Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

https://arxiv.org/pdf/cond-mat/9910332.pdf

Emergence of Scaling in Random Networks

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

/pdf/statistical-mechanics-of-complex-networks-1zfjpvxipu.pdf

Statistical mechanics of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

/pdf/the-structure-and-function-of-complex-networks-34deompc9l.pdf

The Structure and Function of Complex Networks

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

/pdf/community-structure-in-social-and-biological-networks-1jamu4rcfv.pdf

Community structure in social and biological networks

The current state of public and political discourse is in disarray. Politicians lie with impunity. Traditional news organizations amplify fact-free assertions, while outright fake news stories circulate on social media. Public trust in the media, science, and expert opinion has fallen, while segregation into like-minded communities has risen. Millions of citizens blame their economic circumstances on caricatures like “elites” rather than on specific economic forces and policies. Enormously complex subjects like mitigating climate change, or balancing economic growth and inequality, are reduced to slogans. Magical thinking (e.g., that millions of manufacturing jobs can be created by imposing trade restrictions; that everyone can have affordable, high quality, healthcare without individual mandates or subsidies; that vaccines cause autism) has proliferated.

Rebuilding legitimacy in a post-truth age

Abstract Online platforms have banned (“deplatformed”) influencers, communities, and even entire websites to reduce content deemed harmful. Deplatformed users often migrate to alternative platforms, which raises concerns about the effectiveness of deplatforming. Here, we study the deplatforming of Parler, a fringe social media platform, between 2021 January 11 and 2021 February 25, in the aftermath of the US Capitol riot. Using two large panels that capture longitudinal user-level activity across mainstream and fringe social media content (N = 112, 705, adjusted to be representative of US desktop and mobile users), we find that other fringe social media, such as Gab and Rumble, prospered after Parler’s deplatforming. Further, the overall activity on fringe social media increased while Parler was offline. Using a difference-in-differences analysis (N = 996), we then identify the causal effect of deplatforming on active Parler users, finding that deplatforming increased the probability of daily activity across other fringe social media in early 2021 by 10.9 percentage points (pp) (95% CI [5.9 pp, 15.9 pp]) on desktop devices, and by 15.9 pp (95% CI [10.2 pp, 21.7 pp]) on mobile devices, without decreasing activity on fringe social media in general (including Parler). Our results indicate that the isolated deplatforming of a major fringe platform was ineffective at reducing overall user activity on fringe social media.

Deplatforming did not decrease Parler users’ activity on fringe social media

REVIEWS-Small Worlds: The Dynamics of Networks between order and Randomness

“Fake news,” broadly defined as deliberately false or misleading information masquerading as legitimate news, is frequently asserted to be pervasive on the web, and on social media in particular, with serious consequences for public opinion, political polarization, and ultimately democracy. Using a unique multimode data set that comprises a nationally representative sample of mobile, desktop, and television consumption across all categories of media content, we refute this conventional wisdom on three levels. First, news consumption of any sort is heavily outweighed by other forms of media consumption, comprising at most 14.2% of Americans’ daily media diets. Second, to the extent that Americans do consume news, it is overwhelmingly from television, which accounts for roughly five times as much as news consumption as online, while a supermajority of Americans consume little or no news online at all. Third, fake news comprises only about 1% of overall news consumption and 0.15% of Americans’ daily media diet. Although consumption data alone cannot determine that online misinformation in any dose is not dangerous to democracy, our results suggest that the origins of public mis-informedness and polarization are more likely to lie in the content of ordinary news--especially on television--or alternatively in the avoidance of news altogether as they are in overt fakery.

Evaluating the Fake News Problem at the Scale of the Information Ecosystem

The natural tendency for humans to choose with whom to form new relationships and with whom to end established relationships is thought to facilitate the emergence of cooperation. Helping cooperators to mix assortatively is believed to reinforce the rewards accruing to mutual cooperation while simultaneously excluding defectors. However, the relationship between endogenous partner selection, assortativity, and cooperation has been largely unexplored experimentally. Here we report on a series of human subjects experiments in which groups of 24 participants played a multi-player prisoner's dilemma game where, critically, they were also allowed to propose and delete links to players of their own choosing at some variable rate. Over a wide variety of parameter settings and initial conditions, we found that endogenous partner selection significantly increased the level of cooperation, the average payoffs to players, and the assortativity between cooperators. Even relatively slow update rates were sufficient to produce large effects resulting in cooperation levels over 80%. Subsequent increases to the update rate still had a positive, although smaller, effect. For standard prisoner's dilemma payoffs, we also found that assortativity resulted predominantly from cooperators avoiding defectors, not by severing ties with defecting partners, and that cooperation correspondingly suffered. Finally, by modifying the payoffs to satisfy two novel conditions, we found that cooperators did punish defectors by severing ties, leading to levels of cooperation approaching 100% which persisted for longer.

Duncan J. Watts

Papers

Rebuilding legitimacy in a post-truth age

Deplatforming did not decrease Parler users’ activity on fringe social media

REVIEWS-Small Worlds: The Dynamics of Networks between order and Randomness

Evaluating the Fake News Problem at the Scale of the Information Ecosystem

Cooperation and assortativity with endogenous partner selection