Available via license: CC BY-NC-SA 4.0

Content may be subject to copyright.

Contrarian eﬀects and echo chamber formation in opinion dynamics

Henrique Ferraz de Arruda,1Alexandre Benatti,1Filipi Nascimento

Silva,2C´esar Henrique Comin,3and Luciano da Fontoura Costa1

1S˜ao Carlos Institute of Physics, University of S˜ao Paulo,

PO Box 369, 13560-970, S˜ao Carlos, SP, Brazil

2Indiana University Network Science Institute, Bloomington, IN, USA.

3Department of Computer Science, Federal University of S˜ao Carlos, S˜ao Carlos, Brazil

The relationship between the topology of a network and speciﬁc types of dynamics unfolding on it

has been extensively studied in network science. One type of dynamics that has attracted increasing

attention because of its several implications is opinion formation. A phenomenon of particular

importance that is known to take place in opinion formation is the appearance of echo chambers,

also known as social bubbles. In the present work, we approach this phenomenon, with emphasis on

the inﬂuence of contrarian opinions, by considering an adaptation of the Sznajd dynamics of opinion

formation performed on several network models (Watts-Strogatz, Erd˝os-R´enyi, Barab´asi–Albert,

Random geometric graph, and Stochastic Block Model). In order to take into account real-world

social dynamics, we implement a reconnection scheme where agents can reconnect their contacts

after changing their opinion. We analyse the relationship between topology and opinion dynamics by

considering two measurements: opinion diversity and network modularity. Two speciﬁc situations

have been considered: (i) the agents can reconnect only with others sharing the same opinion; and (ii)

same as in the previous case, but with the agents reconnecting only within a limited neighborhood.

Several interesting results have been obtained, including the identiﬁcation of cases characterized not

only by high diversity/high modularity, but also by low diversity/high modularity. We also found

that the restricted reconnection case reduced the chances of echo chamber formation and also led

to smaller echo chambers.

I. INTRODUCTION

Several real-world systems can be eﬀectively repre-

sented and modeled as complex networks [1]. The veriﬁ-

cation that these systems can exhibit marked topological

diﬀerences contributed substantially to establishing the

new area of network science [2]. One of the reasons this

ﬁnding has been so important regards the question of how

much such diverse topologies can inﬂuence the unfolding

of speciﬁc dynamics (e.g. disease spreading [3], neuronal

activation [4], opinion formation [5], and cultural forma-

tion [6]) on the networks.

As human beings are progressively and inexorably in-

terconnected, several important phenomena have been

identiﬁed, including the formation of echo chambers, also

known as social bubbles of opinion [7–11]. More speciﬁ-

cally, people sharing the same opinions tend to form rel-

atively isolated communities in social networks. Because

of its importance, echo chambers have been extensively

studied recently [7–11].

One particularly interesting situation deserving further

investigation regards networks in which agents are al-

lowed to change their connections after having modiﬁed

their opinion [11–16]. In particular, a modiﬁed version of

the Sznajd model of opinion dynamics was employed [11],

considering several network topologies, in order to study

echo chamber formation when agents are allowed to re-

connect, after changing their opinion, to other agents

sharing the new opinion. Several interesting results were

reported, including the fact that the obtained echo cham-

bers tended to have similar sizes and that the same pa-

rameter setting can lead to completely diﬀerent results.

In the present work, we address further this problem

with focus on the eﬀect of contrarian opinions [17–20].

More speciﬁcally, when changing their opinion, some peo-

ple would tend to adopt the position contrary to the pre-

dominant opinion. What would be the eﬀects of this

type of dynamics on the underlying network? Could this

contribute to a larger diversity of opinions and/or echo

chamber formation?

In order to investigate this interesting problem further,

we resorted to a modiﬁed version of the Sznajd model of

opinion formation [11], which was run on several types

of network topologies: Watts-Strogatz, Erd˝os-R´enyi,

Barab´asi–Albert, Random geometric graph, and Stochas-

tic Block Model. Emphasis was placed on performing this

study as a particular case of topology/dynamics interre-

lationship. So, while the network topology was charac-

terized in terms of its modularity [21], the opinion distri-

bution was quantiﬁed with respect to its diversity [22].

Regarding the reconnections induced as a consequence of

changes of opinion, the two following situations have been

considered: (i) the agents can reconnect only with others

sharing the same opinion; and (ii) same as in the previ-

ous case, but with the agents reconnecting only within a

limited neighborhood.

