select

random target] is always applied in order to have the

action done on only one target. This helps keeping a

smooth dynamics in accordance to (A - Restrain).

Attributes. We choose to stay with one of the most

generic attribute available for an agent: his degree.

Agents have perfect information on other agents’ at-

tributes. New attributes can be easily intregrated.

Filter. The main logical comparators: >, <, =, 6=,

are available. The goal of ﬁlters is to narrow the star-

ting elements. Filters can be chained for a stronger

selectivity. A ﬁlter of unique selection, random, is

also available for returning randomly one element of a

list. For example, if agents have two attributes: degree

and the account balance. A behavior can be:

1. Action: add link

2. First ﬁlter: degree lower than mine

3. Second ﬁlter: balance greater than mine

4. Third ﬁlter: Select one agent randomly

It will return one agent from the list of agents having:

• Bigger balance than the acting node

• A degree inferior at the acting node

Some ﬁlters exist without attribute, for example the

random selection.

Actions. The action is applied on the set of agents

returned by the application of all ﬁlters. We are only

interested in the most basic kind of action, i.e. add an

undirected link and remove a link between the acting

agent and another. In order to keep the state of the

system readable, agent can only have one instance of

behavior per action. In other words, agents have a

maximum of two behaviors: one embedding an add

edge action, the other one being a remove link action,

respecting the (A - Restrain) principle.

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3.2.2 Available Behaviors

Implemented behaviors include following actions:

• Add an undirected edge

• Remove an existing edge

these actions are combined with these speciﬁc ﬁlters:

• Acting agent degree greater than (resp. lower

than) the target agent’s degree

• Agents having the highest degree (and the lowest)

• Agents reachable in a path of length n

• Random target

Figure 2: Detail of behavior execution.

3.2.3 Behavior Transmission

Originally we chose one of the most simple way

of transmission for the behaviors: direct imitation.

When an agent A applies on B an action, the agent

B will learn the whole behavior from A. Informa-

tion cascade highly depends on the initial ﬂuctuations

(Easley and Kleinberg, 2010). But networks gener-

ated with the same initial parameters have to be sim-

ilar. To ensure the resilience to ﬁrst transmissions, a

probability of transmission for each behavior is de-

ﬁned rather than passing them at every application (A

- Restrain). In addition, agents can relearn behavior

replacing the previous he has in a speciﬁc action slot

(B - Widen). Thanks to that, behaviors learnt in the

beginning will just ”fuel” the network construction

dynamics.

However, this transmission rule has a drawback.

Some actions will not be able to be applied – and then

transmitted – in some network topology (e.g. the add

link to the node of highest degree will be applied only

once and will not propagate further). For these rea-

sons, we choose another way of transmission: upon

execution of a behavior, the receiver agent will have a

chance to get transmitted one of the acting agent be-

haviors (B - Widen), and not necessary the one that

has been applied. Following the previous example,

let consider an agent A having the highest degree of

the network and having two behaviors:

1. Add edge to highest degree

2. Remove edge randomly

When agent A will apply on agent B the behavior (2.),

the agent B will have the opportunity to learn one of

(1.) or (2.). Agents initialized with starting behaviors

will not replace them during the course of the simu-

lation. It will then avoid the disappearance of behav-

iors solemnly applied (and then transmitted) because

of their too high constraint of application, in accor-

dance with the (B - Widen) principle. Imitation often

provides a step of mutation or personalization of the

behavior (Dawkins, 1976) but we do not include it,

mainly for keeping control on process played during

the network formation (A - Restrain).

3.3 Scheduling

At each simulation step, an agent is chosen randomly.

First, this agent choose randomly one of its available

behaviors. Secondly, the agent tries to apply it by

looking at compatible agents, depending on ﬁlters and

attributes. Finally, The agent on which the behavior

has been executed can learn one of the acting agent

behavior, depending on the transmission probability.

A new step is started with the next agent.

4 SIMULATION AND RESULTS

4.1 Model Parameters and Initialisation

We work on 100 nodes, starting on a random network

of density 0.5. The random network is preferable to

an empty network because the latter make removing

behaviors depend on appliance of adding behavior.

