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Register a new userBounded confidence model on a still growing scale-free network
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Adriano Sousa A. O. Sousa
Publication date
2004
fields
Physics
and research's language is
English
Authors
A.O. Sousa
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A Bounded Confidence (BC) model of socio-physics, in which the agents have continuous opinions and can influence each other only if the distance between their opinions is below a threshold, is simulated on a still growing scale-free network considering several different strategies: for each new node (or vertex), that is added to the network all individuals of the network have their opinions updated following a BC model recipe. The results obtained are compared with the original model, with numerical simulations on different graph structures and also when it is considered on the usual fixed BA network. In particular, the comparison with the latter leads us to conclude that it does not matter much whether the network is still growing or is fixed during the opinion dynamics.
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Several cases of the Sznajd model of socio-physics, that only a group of people sharing the same opinion can convince their neighbors, have been simulated on a more realistic network with a stronger clustering. In addition, many opinions, instead of usually only two, and a convincing probability have been also considered. Finally, with minor changes we obtain a vote distribution in good agreement with reality.
It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically the mean first-passage time (MFPT) as a measure of the efficiency for the trapping process, and obtain a closed-form expression for MFPT, which agrees with direct numerical calculations. We find that, in the limit of a large network order $V$, the MFPT $<T>$ behaves superlinearly as $<T > sim V^{{3/2}}$ with an exponent 3/2 much larger than 1, which is in sharp contrast to the scaling $<T > sim V^{theta}$ with $theta leq 1$, previously obtained for non-fractal scale-free networks. Our results indicate that the degree distribution of scale-free networks is not sufficient to characterize trapping processes taking place on them. Since various real-world networks are simultaneously scale-free and fractal, our results may shed light on the understanding of trapping processes running on real-life systems.
We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $gamma = 1/(2-c)$ up to a cut-off degree $d_c propto L^{2-c}$, where $c$ is the loop exponent for dense polymers ($c=11/8$ in two dimensions) and $L$ is the length of the polymer. Our results exemplify how a scale-free network (SFN) can emerge from standard criticality.
Peoples opinions evolve over time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social interactions in real life are polyadic (i.e., they involve three or more people). In this paper, we extend an asynchronous bounded-confidence model (BCM) on graphs, in which nodes are connected pairwise by edges, to an asynchronous BCM on hypergraphs, in which arbitrarily many nodes can be connected by a single hyperedge. We show that our hypergraph BCM converges to consensus under a wide range of initial conditions for the opinions of the nodes, including for non-uniform and asymmetric initial opinion distributions. We also show that, under suitable conditions, echo chambers can form on hypergraphs with community structure. We demonstrate that the opinions of individuals can sometimes jump from one opinion cluster to another in a single time step, a phenomenon (which we call ``opinion jumping) that is not possible in standard dyadic BCMs. Additionally, we observe that there is a phase transition in the convergence time on {a complete hypergraph} when the variance $sigma^2$ of the initial opinion distribution equals the confidence bound $c$. We prove that the convergence time grows at least exponentially fast with the number of nodes when $sigma^2 > c$ and the initial opinions are normally distributed. Therefore, to determine the convergence properties of our hypergraph BCM when the variance and the number of hyperedges are both large, it is necessary to use analytical methods instead of relying only on Monte Carlo simulations.
A two state sandpile model with preferential sand distribution is developed and studied numerically on scale free networks with power-law degree ($k$) distribution, {em i.e.}: $P_ksim k^{-alpha}$. In this model, upon toppling of a critical node sand grains are given one to each of the neighbouring nodes with highest and lowest degrees instead of two randomly selected neighbouring nodes as in a stochastic sandpile model. The critical behaviour of the model is determined by characterizing various avalanche properties at the steady state varying the network structure from scale free to random, tuning $alpha$ from $2$ to $5$. The model exhibits mean field scaling on the random networks, $alpha>4$. However, in the scale free regime, $2<alpha<4$, the scaling behaviour of the model not only deviates from the mean-field scaling but also the exponents describing the scaling behaviour are found to decrease continuously as $alpha$ decreases. In this regime, the critical exponents of the present model are found to be different from those of the two state stochastic sandpile model on similar networks. The preferential sand distribution thus has non-trivial effects on the sandpile dynamics which leads the model to a new universality class.
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