Several interesting results have been obtained, includ-

ing the identiﬁcation of the great inﬂuence of the average

degree on the formation of the echo chambers, in both

considered situations. In addition, the obtained results

were found to exhibit complementary characteristics as

far as diversity and modularity are concerned. In par-

ticular, regions of the parameter space characterized by

a gradual variation of diversity were found to have very

arXiv:1910.06487v1 [physics.soc-ph] 15 Oct 2019

2

similar modularities, and vice versa. Another interesting

ﬁnding relates to the veriﬁcation that restricted recon-

nection reduced the chances of echo chamber formation,

which also tended to be smaller. We also found that, for

a given set of parameters, two types of topologies can be

obtained: with or without echo chambers.

This article is organized as follows. We start by pre-

senting a previous related work [11] on which the cur-

rent approach builds upon, including the description of

the modiﬁed Sznajd dynamics, the reconnecting schemes,

the deﬁnition of diversity and modularity, as well as the

adopted network models. The results are then presented

and discussed, and prospects for future studies are sug-

gested.

II. ADAPTIVE SZNAJD MODEL

The proposed model is based on the Adaptive Sznajd

Model (ASM) [11], which is a version of the more tradi-

tional Sznajd Model [5]. This new version can give rise

to echo chambers, as described as follows.

Before starting the dynamics, each network node, i, is

assigned to an opinion, Oi, randomly distributed (uni-

form), where Oi∈[0, NO]. The case Oi= 0 corresponds

to nodes with null opinion. The rules applied at each

interaction are presented in Figure 1.

An additional probability w(0 ≤w≤1) can also

be employed, representing the dynamic’s temperature.

In the case of opinion dynamics, this parameter corre-

sponds to the probability of a node randomly changing

its opinion. In order to simplify our analysis, we hence-

forth adopt w= 0.

III. CONTRARIAN-DRIVEN SZNAJD MODEL

This dynamics simulates the case in which people in-

ﬂuenced by their neighbors tend to adopt the contrary

opinion. Here, we considered the ASM and added a rule

that incorporates the contrarian idea, which consists of

allowing an agent to have an opinion that is diﬀerent

from the majoritarian (the less frequent opinion). Dif-

ferently from the previous study [11], here we considered

the starting number of opinions as four. The new rules

are presented in Figure 2.

IV. CONTEXT-BASED RECONNECTION

Taking into account that the probability of a person

ito become a friend of some other person jis inﬂu-

enced by the neighbors of j, we incorporated a new rule

in the above described algorithm. More speciﬁcally, we

included a parameter h, which controls the maximum

topological distance between iand jallowing a change

of opinion by i.

So, we limit the reconnections to happen only between

nodes that are within a distance lower or equal to h. If

there is no possibility of reconnection, the rewiring does

not happen. For the sake of simplicity, here we adopt

h= 2, which means that the reconnections happen only

between the selected node iand the friends of friends of

i.

V. DIVERSITY

In order to quantify how diverse the opinions are, we

employ a respective measurement. There are many pos-

sible ways to deﬁne diversity [22]. Here we consider the

measurement based of information theory [23], deﬁned as

follows

D= exp (H),(1)

where His the Shannon entropy, which is deﬁned as

H=−

No

X

o=0

ρoln(ρo),(2)

where Nois the number of possible opinions and ρois

the proportion of the opinion oon network. The value

of diversity, limited within the range 1 ≤D≤No+ 1,

can be understood as the eﬀective number of states, also

known as Hill number of order q= 1 [24, 25].

VI. MODULARITY

Because diversity only accounts for the variety of opin-

ions, we also consider a measurement of topological mod-

ularity [21] that quantiﬁes the tendency of nodes to form

communities. These communities are deﬁned as groups

of nodes highly interconnected while being weakly linked

to the remaining network [21].

More speciﬁcally, the adopted modularity measure-

ment is calculated as

Q=1

2mX

ij

hAij −kikj

2miδ(ci, cj),(3)

where mis the number of edges, Ais the adjacency ma-

trix, and ci,cjare the communities of the nodes iand j,

respectively. The value of modularity gauges the struc-

tures of clusters of a network. In this study, we consid-

ered the opinions being the communities of the nodes.

