Representing the spread of a meme through a social network

Over the past several years, memes have evolved into an influential sensation that rapidly spreads information among internet users and has attracted public interest as an alternate way of communicating. The concept of a “meme” was derived from the ancient Greek root “mimeme” meaning “imitated thing” and is defined as a noun that conveys the idea of a unit of cultural transmission or a unit of imitation (Dawkins 1976). They proliferate within social networks by means of email, instant messaging, forums, blogs, and other forms of social media (Bauckhage 2011).

So how exactly does a meme spread throughout a network and how does it influence those individuals? One way a social network can be accurately represented is through the Barabási–Albert (BA) model. The BA model consists of a well-known algorithm that uses a preferential attachment apparatus to generate random scale-free networks (Barabási & Márton 2017).

Preferential attachment is a probabilistic mechanism that refers to the notion that the more connected a node is (in our case, a node represents a person), the more likely they are to receive new links or new “acquaintances” (Barabási & Márton 2017). It can be thought of intuitively; the more links a person has, the more well-known that person is and the more relations they have with other people. When somebody new enters into the community, they are more likely to connect with that individual with many links than with somebody who has less links and is relatively unknown (Chen & Lee 2016).

In addition to preferential attachment, a phenomenon also present in social networks is the k-complex contagion model. Complex contagions describe the diffusion of behaviors in a social network that requires influence from multiple contacts in order for an adoption of a belief to be successful (Ebrahimi, et al. 2017). The model progresses in rounds; in any round, any node with at least k > 1 “infected” neighbors also becomes infected (Ebrahimi, et al. 2017). Complex contagions often depend on numerous social and economic factors and are more commonly well known to model the acceptance of new beliefs, fashion trends, and technology innovations (Ebrahimi, et al. 2017).

In our particular model, we aimed to demonstrate the effect of complex contagions on the spread of a meme in a social network structured by preferential attachment. We first created a foundation demonstrating the preferential attachment mechanism using NetLogo (Wilensky & Rand 2015), with the total population set by the observer (3 - 200 agents). Each agent is initially set to a small size and is colored white. The instigator of the meme is then chosen at random or can be chosen to be the most popular individual (the agent with the most links) and is set to a slightly larger size for distinction. The instigator is set to the color blue to demonstrate that they have seen the meme and intend to share it with their link neighbors. Links have no specification; they can represent acquaintances, friends, or family members. Each agent, aside from the instigator, is randomly assigned a “funny” value that ranges between 0 – 99 that will later play a role in if they independently perceive the meme to be funny or not. Agents have the potential to view and/or share the meme and form an opinion up to six times.

The video below demonstrates the creation of a social network within the model:

Complex contagions interact with the model as a toggle option. When turned on, the contagion dynamics sets a probability of transmission that varies with the extent of exposure. We hypothesized that complex contagions, when active within the model, would be a significant influence on the spread of a meme by positively altering more individuals’ perceptions of the meme and thereby contributing to its popularity by encouraging that individual to share it with others.

The observer sets the population, instigator (random or popular), Meme Popularity Level, and whether complex contagions are active. When complex contagions are inactive, the instigator attempts to share the meme with each of their links and the receiving individuals will then independently decide if they believe the meme to be funny. This is determined by their randomly assigned “funny” value and whether it is less than or greater than the Meme Popularity Level. If it is less than the meme popularity level, they believe the meme is funny, turn blue, and attempt to share it with their links that have yet to “see” the meme. If their funny value is greater than the meme popularity level, they do not believe the meme is funny and thus turn violet and will not share the meme with any of their links. This continues until the meme is no longer being shared by any of the agents.

