Dynamical and bursty interactions in social networks

We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents’ behavior at short time scales in which the contact network is formed by disconnected cliques of different sizes. At each time a random agent can make a transition from being isolated to being part of a group or vice versa. Different distributions of contact times and intercontact times between individuals are obtained by considering transition probabilities with memory effects, i.e., the transition probabilities for each agent depend both on its state (isolated or interacting) and on the time elapsed since the last change in state. The model lends itself to analytical and numerical investigations. The modeling framework can be easily extended and paves the way for systematic investigations of dynamical processes occurring on rapidly evolving dynamical networks, such as the propagation of an information or spreading of diseases.

Figure 1

Average state $⟨p⟩$ in the stationary state for different sets of parameters and a population of $N=2000$ agents. (a) $b_1=\lambda =0.7$; (b) $b_0=\lambda =0.7$; (c) $b_0=b_1=0.7$. In (c) we observe the divergence of the average group size as $\lambda \to {0.5}^{+}$. The lines show Eq. (5).

Figure 2

(Color online) Distribution $P_p\left(\tau \right)$ of times during which an agent does not change connectivity $p$. $N=10000$, $b_0=b_1=0.7$, $\lambda =0.8$, and the simulation is run for $T={10}^{5}N$ time steps. The lines are the analytical predictions.

Figure 3

(Color online) Distributions of (a) duration of a contact between two agents; (b) time intervals between the beginnings of successive contacts of an agent A with two different agents B and C; (c) duration of a triangle. $b_0=0.7$, $\lambda =0.8$, $b_1=0.6$ and $0.9$. $N=1000$, $T={10}^{5}N$.