Reinforced communication and social navigation generate groups in model networks

To investigate the role of information flow in group formation, we introduce a model of communication and social navigation. We let agents gather information in an idealized network society and demonstrate that heterogeneous groups can evolve without presuming that individuals have different interests. In our scenario, individuals’ access to global information is constrained by local communication with the nearest neighbors on a dynamic network. The result is reinforced interests among like-minded agents in modular networks; the flow of information works as a glue that keeps individuals together. The model explains group formation in terms of limited information access and highlights global broadcasting of information as a way to counterbalance this fragmentation. To illustrate how the information constraints imposed by the communication structure affects future development of real-world systems, we extrapolate dynamics from the topology of four social networks.

Figure 1

(Color online) Modeling communication and social navigation. 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. For example, the number of bars in ${\mathcal{M}}_i\left(k\right)$ corresponds to the number of elements $m_i\left(k\right)$ of agent $i$’s interest memory that are allocated to agent $k$, with the black bar representing the global and fixed interest. (a) Communication $C$. 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 (agents $i$ and $j$ replace a fraction $\mu$ of their interest memory with $k$. Similarly, both agents reciprocally increase their interest in the other agent) and the information about each other. [Both agents update their recollection and quality memories: ${\mathcal{M}}_i^{\mathrm{rec}}\left(j\right)=j$ and ${\mathcal{M}}_i^{\mathrm{age}}\left(j\right)=0$ for $i$, and ${\mathcal{M}}_j^{\mathrm{rec}}\left(i\right)=i$ and ${\mathcal{M}}_j^{\mathrm{age}}\left(i\right)=0$ for $j$.] The agent with the oldest memory about $k$ updates her information about $k$. [For example, if ${\mathcal{M}}_i^{\mathrm{age}}\left(k\right)>{\mathcal{M}}_j^{\mathrm{age}}\left(k\right)$, agent $i$ makes the updates ${\mathcal{M}}_i^{\mathrm{rec}}\left(k\right)=j$ and ${\mathcal{M}}_i^{\mathrm{age}}\left(k\right)={\mathcal{M}}_j^{\mathrm{age}}\left(k\right)$.] (b) Social navigation $R$. A random agent $i$ selects an agent $k$ proportional to her interest in $k$ and recollects the friend $j={\mathcal{M}}_i^{\mathrm{rec}}\left(k\right)$ who provided her with information about $k$. Subsequently agent $i$ forms a link to her friend’s friend, that is, $j$’s friend $l={\mathcal{M}}_j^{\mathrm{rec}}\left(k\right)$, to shorten her distance to $k$. To keep the number of links fixed in the network, one random agent loses one random link.

Figure 2

(Color online) Local communication generates social groups. From left to right, the networks are generated with increasing interest size $\eta$ [$\eta =1$ in (a), $\eta =10$ in (b), and $\eta =100$ in (c)]. As a function of $\eta$, the bottom panels illustrate the typical module size in (d), the cliquishness in (e), the maximum degree in the network in (f), and social horizon in (g). Simulations are based on $C∕R=10$ communication events per link for each social navigation event in the system, with system size fixed to 100 agents and 150 links. The results are robust to a 100-fold drop in the communication-to-rewiring ratio, but break down at an even lower communication rate when only small groups can be maintained by the communication. In addition, panels (d)–(g) illustrate the dependence of the rate of interest adaptation, or flexibility, with a $\mu =0.01\%$ change of the interest elements per communication event for stubborn adaptation (black lines), and a $\mu =1\%$ change for flexible adaptation (shaded lines). Stubborn adaptation corresponds to a flexibility of 15% change in the interest memory when all links are changed once, whereas flexible adaptation corresponds to complete reallocation. Data are collected from 1000 samples over a time corresponding to 1000 rewirings of each link in the network. Error bars represent standard deviation.

Figure 3

(Color online) Dynamic extrapolation from snapshots of real networks. The dynamics in (a)–(e) were generated from the karate club network [32] by setting the interest size $\eta =30$ to match the typical module size of the original network. The networks are from left to right: (a) the original karate network, (b) the network halfway through the simulation, and (c) the network in the end of the simulation when each link on average has been rewired 500 times. Under the networks, panel (d) illustrates covariance between the total interest in the black node and its degree. Panel (e) shows how the information divergence of the interest memories between the black and the shaded node changes over time, together with the shortest path in the network between the two nodes. Similarly, the dynamics in (f)–(j) were generated from the dolphin social network [33] by setting $\eta =12$ to match the typical module size of the original network.