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Register a new userCharacterizing and Modeling the Dynamics of Activity and Popularity
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Social media, regarded as two-layer networks consisting of users and items, turn out to be the most important channels for access to massive information in the era of Web 2.0. The dynamics of human activity and item popularity is a crucial issue in social media networks. In this paper, by analyzing the growth of user activity and item popularity in four empirical social media networks, i.e., Amazon, Flickr, Delicious and Wikipedia, it is found that cross links between users and items are more likely to be created by active users and to be acquired by popular items, where user activity and item popularity are measured by the number of cross links associated with users and items. This indicates that users generally trace popular items, overall. However, it is found that the inactive users more severely trace popular items than the active users. Inspired by empirical analysis, we propose an evolving model for such networks, in which the evolution is driven only by two-step random walk. Numerical experiments verified that the model can qualitatively reproduce the distributions of user activity and item popularity observed in empirical networks. These results might shed light on the understandings of micro dynamics of activity and popularity in social media networks.
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We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible (SIS) model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.
The dynamics of individuals is of essential importance for understanding the evolution of social systems. Most existing models assume that individuals in diverse systems, ranging from social networks to e-commerce, all tend to what is already popular. We develop an analytical time-aware framework which shows that when individuals make choices -- which item to buy, for example -- in online social systems, a small fraction of them is consistently successful in discovering popular items long before they actually become popular. We argue that these users, whom we refer to as discoverers, are fundamentally different from the previously known opinion leaders, influentials, and innovators. We use the proposed framework to demonstrate that discoverers are present in a wide range of systems. Once identified, they can be used to predict the future success of items. We propose a network model which reproduces the discovery patterns observed in the real data. Furthermore, data produced by the model pose a fundamental challenge to classical ranking algorithms which neglect the time of link creation and thus fail to discriminate between discoverers and ordinary users in the data. Our results open the door to qualitative and quantitative study of fine temporal patterns in social systems and have far-reaching implications for network modeling and algorithm design.
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena and the performance of routing algorithms. Yet, the mechanisms responsible for their observed characteristics remain elusive. Here, we show that many of the observed properties of proximity networks emerge naturally and simultaneously in a simple latent space network model, called dynamic-$mathbb{S}^{1}$. The dynamic-$mathbb{S}^{1}$ does not model node mobility directly, but captures the connectivity in each snapshot---each snapshot in the model is a realization of the $mathbb{S}^{1}$ model of traditional complex networks, which is isomorphic to hyperbolic geometric graphs. By forgoing the motion component the model facilitates mathematical analysis, allowing us to prove the contact, inter-contact and weight distributions. We show that these distributions are power laws in the thermodynamic limit with exponents lying within the ranges observed in real systems. Interestingly, we find that network temperature plays a central role in network dynamics, dictating the exponents of these distributions, the time-aggregated agent degrees, and the formation of unique and recurrent components. Further, we show that paradigmatic epidemic and rumor spreading processes perform similarly in real and modeled networks. The dynamic-$mathbb{S}^{1}$ or extensions of it may apply to other types of time-varying networks and constitute the basis of maximum likelihood estimation methods that infer the node coordinates and their evolution in the latent spaces of real systems.
We investigate the formation of opinion against authority in an authoritarian society composed of agents with different levels of authority. We explore a dissenting opinion, held by lower-ranking, obedient, or less authoritative people, spreading in an environment of an affirmative opinion held by authoritative leaders. A real-world example would be a corrupt society where people revolt against such leaders, but it can be applied to more general situations. In our model, agents can change their opinion depending on their authority relative to their neighbors and their own confidence level. In addition, with a certain probability, agents can override the affirmative opinion to take the dissenting opinion of a neighbor. Based on analytic derivation and numerical simulations, we observe that both the network structure and heterogeneity in authority, and their correlation, significantly affect the possibility of the dissenting opinion to spread through the population. In particular, the dissenting opinion is suppressed when the authority distribution is very heterogeneous and there exists a positive correlation between the authority and the number of neighbors of people (degree). Except for such an extreme case, though, spreading of the dissenting opinion takes place when people have the tendency to override the authority to hold the dissenting opinion, but the dissenting opinion can take a long time to spread to the entire society, depending on the model parameters. We argue that the internal social structure of agents sets the scale of the time to reach consensus, based on the analysis of the underlying structural properties of opinion spreading.
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