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Register a new userInformation Cascades in Feed-based Networks of Users with Limited Attention
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We build a model of information cascades on feed-based networks, taking into account the finite attention span of users, message generation rates and message forwarding rates. Using this model, we study through simulations, the effect of the extent of user attention on the probability that the cascade becomes viral. In analogy with a branching process, we estimate the branching factor associated with the cascade process for different attention spans and different forwarding probabilities, and demonstrate that beyond a certain attention span, critical forwarding probabilities exist that constitute a threshold after which cascades can become viral. The critical forwarding probabilities have an inverse relationship with the attention span. Next, we develop a semi-analytical approach for our model, that allows us determine the branching factor for given values of message generation rates, message forwarding rates and attention spans. The branching factors obtained using this analytical approach show good agreement with those obtained through simulations. Finally, we analyze an event specific dataset obtained from Twitter, and show that estimated branching factors correlate well with the cascade size distributions associated with distinct hashtags.
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Online traces of human activity offer novel opportunities to study the dynamics of complex knowledge exchange networks, and in particular how the relationship between demand and supply of information is mediated by competition for our limited individual attention. The emergent patterns of collective attention determine what new information is generated and consumed. Can we measure the relationship between demand and supply for new information about a topic? Here we propose a normalization method to compare attention bursts statistics across topics that have an heterogeneous distribution of attention. Through analysis of a massive dataset on traffic to Wikipedia, we find that the production of new knowledge is associated to significant shifts of collective attention, which we take as a proxy for its demand. What we observe is consistent with a scenario in which the allocation of attention toward a topic stimulates the demand for information about it, and in turn the supply of further novel information. Our attempt to quantify demand and supply of information, and our finding about their temporal ordering, may lead to the development of the fundamental laws of the attention economy, and a better understanding of the social exchange of knowledge in online and offline information networks.
Although the many forms of modern social media have become major channels for the dissemination of information, they are becoming overloaded because of the rapidly-expanding number of information feeds. We analyze the expanding user-generated content in Sina Weibo, the largest micro-blog site in China, and find evidence that popular messages often follow a mechanism that differs from that found in the spread of disease, in contrast to common believe. In this mechanism, an individual with more friends needs more repeated exposures to spread further the information. Moreover, our data suggest that in contrast to epidemics, for certain messages the chance of an individual to share the message is proportional to the fraction of its neighbours who shared it with him/her. Thus the greater the number of friends an individual has the greater the number of repeated contacts needed to spread the message, which is a result of competition for attention. We model this process using a fractional susceptible infected recovered (FSIR) model, where the infection probability of a node is proportional to its fraction of infected neighbors. Our findings have dramatic implications for information contagion. For example, using the FSIR model we find that real-world social networks have a finite epidemic threshold. This is in contrast to the zero threshold that conventional wisdom derives from disease epidemic models. This means that when individuals are overloaded with excess information feeds, the information either reaches out the population if it is above the critical epidemic threshold, or it would never be well received, leading to only a handful of information contents that can be widely spread throughout the population.
Much effort has been devoted to understand how temporal network features and the choice of the source node affect the prevalence of a diffusion process. In this work, we addressed the further question: node pairs with what kind of local and temporal connection features tend to appear in a diffusion trajectory or path, thus contribute to the actual information diffusion. We consider the Susceptible-Infected spreading process with a given infection probability per contact on a large number of real-world temporal networks. We illustrate how to construct the information diffusion backbone where the weight of each link tells the probability that a node pair appears in a diffusion process starting from a random node. We unravel how these backbones corresponding to different infection probabilities relate to each other and point out the importance of two extreme backbones: the backbone with infection probability one and the integrated network, between which other backbones vary. We find that the temporal node pair feature that we proposed could better predict the links in the extreme backbone with infection probability one as well as the high weight links than the features derived from the integrated network. This universal finding across all the empirical networks highlights that temporal information are crucial in determining a node pairs role in a diffusion process. A node pair with many early contacts tends to appear in a diffusion process. Our findings shed lights on the in-depth understanding and may inspire the control of information spread.
Interactions between elements, which are usually represented by networks, have to delineate potentially unequal relationships in terms of their relative importance or direction. The intrinsic unequal relationships of such kind, however, are opaque or hidden in numerous real systems.For instance, when a node in a network with limited interaction capacity spends its capacity to its neighboring nodes, the allocation of the total amount of interactions to them can be vastly diverse. Even if such potentially heterogeneous interactions epitomized by weighted networks are observable, as a result of the aforementioned ego-centric allocation of interactions, the relative importance or dependency between two interacting nodes can only be implicitly accessible. In this work, we precisely pinpoint such relative dependency by proposing the framework to discover hidden dependent relations extracted from weighted networks. For a given weighted network, we provide a systematic criterion to select the most essential interactions for individual nodes based on the concept of information entropy. The criterion is symbolized by assigning the effective number of neighbors or the effective out-degree to each node, and the resultant directed subnetwork decodes the hidden dependent relations by leaving only the most essential directed interactions. We apply our methodology to two time-stamped empirical network data, namely the international trade relations between nations in the world trade web (WTW) and the network of people in the historical record of Korea, Annals of the Joseon Dynasty (AJD). Based on the data analysis, we discover that the properties of mutual dependency encoded in the two systems are vastly different.
We investigate the abrupt breakdown behavior of coupled distribution grids under load growth. This scenario mimics the ever-increasing customer demand and the foreseen introduction of energy hubs interconnecting the different energy vectors. We extend an analytical model of cascading behavior due to line overloads to the case of interdependent networks and find evidence of first order transitions due to the long-range nature of the flows. Our results indicate that the foreseen increase in the couplings between the grids has two competing effects: on the one hand, it increases the safety region where grids can operate without withstanding systemic failures; on the other hand, it increases the possibility of a joint systems failure.
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