Modeling gossip networks

Description

Motivation

Work has been done on how information passing through networks influences strength of edges it passes over (e.g. neurons), but nothing done on how information passing alone one edge affects strengths of other edges in network.
Work has also been done to see how structure of network influences the flow of gossip / spreading of rumors (e.g. ??), but nothing has yet been done on how gossip affects structure of network.

We propose to build some simple models to explore how gossip influences social network structure. We define gossip as information passed between two individuals, A and B, about a third individual C, that has the potential to influence the strength of all three connections AB, BC, and AC.

Simplest (Null?) Model

schematic for modeling two possible ways in which gossip affects network structure -- both cases are where individual A passed gossip to individual B about individual C

start with fully-connected network with N nodes, pick triads of connected nodes
run simulations under two different scenarios:

negative gossip: pick connected triad, strengthen one connection and weaken other two and repeat at random (potentially drop connections of they fall below a certain threshold)
positive gossip: pick V-shaped connection (see figure), add third connection

[NOTE: I think it's important to keep the sum of the weights of all edges in the network constant. I think this is easily done for negative gossip, but less obvious how to do so for positive gossip...]

[NOTE (Milena): Maybe in the case of positive gossip we should start from a sparse random network and see to what structure the process converges (complete newtork?). Actually, I was thinking that if we use the same logic as in negative gossip, on of the the two initial links has to become stronger since the sharing of gossip increases trust. In this case, the sum of the weights cannot be kept constant. Alternatively, we can assume that if B shares with A positive gossip about C, A diverts time from her relationship with B and starts hanging out with C. That way the sum of the wights could be kept constant.]

what is the resulting network? do simulations using either of these rules alone converge? how are the resulting networks different?

(a priori expect that negative gossip will result in network becoming more fragmented and positive gossip will result in the network becoming more connected)

Extensions/Variants

initial network structure: start with a different type: small-world, random, other?
non-random node choice: pick nodes with respect to their overall connectedness (either picking strongly or weakly connected individuals more)
non-random edge choice: stronger (or weaker) edges are more likely to have gossip passed along them
combined gossip types: pass both positive and negative gossip through network, vary % positive
individual variation: tendency to gossip, gossip target, impact of gossip
individual behavior: individuals can choose to pass on the gossip, ignore it, or reject the gossiper and sever the connection
Can individuals influence their location in a network (e.g. increase centrality) by changing their gossiping frequency?
How does gossip spread in different networks?
How do individual properties (e.g. range of social circle, poverty, wealth, the information itself, or geographic location) speed up or slow down the spread of gossip?

Predictions

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Relevant Literature

The science of gossip

The effect of networks on the spread of gossip is well understood: some of the social dynamics at play include biases in the selection of trusted third parties (one draws a sample of information consistent with one’s predisposition), the reinforcement of opinions in dyads due to an etiquette mechanism, the exaggeration of information in triads due to echo effects. -- Milena, could you include any references for these examples?

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Members

Original Discussion

It could be neat to develop a model of gossip networks. If you define gossip as information passed between 2 individuals (call them A and B) about a third party (C), then the act of gossiping has the potential to change the status/connection strength of all parties involved (e.g. maybe strength A-B, and weaken A-C and B-C bonds). Essentially passing information along a path in the network changes the value of BOTH edges in the direct pathway as well as other edges in the network. These are just preliminary ideas, but perhaps we could model how gossip tendency/frequency influences the structure of a network. Also, is it possible for individuals to influence their location in a network (e.g. increase centrality) by changing their gossiping frequency? (Although this is potentially a complicated rather than complex model idea...) Let me know what you guys think! Allison Shaw

Milena Tsvetkova: This is a very interesting idea from sociological point of view. The effect of networks on the spread of gossip is well understood: some of the social dynamics at play include biases in the selection of trusted third parties (one draws a sample of information consistent with one’s predisposition), the reinforcement of opinions in dyads due to an etiquette mechanism, the exaggeration of information in triads due to echo effects. However, I am not aware of any studies that investigate how the spread of gossip affects network structure. My work is on the coevolution of behavior and social networks so we should talk!

XOXO Chang Yu:Interesting! Gossip is not always bad. If we can model its spreading mechanism, it could help especially when you want to spread information unofficially. I get some inspirations from Tom’s last lecture on Friday. In the gossip network, what kind of properties of these agents can speed up or reduce information spread, the range of social circle, poverty, wealth, the information itself, or even the locations of houses in a community? I think we may model the different spreading results under different properties.

David Brooks: I agree that this concept of Gossip Networks is a generic for the analysis of several potential problems. I would like to talk to you about your intended direction and methods.

Gustavo Lacerda: sounds like some interesting dynamics, but how are you going to get data?

Milena Tsvetkova: This article may be a good starting point for a first discussion: it suggest that gossip is a mechanism for bonding social groups. Should we try and schedule a brainstorming session?

Allison Shaw: Let's meet tomorrow (Thursday) around lunchtime (maybe 1pm after we've eaten?) to discuss this project in more depth -- anyone is welcome to join in!

Roozbeh Daneshvar: I'd like to join this team. It's good that we are doing a research with the same theme (Contagion in Networks). I can share the results from the heterogeneous network research group.