The contrapositive is also true for complete network;

others starting networks have no justiﬁcation for a

generic approach.

One behavior of each kind is distributed among

the population. Behaviors for the simulation and their

probability of transmission will then deﬁne the type

of network reachable by the simulation – if reaching

a stable ﬁnal state. Besides, we initialize the other

nodes of the network with the following combinaison

of behavior: [Add an edge to a random node,remove

an edge from a random node], with a probability of

transmission of 0. This is made for ease initial behav-

ior transmissions. Two runs of simulations will then

differ on the probability of transmission for each of

these behavior.

A simulation is run on every combination of be-

havior distribution on the starting network, along with

Dynamic Agent-based Network Generation

603

combination of theirs probability of propagation. For

example, two behaviors with probability ranging from

0 to 0.2 with a step of 0.1 will provide 3

conﬁgura-

tion starting points.

4.2 Exploration

4.2.1 Computation of a Distance Between

Networks

The selection process of a good network highly de-

pends on which properties are taking into account in

the computation of the distance to the target network.

The weights between properties matters. Without any

information on the wanted network, we consider all

properties in a equivalent fashion. We then determine

a score of dissimilarity from 0 to 100 for each prop-

erties we ﬁnd relevant, 0 being the equality. We then

normalize this distance at 100 for each properties.

(

(x − y)

maximum amplitude

) ∗ 100 (2)

with x and y being values of a properties, ranged

from 0 to maximum amplitude. We choose to take

into account the average degree distribution, the de-

gree distribution interquartile, the average clustering

of the nodes and the number of edges.

4.2.2 Automatic Space Research

The exploration is done in a exhaustive way, launch-

ing simulation for every combination of parameters,

waiting for the network to stabilize and comparing the

output to the target network. A score of distance is

computed, and the best network among the resulting

ones is selected.

4.3 Final State of the Dynamics of

Network Construction

We use the temporal variation of the network density

has a marker of stability: we consider that a network

is stable when its variation is below a given value.

Three state of behavior transmission dynamics can be

reached:

• Still Behaviors are not propagating anymore. Dis-

tribution of the different behavior in the popula-

tion has reached a ﬁnal state;

• Cycling Spreading is still occurring. The distribu-

tion of behaviors is cycling among the population.

It is not still but can yet be detected;

• Chaotic Spreading occurs. The distribution dy-

namics does not follow any pattern.

Table 1: Final states reachable.

Behaviour spreading

Steady Cyclic Chaotic

Behavior

execution

Steady I.A - -

Cyclic II.A II.B -

Chaotic III.A III.B III.C

The same goes for behaviors execution. Table 1

is summarizing the possible joint states. Behavior

executed by agents do not necessary imply behavior

transmission, e.g. when the probability of transmis-

sion is at 0. There are some corner cases, for ex-

ample (II.A) where two agents cycle adding and re-

moving link between then, those two protagonists al-

ready sharing the same behaviors. Ideally, we would

like to have some networks generated after reaching

a (I.A) state, although it does not guaranty to behave

in a good way upon nodes addition (potentially not

propagating to them any behavior). Realistically, dy-

namics generating stable enough networks are more

in (II.A) and (II.B). Du to the dynamical process of

formation, the network won’t stop ﬂuctuating most

of the time – both in term of behavior execution and

transmission. We decide to stop a run when the tem-

poral variation of the density reach a stability, or after

too many agents action.

4.4 Results

4.4.1 Target

The target network is a Scale-Free network, build with

the Preferential-Attachment model, with 100 nodes.

4.4.2 Run

The behaviors availables are :

• (I) Add edge to a node with a degree superior to

the acting agent (Add edge degree > mine)

• (II) Add edge to a node connected to a connected

node of the acting agent (Transitivity)

• (III) Add edge to the node with the highest degree

• (IV) Remove edge degree > mine

• (V) Remove edge degree < mine

Each behavior b have a probability of transmis-

sion P

(b) ranging from 0 to .9 with a .03 step. We

run the simulation for every combinaison of P

(b). In

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604

order to have a idea of the reproductability of the net-

work creation process starting from the same conﬁg-

uration, we repeat three run of the same conﬁguration

and compute Standard Deviation (SD) on each prop-

erties of the resulting networks.