VII. NETWORK TOPOLOGIES

In order to account for diﬀerent network topologies, we

perform the dynamics considering ﬁve diﬀerent models as

follows:

3

A node, i, is randomly chosen, then:

•if Oi= 0 the iteration ends;

•if Oi6= 0, a random ineighbor, j, is selected. By considering the opinion Oj, the next action is determined as:

–if Oj= 0, the node jchanges its opinion to agree with the node i(Oj=Oi);

–if Oj6=Oi, the iteration ends;

–if Oj=Oi, each of the ineighbors can change their opinions to Oi, with probability 1/ki, where kiis the

degree of node i. The same procedure is applied to the neighbors of j, but with probability 1/kj;

–When the opinion Oi, of given node i, changes, one of the following three rules are applied with

probability q.

∗If the new opinion Oiis unique on the network, nothing happens;

∗If all of the ineighbors agree with your new opinion, nothing happens;

∗If the above two rules are not applied, iloses a connection with an aleatory neighbor that has a

diﬀerent opinion, and connects to some other random node having the same opinion as i.

FIG. 1. Pseudocode of the adaptive Sznajd model (ASM).

A node, i, is randomly chosen, then:

•if Oi= 0 the iteration ends;

•if Oi6= 0, a random ineighbor, j, is selected. By considering the opinion Oj, the next action is determined as:

–if Oj= 0, the node jchanges its opinion to agree with the node i(Oj=Oi);

–if Oj6=Oi, the iteration ends;

– if Oj=Oi:

∗Each of the ineighbors can change their opinions to Oi, with probability 1/ki. For each i

neighbor that does not replace its opinion, the neighbor can change to the contrarian

with probability g;

∗Each of the jneighbors can change their opinions to Oi, with probability 1/kj.

–When the opinion Oi, of given node i, changes, one of the following three rules are applied with

probability q.

∗If the new opinion Oiis unique on the network, nothing happens;

∗If all of the ineighbors agree with your new opinion, nothing happens;

∗If the above two rules are not applied, iloses a connection with an aleatory neighbor that has a

diﬀerent opinion, and connects to some other random node having the same opinion as i.

FIG. 2. Pseudocode of the proposed survey-driven Sznajd model.

•Watts-Strogatz (WS) [26]: departing from a 2D

toroidal lattice;

•Erd˝os-R´enyi (ER) [27]: having uniformly random

connections with probability p;

•Barab´asi–Albert (BA) [28]: yielding scale free de-

gree distributions;

•Random geometric graph (GEO) [29]: the positions

of the nodes were initially set as a 2D lattice;

•Stochastic Block Model (SBM) [30]: we conﬁgured

the model concerning four well-deﬁned communi-

ties with the same size.

In all the above cases, the parameters were chosen so

as to yield the same expected average degree hki.

For all these adopted networks, we considered the

number of nodes as being approximately 1000. Fur-

thermore, we employed three diﬀerent average degrees

(hki= 4,8,12). However, in the case of the GEO model,

we considered only hki= 8,12 since it is diﬃcult to

achieve a single connected component with a lower av-

erage degree. More information regarding several of the

adopted network models can be found in [2].

4

VIII. RESULTS AND DISCUSSION

Here, we present the results according to two respective

subsections considering the no-reconnection constraint

and context-based reconnections. In both cases, we ana-

lyze the opinions diversity and opinions modularity.

A. No reconnection constraint

First, we analyzed the diversity (D) behavior in terms

of the reconnection probability (q) and contrarian prob-

ability (g) for all considered topologies and three average

degrees (hki= 4,8,12). For most of the dynamics, we

executed 1,000,000 of iterations, except for GEO which

was performed 100 million (for average degree 8) and

25 million (for average degree 12). For all of the con-

sidered topologies, we calculated Dby varying qand g.

An example regarding the WS network is shown in Fig-

ures 3(a) (b) and (c), in which well-deﬁned regions can

be observed. For almost all network models, the results

were found to be similar. The lower diversity values were

observed for lower values of qand g. Interestingly, even

when we consider q= 0 (no reconnections), some val-

ues of glead the dynamics to converge to high values of

opinion diversity, D. In other words, we veriﬁed that the

employed parameter conﬁguration strongly aﬀects the di-

versity (D).

In order to better understand the variation of the di-

versity with the parameters, we ﬂattened the obtained

values of Dand calculated the respective PCA (Principal

Component Analysis) projection [31, 32] (see Figure 4).

An interesting result concerns the separation of the cases

into three regions in terms of the average degree, identi-

ﬁed by respective ellipses in Figure 4. For the two highest

values of average degree, the samples were found to be

more tightly clustered. Furthermore, for hki= 4, the

group is more widely scattered. This result suggests that

the average degree plays a particularly important role in

deﬁning the characteristics of the opinion dynamics in

the considered cases.

