Modeling the origin of interest groups
This applet visualizes a model of communication and social climbing. The two figures below illustrate the two components of the model. A more detailed description can be found under "Instructions". To run the applet you need Java Runtime Environment installed.
Communication

Communication A random agent i selects one of her neighbors j proportional to her interest in j. Similarly either of the two agents selects agent k from her interest memory. When agents i and j communicate, they update: their interest memories, the information about each other, and the agent with the oldest memory about k updates her information about k.
Communication

Social climbing A random agent i selects an agent k proportional to her interest in k and recollects the friend j = Mirec(k) who provided her with information about k. Subsequently agent i forms a link to her friend's friend, that is j's friend l = Mjrec(k), to shorten her distance to k. To keep the number of links fixed in the network, one random agent loses one random link.

Communication and social climbing generate interest groups. Nodes are colored according to their relative interest in the node with the blue halo versus the node with the orange halo. The node sizes illustrate the selected blue node's interest in the different nodes, which correspond to the height of the bars in the interest memory to the right. The green path from the selected orange to the selected blue node traces the information percolation path between the two nodes, with bright green for new information and dark green for old information. To move a node, select the mouse function "Move node" and click on a node and drag the node with pressed mouse button to a new position and release. To add or remove a link, select "Rewire link" and click and drag from one node to another node. To change the source oor target of the information path, select "Move path" and move one of the halos to a new node by clicking and dragging. This can also be achieved by dragging the small rectangles indicating the selected nodes under the interest memory.
Instructions

N=75 agents connected by L=110 links communicate with each other to acquire new information about agents they find interesting. What they find interesting is what their friends talk about.

To get better access to new information, an agent can use the friend who provided her with the most recent information about the agent in question and establish a new connection: The friend has a friend that has even newer information information about the interesting agent. The communication level and the interest allocation in the applet change the strength of the two main components of the model:
1. Communicate to exchange information and interests with friends
→ map of network
→ interest in other agents

2. Climb the social ladder to shorten information pathways
→ dynamic network

Output

In the applet, the network illustrates the pattern of interactions between the agents. Two agents can only communicate with each other if they are connected by a link. The node sizes represent the agents interest in the node with the blue halo.

The lower right panel follows two agents over time, the nodes with blue and orange halos (they can be changed as described in the caption). The panel shows the network distance and the divergence between the priorities of the two agents. When two agents are close to each other in the network, their priorities are typically similar. The panel therefore demonstrates the popular saying: "Tell me who your friends are, and I will tell you who you are."

The histogram on the right hand side illustrates the actual priorities of the agent with the blue halo (log scale). High value means high priority, and implies that the agent often would like to talk about or reconnect to the agent in question.

The color of the bars represents the age of the information that the blue agent has about the agent in question. The age of the information measures the quality of information: High quality corresponds to new information (light green) and low quality corresponds to old information (dark green). The information is aging as it percolates from source to target and the agents will therefore new information about close neighbors and old information about remote agents.

Details

Each agent i has an individual memory Mi that consists of three one-dimensional arrays
  1. Mirec, a recollection of who provided the information,
  2. Miage, the quality (age) of the information,
  3. Miint, the interest preferences in agents.
The first two arrays have the same length as the number of agents N in the system and allow each agent to form a simple local map of information flow in the network: The recollection memory contains N names of the friends Mirec(j) that provided information about agents j = 1...N. To compare the quality of the information with friends, the quality memory stores the age of each of the N pieces of information. The memories Mirec and Miage constitute agent i's local map of the social structure.

The third array is the interest memory and it contains Nη ≥ N names of agents to a proportion that reflects the agent's interest in these agents. The first N elements of the interest memory form the global interest and the remaining Nη-N elements form the local interest. The N elements of the static global interest are fixed to each of the N agents' names, whereas the elements in the local interest are updated by communication. As a consequence, each time an agent selects a topic of communication or a goal of social climbing, this selection is biased toward recent gossiping to an extent given by the parameter η. With the interest memory, we incorporate simplified human behavior by introducing rules that mimic individuals' choices when selecting who they want to talk about or connect to.

The network model is executed in time steps, each consisting of one of the two events
  1. Communication C,
  2. Social climbing R,
where selection of communication topic and social-climbing direction are associated to interests as described in Figs. 1 and 2, respectively.

