Modeling self-organization of communication and topology in social networks

This paper introduces a model of self-organization between communication and topology in social networks, with a feedback between different communication habits and the topology. To study this feedback, we let agents communicate to build a perception of a network and use this information to create strategic links. We observe a narrow distribution of links when the communication is low and a system with a broad distribution of links when the communication is high. We also analyze the outcome of chatting, cheating, and lying, as strategies to get better access to information in the network. Chatting, although only adopted by a few agents, gives a global gain in the system. Contrary, a global loss is inevitable in a system with too many liars.

Figure 1

(Color online) Communication as modeled in this paper: Agents communicate with their neighbors in the network about a third target agent and estimate the quality of the information by its age. The agent with the oldest information adopts the viewpoint of the agent with the newest information. Here, agent $\mathbf{A}$ learns that $\mathbf{B}$ has newer information about $\mathbf{H}$, disregards its old information, and changes its pointer towards $\mathbf{H}$ to $\mathbf{B}$. The information in the bottom bubbles are $\mathbf{A}$’s knowledge about the network based on communication with its neighbors before and after the communication event with $\mathbf{B}$: For each agent (top row) the time of the most recent information is stored (middle row) together with the acquaintance that provided the information (bottom row).

Figure 2

(Color online) Rewiring as modeled in this paper: Agents create new contacts based on their available information (see Fig. 1). In this example $\mathbf{A}$ uses $\mathbf{B}$, the agent that $\mathbf{A}$ got the newest information about $\mathbf{H}$ from, to get a better position relative to $\mathbf{H}$. $\mathbf{A}$ then creates a link to $\mathbf{E}$, the agent that $\mathbf{B}$ got its information about $\mathbf{H}$ from. Thereafter a random agent loses a random link, in this example the connection between $\mathbf{C}$ and $\mathbf{D}$.

Figure 3

(Color online) Illustration of the two types of social bonds in the network at two different levels of communication. (a) and (b) show the communication backbone over which agents communicate. (c) and (d) show the perception network associated to the agents’ directions to other agents in the network. The pointers are colored black when they are updated and coincide with active connections. In the network with high communication (right panel), almost all pointers overlap with the communication backbone.

Figure 4

(Color online) Illustration of the feedback of communication on the topology of both communication backbone and perception network at four different levels of communication $C$. $C=1$ corresponds to on average one communication event per link and rewiring event. Network size is $N=1000$ agents connected by $L=2500$ links in the communication backbone.

Figure 5

(Color online) The topology of the generated networks at two different levels of communication $C$. $C=0.01$ in left panel and $C=1$ in the right panel. The first row shows the correlation profile, the second row the average neighbor degree, as a function of degree, and the third row the clustering measured as the number of triangles. All measures are compared with randomized counterparts of the networks with unchanged degree sequence.

Figure 6

(Color online) Topological consequences of introducing strategic agents, quantified through efficiency (defined as $E=⟨1∕d_{ij}⟩$) respectively maximum degree of both the strategic agents (circles) and the remaining agents (squares). (a) and (b) Effect of having $N_{\text{chatters}}$ agents which communicate twice as much as the remaining $N-N_{\text{chatters}}$ agents in network. (c) and (d) Effect of $N_{\text{cheaters}}$ agents that cheat by running their internal clock at half the speed of the other $N-N_{\text{cheaters}}$ agents’ clocks. (e) and (f) Effect of a more brutal strategy where $N_{\text{liars}}$ agents always pretend that their information about all other agents is very new (of the order of what the remaining $N-N_{\text{liars}}$ agents have for their nearest or next nearest neighbors). The communication rate is $C=1$ in a system with $N=1000$ nodes and $L=2500$ links. In (c) and (d) open squares and circles correspond to a simulation with stochastic cheaters.

Figure 7

(Color online) Perception consequences of introducing strategic agents, quantified through communication distance, $d_{\mathrm{com}}$, and reliability of routed messages, $R_{\text{route}}$. (a) and (b), (c) and (d), and (e) and (f) In a society the information horizon is set by each individual’s social contacts, which in turn is a part of the global network of human communication and corresponds to the same strategies as in Fig. 6. In (c) and (d) open squares and circles correspond to a simulation with stochastic cheaters.