Alternatively, if complex contagions are switched on, the method in which the agent determines if the meme is funny is altered. The first time an individual sees the meme, their opinion is formed via their funny value (the process mentioned above). The second and third time an individual sees the meme, their opinion will take on the majority of their neighbors’ opinion. So if a given individual has more links to individuals that find the meme funny than links to individuals who do not, they will automatically adopt the perception that the meme is funny when it is shared with them and will continue to share it with others regardless of their originally assigned funny value. It also works reversely; if a given individual has more links that do not find the meme funny, they will automatically decide that the meme is not funny and will not share it with any of their links. The sixth potential time the individual views the meme, they will automatically believe it to be funny due to the number of repeated exposures and will stop sharing the meme at this point. The model is over once agents can no longer share the meme.

The video below demonstrates the spread of a meme among 150 agents at an 80% Meme Popularity Level, Popular Instigator, and Complex Contagions turned on:

The model was ran 10 separate times (adjusting the Meme Popularity Level in 10% intervals) for both random and popular instigators with complex contagions active and then 10 times each again for random and popular instigators without complex contagions. The population and their given funny values remained constant in order to accurately detect changes in the data. The percentage of trendiness was recorded for each trial.

The results of the data yielded that Complex Contagions gave higher trend percentages when the meme was at a lower popularity level (~10 – 50%) and evened out to match the trends of Independent Influence in higher popularity levels (60% +). Additionally, popular instigators were found to be more influential in spreading the trend when the Meme Popularity Level was low compared to their random counterparts, but there was no significant difference in trendiness when the Meme Popularity Level was approximately 50% or higher. Overall, complex contagions with a popular instigator resulted in the highest trend when the Meme Popularity Level was set to a percentage at or below 40%, and Independent Influence with a Random Instigator resulted in the highest trend when the Meme Popularity Level was at 50% or above.

The results of the simulation suggest that complex contagions are better for spreading a meme at a low popularity level than via independent influence, which confirms a component of our hypothesis. But it is interesting to note that complex contagions were just as effective as independent influence (if a little less effective) beginning around a 40% popularity level. Furthermore, having a popular instigator is helpful when trying to spread an unpopular meme, but if the meme is already at a high popularity level, there is not a significant difference in trendiness when the instigator is chosen randomly or chosen for popularity.

These implications are consistent with both existing theories of preferential attachment and complex contagions. It makes sense that complex contagions are more effective at spreading the meme at a lower popularity level, but when the meme is at a high level, the popularity makes up for the difference between the two conditions. In regards to the instigator, the results cohere with the notion that if they are more popular, they would be more effective at spreading a meme because they are able to contact more people at one given time than when the instigator is chosen at random and may have fewer links. This pattern is evident in some cases of real-world examples of proliferation of information across the internet, and from this simulation we can better understand the flow of information and what factors promote or inhibit the spread. These insights can further be applied to solve countless problems such as social innovation, organizational change, or cultural evolution.

References

Barabási Albert-László, and Pósfai Márton. Network Science: THE BARABÁSI-ALBERT MODEL. Cambridge University Press, 2017.

Bauckhage, Christian. “Insights into Internet Memes.” Association for the Advancement of Artificial Intelligence, 2011.

Centola, Damon. “How Behavior Spreads: The Science of Complex Contagions (Introduction).” How Behavior Spreads, 2018, pp. 1–10., doi:10.23943/9781400890095-002.

Chen, Zhuo, and Jay Lee. “An Agent-Based Model for Information Diffusion over Online Social Networks.” Kent State University, 2016.

Dawkins, Richard. The Selfish Gene. Oxford University Press, 1976.

Ebrahimi, Roozbeh, et al. “How Complex Contagions Spread Quickly in Preferential Attachment Models and Other Time-Evolving Networks.” IEEE Transactions on Network Science and Engineering, vol. 4, no. 4, 2017, pp. 201–214., doi:10.1109/tnse.2017.2718024.

Jordan, Mark A. “What’s In A Meme?” Richard Dawkins Foundation, 4 Feb. 2014, www.richarddawkins.net/2014/02/whats-in-a-meme/.

Wilensky, U. & Rand, W. (2015). Introduction to Agent-Based Modeling: Modeling Natural, Social and Engineered Complex Systems with NetLogo. Cambridge, MA. MIT Press.