Communication

Fig. 1 Communication A random agent i selects one of her neighbors j proportional to her interest in j. Similarly either of the two agents selects agent k from her interest memory. When agents i and j communicate, they update: their interest memories,a the information about each other,b and the agent with the oldest memory about k updates her information about k.c
aAgents i and j replace a fraction μ of their interest memory with k. Similarly, both agents reciprocally increase their interest in the other agent.
bBoth agents update their recollection and quality memories: Mirec(j) = j, Miage(j) = 0, Mjrec(i) = i, Mjage(i) = 0.
cFor example, if Miage(k) > Mjage(k), agent i makes the update Mirec(k) = j and Miage(k) = Mjage(k).


The depicted memory illustrates, from left to right, agent indices for the recollection memory, clocks for the quality memory, and bars for the interest memory. The number of bars corresponds to the number of times an agent occurs in the interest memory, with the black bar representing the static global interest.

Communication

Fig. 2 Social climbing A random agent i selects an agent k proportional to her interest in k and recollects the friend j = Mirec(k) who provided her with information about k. Subsequently agent i forms a link to her friend's friend, that is j's friend l = Mjrec(k), to shorten her distance to k. To keep the number of links fixed in the network, one random agent loses one random link.

We initiate each simulation by filling the local interest memory with random names. Later, when agent i communicates with or about another agent j, the name of j randomly replaces a small fraction of i's dynamic interest memory. Thereby old priorities will slowly fade as they are replaced by new topics of interest. We denote by mi(k) the number of elements of agent i's interest memory that is allocated to agent k. When selecting communication topic or aim of social climbing, agent i, by choosing a random element in her interest memory, selects agent k proportional to mi(k). For η=1 any topic is selected with equal chance, whereas larger η increases the ratio of proportionate local interest selection to random global interest selection. η is regulated by the scrollbar "Interest allocation", and is large when "local" is dominating.

We increment the age Mage by one for all agents when every link has participated in, on average, one communication event in the system. Because every agent always has information with age 0 about itself, Miage(i) = 0, the age of the information about an agent becomes older as it by communication percolates away from the agent in the network. Consequently, when two agents communicate about a third agent and evaluate the quality of the information based on its age, the agent with the newest information tends to be closer to the third agent. This guarantees that the recollection memory becomes a working map of the social structure.

The social climbing, which corresponds to rewiring of the network, is a slow process compared to gossiping. Thus, the results are most interesting if communication dominates over social climbing (C >> R), which can be adjusted by the scrollbar "Communication level".
Philosophy

Social networks represent communication channels and therefore also limits on information access in a society. The applet considers agents who try to bypass these information constraints. Thereby they drive an ever-changing social network. A dynamics of individual social climbing on social ladders that may fragment or dissolve with the ongoing climbing of all the other agents; a "red queen" dynamics, in which agents keep on climbing just barely maintaining an acceptable social position.

Agents improve their positions in the ever changing network based on their limited local perception of the system. To maintain this perception, they continuously communicate with connected friends to obtain information about other agents in the network. This indirect information-gathering resembles the frequent gossiping in everyday life. The local information gathering is associated with building of interests, such that communicating agents gradually align their interests. The agents also attempt to adjust their position in the network, using acquired information to build new links toward other agents they are interested in. Thereby the local perception of a social hierarchy feeds back to the social structure between the agents. A feedback in which an increased ratio of local gossip to global broadcasting guides the network toward increased social fragmentation.

The social fragmentation is triggered by the limits set on the individuals' information horizons, specified by the extent that individuals gather interests from neighbors rather than from global broadcasting. This can directly be observed in the applet by regulating the scrollbar "Interest allocation".

In addition, the applet contains a scrollbar that regulates the amount of communication relative to social climbing. When the communication level is low, transmitted information is meaningless and the network becomes random, without the possibility to evolve modules or nodes with high degrees. The applet accordingly illustrates how the distribution of information guide the self-organization of social structures: from random chaotic networks to hierarchical networks with large hubs, or to fragmented social networks.

The three main feedback mechanisms of social dynamics that the applet incorporates:
  1. Network centrality
    being central ↔ new information

  2. Positive assortment
    agent's interest ↔ neighbor's interest

  3. Group formation
    move toward interest ↔ localization of interest.

Without local interests only the first feedback is active, which in itself drive the network toward a broad degree-distribution. The two subsequent reinforcements generate interest groups.