4.4.3 Results and Score

The top results are in 2. The ﬁve behaviors b are

those describe in section 4.4.2. P

(b) is the proba-

bility of transmission of the behavior b upon execu-

tion. Each conﬁguration is repeated 3 times, average

and Standard Deviation (SD) are computed on score

for each properties and on the result (we only display

SD on score). Density is the density of the ﬁnal net-

work reach, avg DD the average degree distribution

over the three runs, DD interqtl, avg clust and avg

score being respectively the average degree distribu-

tion interquartile, the average clustering and the aver-

age score for the runs. This ﬁve properties are the one

used in the calcul of distance between the target and

the synthetic network. The lower score the better. The

ﬁrst line of the array, Real Network, is the properties

of the target network. Others line are simulated one.

Figure 3: Network generated with the best set of behaviors.

Figure 4: Degree distribution of nodes in the best network.

3 is the network obtains. The ﬁnal distribution of

behavior is:

• (I): 1% Add edge to a node with a degree superior

to the acting agent (Add edge degree > mine)

• (II): 1% Add edge to a node connected to a con-

nected node of the acting agent (Transitivity)

• (III): 95% Add edge to the node with the highest

degree

• (IV):1% Remove edge degree > mine

• (V): 98% Remove edge degree < mine

• (-): 1% Add edge to a random node (Initialization)

• (-): 1% Remove edge from a random node (Ini-

tialization)

even with a probability of transmission of a behavior

to 0, initial behavior are still available because starting

behavior on nodes cannot be replaced. 4 is the degree

distribution of the network with the best score.

Because no special weight has been associated to

the properties considerated for the score, networks

having some nodes without edges are not penalized

and have good results. The best network with a good

density is the second of the array, the previous one

having to many nodes without edges.

5 DISCUSSION AND FUTURE

IMPROVEMENTS

We are making some assumptions in the model, the

most important one being that we consider possible

to ﬁnd rules that will lead to any kind of networks. In

other words, we try to ﬁnd a dynamic process that will

generate a precise network, without being the original

process. Nothing guarantees that this process can be

used properly in a change of scale purpose, i.e. pre-

dicting the growth of the real network or even gener-

ating bigger network with the same properties. They

are initial conﬁgurations which do not converge to a

stable network, and the detection can be difﬁcult, the

density undertaking strong variation.

The exhaustive research of the best initial conﬁgu-

ration, depending on the precision, can be pretty long

(3-4hours on a laptop) and a future amelioration will

be the use of a genetic algorithm to ﬁnd the best set of

parameters.

Another very important improvement will be the

introduction of behaviors allowing adding or remov-

ing nodes in the network. This possibility open the

framework to imitate dynamical time evolution of net-

work, but will also be much more difﬁcult to conﬁg-

ure, and will necessitate several ”pictures” of the tar-

geted network at different time to ﬁgure out the dy-

namic.

Dynamic Agent-based Network Generation

605

Table 2: Result of a simulation with ﬁve behaviors. See 4.4.3.

(I) P

(II) P

(III) P

(IV ) P

(V) density avg DD DD interqtl avg clust avg score SD score

Real network 0.02 1.98 1 0 0 0

0.03 0 0.6 0.06 0 0.001 0.12 0 0 6.71 0.06

0.06 0.06 0.06 0.06 0 0.01 1.14 1 0.046 6.9 0.89

0.09 0.6 0.06 0.09 0 0.028 2.86 5 0.09 16 3

6 CONCLUSION

Social network generation processes are often too

complicated to use or too abstract in the resulting net-

work properties. We offer a model of networks gen-

eration aiming a reproducing any kind of network,

guided by a topological distance to a target. Our

model is independant of the underlying process of

the target network formation, but it can be see as an

explainatory model. Mechanisms have been kept to

the simplest for readable and tractable purpose, and

the model do not need any conﬁguration. We used a

Scale-Free network as a toy target, and results on gen-

erating this simple abstract model are promising. We

aim in future work at copying more complex struc-

tures.

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