Next, we analyzed how the opinions modularity (Q)

changes according to the model parameters. We com-

pute Qfor all network variations, and for hki= 4,8,12

using the same set of parameters we employed in the pre-

vious case. Figures 3(d) (e) and (f ) illustrate examples

of Qfor WS networks, in which well-deﬁned regions can

also be found. For the highest of the considered values

of gand q, high values of Qwere obtained, except for

hki= 12. This result can be understood as an indication

of the existence of echo-chambers. The other parameter

conﬁgurations led to networks without well-deﬁned com-

munities. Similar results were also observed for the other

models.

It is known that the average degree of the network also

inﬂuences Q[33], with a higher average degree tending to

imply lower values of Q. So, for higher average degrees,

Qtends to be lower for all possibilities of parameters (g

and q). Another critical aspect involved in interpreting

the Qmeasurement is setting the limit of detection [34].

For example, in the cases in which D > 4, there are

disconnected nodes that have a null opinion.

Now, we proceed to discussing the results obtained for

diversity and modularity in an integrated way. The mod-

ularity analysis reveals a pattern not evidenced by the

diversity analysis (see Figure 3). More speciﬁcally, for

the highest values of diversity D, the modularity Qwas

found to be more sensitive for grasping the variations. In

a complementary fashion, for the lowest values of mod-

ularity, the diversity was also found to be particularly

responsive (as can be seen in Figure 3). In general, both

measurements are equally important to describe the pre-

sented dynamics behavior. Furthermore, the formation

of echo chamber can happen only for high values of D

and Q. In other words, Ddescribes the eﬀective number

of opinions and Qis a quantiﬁcation of the communities

organization.

Figure 5 illustrates the resulting topologies when start-

ing with BA networks. More speciﬁcally, we present a

heatmap of Qvalues and some respective examples of

the resulting networks. In the well-deﬁned region with Q

next to zero, the dynamics converge to a single opinion

(see Figure 5(a)). Figures 5(b) and (c) were obtained

in regions with intermediate values of Q. In this case,

the communities are not well-deﬁned. Even so, in both

cases there is a high level of diversity, indicated by the

visualization colors. Networks with distinct communities

were characteristic of the regions in Figures 5(d) and (e).

The network shown in Figure 5(e) has communities that

are disconnected among themselves. For some conﬁg-

urations, both behaviors, with and without community

structure, can be found for the same parameter conﬁgu-

rations (see Figures 5(f) and (g)). This situation was also

identiﬁed for another opinion dynamics (ASM), reported

in [11].

B. Context-based reconnection

In this subsection, we explore the eﬀects of the pro-

posed dynamics when the interactions are restricted.

This constraint simulates the fact that people tend to

become a friend of a friend (h= 2). In this case, we con-

sidered only the SBM and GEO networks because these

networks have higher diameters than the other considered

models. So, the eﬀect of the context-based reconnection

is more visible.

By considering the diversity, the results were found

to be similar to the no-reconnection constraint dynam-

ics (see Figure 6(a) (b) and (c)). However, the regions

with lower values of Dare found only for smaller regions

deﬁned by speciﬁc combinations of parameters. Also,

comparing with the previous model, the modularity val-

ues were found to be diﬀerent. In this case, the region in

which Qtends to zero is considerably ampler.

Figure 7 shows some possibilities of resulting topolo-

5

(a)(hki= 4). (b)(hki= 8). (c)(hki= 12).

(d)(hki= 4). (e)(hki= 8). (f)(hki= 12).

FIG. 3. Comparison between Dand Qfor a given set of parameters, in which items (a), (b), and (c) are respective to D, while

(d), (e), and (f) relate to Q. The WS network was considered in this example. The variation of Qfor hki= 12 is much lower

due to the high values of average degrees. Each of the computed points was calculated for 100 network samples.

10 5 0 5 10 15 20

PC1 (75.85%)

4

2

0

2

4

6

PC2 (10.40%)

BA (4)

BA (8)

BA (12)

ER (4)

ER (8)

ER (12)

GEO (8)

GEO (12)

SBM (4)

SBM (8)

SBM (12)

WS (4)

WS (8)

WS (12)

〈k〉= 4

〈k〉= 8

〈k〉= 12

FIG. 4. PCA projection of D, by employing the same set of

parameters as Figure 3. It is possible to observe groups of

samples (identiﬁed by ellipses), according to hki.

gies when starting with GEO networks (hki= 8). Fig-

ure 7(a) illustrates an example for q= 0 (no reconnec-

tions are allowed), characterized by high value of Dand

low value of Q. The opinions were found to deﬁne rel-

atively small groups. In the case of Figure 7(b), there

is also a wide range of opinions, but with the formation

of echo chambers. Furthermore, nodes from completely

separated communities can have the same opinion. Fig-

ure 7(c) shows another possibility of resulting network

with high value of Dand low value of Q. As in the previ-

ous result, isolated nodes can also be found. In summary,

by considering this restriction (h= 2), we found that it

is much easier to have parameters that give rise to high

diversity. However, there is a lower range of possibilities

to obtain high modularity.

