Dynamics Of Random Networks Research Articles

Crossover phenomenon in adversarial attacks on voter model

A recent study (Chiyomaru and Takemoto 2022 Phys. Rev. E 106 014301) considered adversarial attacks conducted to distort voter model dynamics in networks. This method intervenes in the interaction patterns of individuals and induces them to be in a target opinion state through a small perturbation ε. In this study, we investigate adversarial attacks on voter dynamics in random networks of finite size n. The exit probability P +1 to reach the target absorbing state and the mean time τ n to reach consensus are analyzed in the mean-field approximation. Given ε > 0, the exit probability P +1 converges asymptotically to unity as n increases. The mean time τ n to reach consensus scales as for homogeneous networks with a large finite n. By contrast, it scales as for heterogeneous networks with a large finite n, where µ 1 and µ 2 represent the first and second moments of the degree distribution, respectively. Moreover, we observe the crossover phenomenon of τ n from a linear scale to a logarithmic scale and find above which the state of all nodes becomes the target state in logarithmic time. Here, α = 1 for homogeneous networks and for scale-free networks with a degree exponent .

Topological transition in a coupled dynamics in random networks

In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better understand the two observed phases, so we use another network structure (the so called random geometric graph — RGG) together with other metrics borrowed from network science. We observed a topological transition on the two associated networks, which are subgraphs of the full network. As the links have two possible states (friendly and non-friendly), we defined each associated network as composed of only one type of link. The (non) friendly associated network has (non) friendly links only. This topological transition was observed from the domain distribution of each associated network between the two phases of the system (absorbing and active). We also showed that another metric from network science called modularity (or assortative coefficient) can also be used as order parameter, giving the same phase diagram as the original order parameter from the seminal work. On the absorbing phase the absolute value of the modularity for each associated network reaches a maximum value, while on the active phase they fall to the minimum value.

Traffic dynamics on homogeneous networks with community structure

In complex networks, how topology structures influence the traffic dynamics on networks is a hot topic. The existence of structure within communities may affect the transmission of data packets in the network. In this paper, we investigate the impact of community structure on traffic dynamics in random networks which are homogeneous. It is found that three key factors influence traffic capacity in such community networks: community number, community strength, and average node degree. The increase of average node degree increases traffic capacity, while the increase of community number and community strength decreases traffic capacity.

Topological Transition in a Coupled Dynamics in Random Networks

Topological Transition in a Coupled Dynamics in Random Networks

Pair approximation for the noisy threshold q-voter model.

In the standard q-voter model, a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size q. A more realistic extension is the threshold q voter, where a minimal agreement (at least 0<q_{0}≤q opposite opinions) is sufficient to flip the central agent's opinion, including also the possibility of independent (nonconformist) choices. Variants of this model including nonconformist behavior have been previously studied in fully connected networks (mean-field limit). Here we investigate its dynamics in random networks. Particularly, while in the mean-field case it is irrelevant whether repetitions in the influence group are allowed, we show that this is not the case in networks, and we study the impact of both cases, with or without repetition. Furthermore, the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions.

Kinetic-exchange-like opinion dynamics in complex networks: roles of the dimensionality and local interaction topology

We study a kinetic-exchange-like opinion dynamics model with both positive and negative interactions in various complex networks. The control parameter p ∈ [0, 1] denotes the probability of the presence of negative outcome in the pairwise interaction, which indicates that the difference between the standpoints of the two focal individuals becomes even more large because of disagreement. Accordingly, with probability 1 − p they become more similar (positive interaction). The average opinion of the population serves as the order parameter of the system. We find that in random homogeneous networks the ordering process displays an anomalous jump at some special value of the control parameter p*, which gives rise to two distinct critical points pc for p p*, respectively. Whenever the underlying interaction network has heterogeneous interaction patterns and/or planar property, the anomalous ordering phenomenon disappears. Finite-size scaling analysis of the simulation results shows that the critical exponents for the opinion dynamics in random networks are in accordance with those of the mean-field Ising model, no matter whether the degree distribution is homogeneous or heterogeneous and the anomalous jump of the order parameter is presence or absence. The critical exponents for the opinion dynamics in spatially embedded networks (in two dimensions) belong to different universality classes, which depend closely on the configuration of local interactions. Particularly, whenever the local interactions are homogeneously distributed, two-dimensional Ising model universality class is recovered. Mean-field theoretical analysis corroborates well our findings. Our results highlight the importance of both the dimensionality and the local topology of the underlying interaction network in the phase transition behavior of the opinion dynamics.

SIR dynamics in random networks with communities.

This paper investigates the effects of the community structure of a network on the spread of an epidemic. To this end, we first establish a susceptible-infected-recovered (SIR) model in a two-community network with an arbitrary joint degree distribution. The network is formulated as a probability generating function. We also obtain the sufficient conditions for disease outbreak and extinction, which involve the first-order and second-order moments of the degree distribution. As an example, we then study the effect of community structure on epidemic spread in a complex network with a Poisson joint degree distribution. The numerical solutions of the SIR model well agree with stochastic simulations based on the Monte Carlo method, confirming that the model is reliable and accurate. Finally, by strengthening the community structure in the simulation, i.e. fixing the total degree distribution and reducing the number ratio of the external edges, we can increase or decrease the final cumulative epidemic incidence depending on the transmissibility of the virus between humans and the community structure at that point. Why community structure can affect disease dynamics in a complicated way is also discussed. In any case, for large-scale epidemics, strengthening the community structure to reduce the size of disease is undoubtedly an effective way.

A note on a paper by Erik Volz: SIR dynamics in random networks

Recent work by Volz (J Math Biol 56:293-310, 2008) has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to account for effects due to heterogeneity and finiteness of degree that are neglected in the standard mass-action SIR equations. In this note we offer an alternate derivation which arrives at a simpler-though equivalent-system of governing equations to that of Volz. This new derivation is more closely connected to the underlying physical processes, and the resulting equations are of comparable complexity to the mass-action SIR equations. We further show that earlier derivations of the final size of epidemics on networks can be reproduced using the same approach, thereby providing a common framework for calculating both the dynamics and the final size of an epidemic spreading on a random network. Under appropriate assumptions these equations reduce to the standard SIR equations, and we are able to estimate the magnitude of the error introduced by assuming the SIR equations.

SIR dynamics in random networks with heterogeneous connectivity

Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by showing how the SIR dynamics can be modeled with a system of three nonlinear ODE’s. The method makes use of the probability generating function (PGF) formalism for representing the degree distribution of a random network and makes use of network-centric quantities such as the number of edges in a well-defined category rather than node-centric quantities such as the number of infecteds or susceptibles. The PGF provides a simple means of translating between network and node-centric variables and determining the epidemic incidence at any time. The theory also provides a simple means of tracking the evolution of the degree distribution among susceptibles or infecteds. The equations are used to demonstrate the dramatic effects that the degree distribution plays on the final size of an epidemic as well as the speed with which it spreads through the population. Power law degree distributions are observed to generate an almost immediate expansion phase yet have a smaller final size compared to homogeneous degree distributions such as the Poisson. The equations are compared to stochastic simulations, which show good agreement with the theory. Finally, the dynamic equations provide an alternative way of determining the epidemic threshold where large-scale epidemics are expected to occur, and below which epidemic behavior is limited to finite-sized outbreaks.