Distributing information in small world networks: Four social cases of process of contagion

Simone Belli *, Leonardo Reyes **

* School of Social Sciences, YachayTech, Ecuador** School of Physics, YachayTech, Ecuador

Network Theory and Methods: Combining Structure, Content and Meanings?Workshop on research advances in social and semantic networks31 August ─ 1 September, 2015VU University Amsterdam, Amsterdam, the Netherlands

http://yachaytech.edu.ec

http://www.yachay.gob.ec/

Outline:

- Motivation

- Dynamics on Networks

- Global Activity: a phase transition

- Model System, Results

- Cases Studies

- Conclusion and Discussion

Collective behaviour

individual vs.

collective states

appropriate dynamic laws ?

Three states:

Rest (Susceptible)

Excited

Refractory (Passive)

excitable dynamics: three states, a threshold, a recovery time

Transitions between states: interaction with neighbours

A excited cell: an activist

→ people becomes an activist when in contact with an activist, but

with probability r. The parameter r is a measure of the excitability of thepopulation. It can also be interpreted as a degree of confidence in activismor as a degree of confidence in the movement.

The model (Greenberg Hastings):

We start with a regular network, with each node conected to it's K nearest neighbours.

Then we rewire each connection with probability p.

Watts-Strogatz Small-World Network model

F: average density of neighbours in the excited state

A point in these figures corresponds to a collective active state

http://arxiv.org/abs/1505.00182

We can switch to a colletively active state by increasing K, p or r

At the transition, there are long range correlations in the system: large fluctuations

MethodologyThe case-study is based in the Spain area between 2011 and 2014 on four social institutions and affective processes involved in what normally is referred to as social movement:

• Actor 1 from Plataforma de Afectados por la Hipoteca (PAH - Movement of Mortgage Victims);

• Actor 2 from 15Mpedia/InformaSol/Padland/Peoplewitness;

• Actor 3 from Candidatura d'Unitat Popular (CUP - Popular Unity Candidates);

• Actor 4 from Asamblea Vivienda Centro (AVC - Housing Center Assembly).

We present these institutions because they embody a type of innovation in the Spanish scenario. They offer different examplesof how information is distributed in small-world networks through narratives and actions

AnalysisWe show different dynamics within small-world networks of citizens’ organization by going through the following steps:

1. Identifying alliance patterns;

2. Look for robust small-world attributes and how are constructed;

3. Interpreting the three modes of our model (excited, passive, and susceptible node).

Our interest here focuses on distributed information of different small-word networks and processes of contagion within specific local settings.

1. Identifying alliance patterns.

Actors: Excited nodes and susceptible nodes at time t

In indignados movement in Madrid 2011, the network is constructed by multiple excited nodes:

Actor 2: “And finally, a map was constructed to presents these networks and the community begins to use this technology. The first version of the map starts in “Democracy Real Now" platform, where pro-mobilization citizenship, like 300 associations and collectives, begins to share information for a call to protest, visiting centers, associations, social centers, occupied places, to feed the protest, to convert this event in a massive event.”

Context of the contagion: May of 2011, Madrid (Spain). The crisis affected the society. At time t: 300 excited nodes that share and move information to others nodes. They start the distribution of information (i.e. a call to protest)

At time t+1: Some susceptible nodes remains at the same state, don’t share this information with others nodes. Somesusceptible nodes are affected to this information, and share the information. This dynamic happens for the contagious process to convert a susceptible node in an excitated node.

At time t: At time t+1:

• Criticality rcrit in society can be achieved in some contexts and not achieved in others.

• Where the susceptible nodes may have not a close relationship (with excited nodes) but at criticality can begin to share information to others nodes that usually don’t have any connection to them (i.e West End’scase in Granovetter, 1976).

• Our paramenter r: Jacobs (1961) stresses the importance of a few people, “hop-skip”, because of theirunusual sets of connections may bring together disparate parts of a community. This process is the key to provoke or not provoke a collective contagious in small-world networks. These hop-skip are the excitednodes that can communicate with many other nodes in a critical state of the system. The number of thesehop-skip marking the difference between the success or fail of a social movement.

2. Looking for robust small-world attributes and how are constructed.

Robust ties between nodes of networks means strong links of trust between actors.

Actor 2 explains how indignados movement was distributedfrom the centre to the periphery of the city of Madrid thanksto these robust small-world ties.

Actor 2: “Assemblies and meetings continue months later that 15-M, in the squares of different neighborhoods. Many people understand this distribution like a fade of the focus of the movement, but probably it is not a correct analysis. In the neighborhoods, the assemblies have encountered the perfect context to act from the basis of the society. For this, CUP ((Actor 3)), Podemos ((“We can”)), Partido X ((X Party)), Carta por la Democracia ((“Letter for Democracy”)) and many others social institutions, found the perfect playground to construct the technology of the horizontal democracy. It is a step in which the 15-M begins its participation decline, it doesn't have the same start force, but it arrives to a limit about what people and tools can do to an assembly movement. And when this limit is arrived, the people find other forms to continue the fight, the empowerment. It is a long process that arrives until today, where we have played, tried and gave possibilities in other places. In this route we have arrived to social institutions yet existed where each technology that we have used, we have loved it, because it was a form of empowerment. “

• Empowerment is achieved by increasing the connectivity parameter K.