IX. CONCLUSIONS

The relationship between topology and dynamics in

complex networks constitutes one of the main topics of

current interest in network science [2]. One related topic

of particular interest consists in the study of opinion for-

mation, and in particular echo chamber formation, in

social networks [7–11].

In the present work, we approached the problem of

echo chamber formation in several types of complex net-

works, as modeled by a modiﬁed Sznajd model. In par-

ticular, we focused attention on the eﬀects of contrarian

opinions. Two situations were studied: (i) the agents

can reconnect only with others sharing the same opin-

ion; and (ii) same as in the previous case, but with the

6

agents reconnecting only within a limited neighborhood.

Several interesting results have been obtained and dis-

cussed. Regarding the analysis based on diversity and

modularity, the obtained results were found to exhibit

complementary characteristics. More speciﬁcally, we

found that some regions of the parameter space are char-

acterized by a gradual variation of diversity while display-

ing very similar modularities, and vice versa. For speciﬁc

parameter conﬁgurations, two types of topologies can be

observed: with or without echo chambers. Furthermore,

one of the factors that strongly inﬂuences the dynamics

was found to be the average degree, which is related to

the formation of the echo chambers. This result means

that the number of friends plays an essential role in the

dynamics. In the case of the context-based reconnections,

it reduced the chances of echo chamber formation, which

also tended to be smaller.

The ﬁndings reported in this article motivate several

further investigations. In particular, it would be interest-

ing to study the eﬀect of the Sznajd model temperature

parameter (spontaneous opinion changes). Another pos-

sibility is to consider weighted and/or directed complex

networks.

ACKNOWLEDGMENTS

Henrique F. de Arruda acknowledges FAPESP for

sponsorship (grant no. 2018/10489-0). Alexandre Be-

natti thanks Coordena¸c˜ao de Aperfei¸coamento de Pes-

soal de N´ıvel Superior - Brasil (CAPES) - Finance

Code 001. Luciano da F. Costa thanks CNPq (grant

no. 307085/2018-0) and NAP-PRP-USP for sponsor-

ship. C´esar H. Comin thanks FAPESP (grant num-

ber 18/09125-4) for sponsorship. This work has been

supported also by FAPESP grants 11/50761-2 and

2015/22308-2.

[1] L. da F Costa, O. N. Oliveira Jr, G. Travieso, F. A.

Rodrigues, P. R. Villas Boas, L. Antiqueira, M. P. Viana,

and L. E. Correa Rocha, Advances in Physics 60, 329

(2011).

[2] L. da F Costa, Luciano, F. A. Rodrigues, G. Travieso,

and P. R. Villas Boas, Advances in physics 56, 167

(2007).

[3] G. Ferraz de Arruda, F. Aparecido Rodrigues,

P. Mart´ın Rodr´ıguez, E. Cozzo, and Y. Moreno, Journal

of Complex Networks 6, 215 (2017).

[4] L. Dalla Porta and M. Copelli, PLOS Computational Bi-

ology 15, e1006924 (2019).

[5] K. Sznajd-Weron and J. Sznajd, International Journal of

Modern Physics C 11, 1157 (2000).

[6] P. F. Gomes, S. M. Reia, F. A. Rodrigues, and J. F.

Fontanari, Physical Review E 99, 032301 (2019).

[7] M. Del Vicario, A. Bessi, F. Zollo, F. Petroni, A. Scala,

G. Caldarelli, H. E. Stanley, and W. Quattrociocchi,

arXiv preprint arXiv:1509.00189 (2015).

[8] P. T¨ornberg, PloS one 13, e0203958 (2018).

[9] L. Jasny, J. Waggle, and D. R. Fisher, Nature Climate

Change 5, 782 (2015).

[10] L. Jasny, A. M. Dewey, A. G. Robertson, W. Yagatich,

A. H. Dubin, J. M. Waggle, and D. R. Fisher, PloS one

13, e0203463 (2018).

[11] A. Benatti, H. F. de Arruda, F. N. Silva, C. H. Comin,

and L. da F Costa, arXiv preprint arXiv:1905.00867

(2019).

[12] M. He, B. Li, and L. Luo, International Journal of Mod-

ern Physics C 15, 997 (2004).

[13] P. Holme and M. E. Newman, Physical Review E 74,

056108 (2006).

[14] F. Fu and L. Wang, Physical Review E 78, 016104 (2008).

[15] R. Durrett, J. P. Gleeson, A. L. Lloyd, P. J. Mucha,

F. Shi, D. Sivakoﬀ, J. E. Socolar, and C. Varghese, Pro-

ceedings of the National Academy of Sciences 109, 3682

(2012).

[16] G. Iniguez, J. Kert´esz, K. K. Kaski, and R. A. Barrio,

Physical Review E 80, 066119 (2009).

[17] Y. Dong, M. Zhan, G. Kou, Z. Ding, and H. Liang,

Information Fusion 43, 57 (2018).

[18] S. Galam, Physica A: Statistical Mechanics and its Ap-

plications 333, 453 (2004).

[19] N. Crokidakis, V. H. Blanco, and C. Anteneodo, Physical

Review E 89, 013310 (2014).

[20] S. Galam and F. Jacobs, Physica A: Statistical Mechanics

and its Applications 381, 366 (2007).

[21] M. E. Newman, Proceedings of the national academy of

sciences 103, 8577 (2006).

[22] L. Jost, Oikos 113, 363 (2006).

[23] E. C. Pielou, The American Naturalist 100, 463 (1966).

[24] M. O. Hill, Ecology 54, 427 (1973).

[25] A. Chao, C.-H. Chiu, and L. Jost, Biodiversity Conser-

vation and Phylogenetic Systematics , 141 (2016).

[26] D. J. Watts and S. H. Strogatz, nature 393, 440 (1998).

[27] P. Erd˝os and R. A., Publ. Math. (Debrecen) 6, 290

(1959).

[28] A.-L. Barab´asi and R. Albert, science 286, 509 (1999).

[29] M. Penrose, Random geometric graphs, 5 (Oxford Uni-

versity Press, 2003).

[30] P. W. Holland, K. B. Laskey, and S. Leinhardt, Social

networks 5, 109 (1983).

[31] I. Jolliﬀe, Principal component analysis (Springer, 2011).

[32] F. L. Gewers, G. R. Ferreira, H. F. de Arruda, F. N.

Silva, C. H. Comin, D. R. Amancio, and L. da F Costa,

arXiv preprint arXiv:1804.02502 (2018).

[33] S. Fortunato, Physics reports 486, 75 (2010).

[34] S. Fortunato and M. Barthelemy, Proceedings of the na-

tional academy of sciences 104, 36 (2007).

[35] F. N. Silva, D. R. Amancio, M. Bardosova, L. da F Costa,

and O. N. Oliveira Jr, Journal of Informetrics 10, 487

(2016).

7

0.00 0.20 0.40 0.60 0.80 1.00

q

0.000.040.070.110.150.18

g

0.0

0.2

0.4

0.6

0.8

1.0

Modularity

(g) (f)

(e)

(d)

(c)

(b)

(a)

FIG. 5. Some examples of the resulting networks for given parameters. The heatmap represents Qvalues obtained after the

execution of our dynamics. Here, we employ the BA network, for hki= 4. Interestingly, for q= 0.40 and g= 0.02 more than

one type of network organization can be obtained. The node colors in the network visualizations represent the opinions. Each

of the computed points was calculated for 100 network samples. The network visualization were created using the software

implemented in [35].

8

(a)SBM (hki= 4). (b)SBM (hki= 8). (c)SBM (hki= 12).

(d)SBM (hki= 4). (e)SBM (hki= 8). (f)SBM (hki= 12).

FIG. 6. Comparison between Dand Qfor a given set of parameters, in which items (a), (b), and (c) are respective to D, while

(d), (e), and (f) relate to Q. Here, we considered SBM networks and the context-based reconnection dynamics (h= 2).

(a)q= 0.00 and g= 0.09 (b)q= 0.10 and g= 0.02 (c)q= 0.30 and g= 0.09

FIG. 7. Visualizations of resultant topologies when starting with GEO networks (hki= 8). The employed dynamics is based on

the context-based reconnection (h= 2). Each of the computed points was calculated for 100 network samples. These network

visualization were created using the software implemented in [35].