• Empowerment and strong positive emotions, which enforces confidence and that can be viewed as increasing the parameter r, helps to construct these robust ties between nodes. Information in this extract circulates from the core to the periphery to the movement without lost the force and the intensity.

• Robust ties are constructed thanks to trust-shared between actors of this small-world.

Actor 2: ‘Wow, this mail was sent from that person, that I had never spoken about these things, and now this person is interested and care about ourselves and to not dissolve a protest that I've never mentioned with that person.’"

• In a critical state, some nodes that normally do not share information, suddenly communicatebetween them. The SMS message from an excited node to a susceptible node causes surprise in Actor 2.

• Susceptible node at time t+1 become an excited node because share the same statement in thenetwork.

• Maybe this susceptible node can be described like a contagious healthy, a node which is sensible to the situation and agrees with the change of status.

• Actor 4 explains that a collective action, (i.e. collecting signatures), is useful to create robust ties to share

information and to establish connections between nodes. Some actors that sign are susceptible nodes at

time t, and at time t+1 become excited nodes thanks to this strategy of collecting signatures, creating

new ties.

Actor 4: “Our work is empowering persons and to borrow the barrierthat you are the case and I am the activist. It is a progressive workto elevate the person to empowering people.”

Strategies to construct a network

Our probability of contagion r is the probability of empowerment that excited nodes transmit to susceptible nodes. Teaching how borrow barriers between activism and no activism status.

Actor 4: When someone enter in an assembly, they need to understand that the case are shared. My

problem is your problem and vice versa. There is not only your problem. Everything is collectivized.

Nobody is an expert. But we learn to be an expert in the process. Empowering is a conjunction of

networks. An assembly cannot exist without these networks.”

• At time t: The sponsor figure is an excited node that know a susceptible node to pass information on Housing Center Assembly, and to present her in the Meeting Monday Evening.

• At time t+1: the susceptible node will be an excited node and she will be a sponsor to another susceptible

node.

• Networks like these criticize the individualism to look for a subjectivity transformation to take

empowerment, it is the key to understand how robust small-world attributes are constructed.

The sponsor figure

3. Interpreting the three modes of our model (or how information is circulated in small-world network following the Greenberg-Hasting’s model).

Actor 2: The common problem is that many times the communication management is centered in one person thatshe is saturated of all this information, too many mails, too many tweets, and she cannot continue and so theassembly lost connection, it is becoming marginalized and isolated. Many of these assemblies disappear becausethe voice doesn't arrive.”

• Information is distributed in this network apparently following a chaos: From an excited(and saturated) node to the rest of the network.

• After these early days of saturated information, many actors of the indignados movement needed a disconnection to avoid falling into a burnout situation. Actor 2 explains how he removed himselffrom different mailing lists and whatsapp, line, telegram groups, and turns off mobile phone alerts.

• So the contagion is interrupted, many actors becomes passive nodes.

• The probability r is so important for the success of a movement: The parameter r is a measureof the excitability degree of a population. In our case is interpreted as a degree of confidence in activism or in the movement, the number of HOP-SKIPS, and the empowerment constructedbetween actor.

Conclusions• Network processes are the movement, the distributed information is the movement;

• Sharing information in these small-world networks have the common characteristic of all complex systems, that they display organization without any external organizing principle being applied, a central characteristic is adaptability (Amaral and Ottino, 2004);

• We have observed how is important at time t have excited nodes to contagious the rest of the nodes, and how these excited nodes have to improve empowerment at rcrit to the rest of the small-world.

The application of this physical model to a social context is interesting for two reasons:

1. It helps to explain how social movements have success or not to distribute information.

2. We can explain how at rcrit many systems respond to the same way to a critical situation in different areas.

Next step: It will be represented to apply this contagion model in semantic networks to understandhow actors share the same information and use the same terms in a contagious dynamic.

Bibliography

• Amaral L., Ottino J. (2004). Complex systems and networks: challenges and opportunities for chemical and biological engineers. Chemical Engineering Science, 59, 1653-1666.

• Granovetter, M. (1976). Network sampling: Some first steps. American Journal of Sociology, 1287-1303.

• Jacobs, J. (1961). The Death and Life of Great American Cities. New York: Random House.

• Watts, D. J., Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393(6684), 440-442.

Distributing information in small world networks: Four social cases of process of contagion

Simone Belli *, Leonardo Reyes **

* School of Social Sciences, YachayTech, Ecuador** School of Physics, YachayTech, Ecuador

Network Theory and Methods: Combining Structure, Content and Meanings?Workshop on research advances in social and semantic networks31 August ─ 1 September, 2015VU University Amsterdam, Amsterdam, the Netherlands

http://yachaytech.edu.ec