Networks portray a multitude of interactions through which people meet, ideas are spread and infectious diseases propagate within a society 1-5 . Identifying the most efficient 'spreaders' in a network is an important step towards optimizing the use of available resources and ensuring the more efficient spread of information. Here we show that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the most highly connected or the most central people 6-10 . Instead, we find that the most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis [11][12][13] , and that when multiple spreaders are considered simultaneously the distance between them becomes the crucial parameter that determines the extent of the spreading. Furthermore, we show that infections persist in the high-k shells of the network in the case where recovered individuals do not develop immunity. Our analysis should provide a route for an optimal design of efficient dissemination strategies.Spreading is a ubiquitous process, which describes many important activities in society [2][3][4][5] . The knowledge of the spreading pathways through the network of social interactions is crucial for developing efficient methods to either hinder spreading in the case of diseases, or accelerate spreading in the case of information dissemination. Indeed, people are connected according to the way they interact with one another in society and the large heterogeneity of the resulting network greatly determines the efficiency and speed of spreading. In the case of networks with a broad degree distribution (number of links per node) 6 , it is believed that the most connected people (hubs) are the key players, being responsible for the largest scale of the spreading process [6][7][8] . Furthermore, in the context of social network theory, the importance of a node for spreading is often associated with the betweenness centrality, a measure of how many shortest paths cross through this node, which is believed to determine who has more 'interpersonal influence' on others 9,10 .Here we argue that the topology of the network organization plays an important role such that there are plausible circumstances under which the highly connected nodes or the highest-betweenness nodes have little effect on the range of a given spreading process. For example, if a hub exists at the end of a branch at the periphery of a network, it will have a minimal impact in the spreading process through the core of the network, whereas a less connected person who is strategically placed in the core of the network will have a significant effect that leads to dissemination through a large fraction of the population. To identify the core and the periphery of the network we use the k-shell (also called k-core) decomposition of the network [11][12][13][14] . Examining this quantity in a number of real networks enables us to identify the best individual spreaders in the network when th...

Node characteristics and behaviors are often correlated with the structure of social networks over time. While evidence of this type of assortative mixing and temporal clustering of behaviors among linked nodes is used to support claims of peer influence and social contagion in networks, homophily may also explain such evidence. Here we develop a dynamic matched sample estimation framework to distinguish influence and homophily effects in dynamic networks, and we apply this framework to a global instant messaging network of 27.4 million users, using data on the day-by-day adoption of a mobile service application and users' longitudinal behavioral, demographic, and geographic data. We find that previous methods overestimate peer influence in product adoption decisions in this network by 300 -700%, and that homophily explains >50% of the perceived behavioral contagion. These findings and methods are essential to both our understanding of the mechanisms that drive contagions in networks and our knowledge of how to propagate or combat them in domains as diverse as epidemiology, marketing, development economics, and public health.dynamic matching estimation ͉ peer influence ͉ social networks ͉ identification T he recent availability of massive networked data sets has enabled studies of population-level human interaction at unprecedented scale (1-3). Such studies document the persistent structural properties of networks (4), how they form, evolve, and dissolve (5), and how their structure is correlated with social interaction (1, 6, 7), individual and collaborative team performance (8-11), health outcomes (12-14), and global product demand patterns (15). Networks of interactions among individuals also provide the primary pathways along which viral contagions spread in social, biological, technological, and economic systems (16-18), which may explain why network structure is correlated with such a variety of outcomes. Yet although many studies model the dynamics of viral spreading by using assumptions about susceptibility rates, transition probabilities, and their relationships to network structure, few large-scale empirical observations of networked contagions exist to validate these assumptions (16)(17)(18).We analyze a new, large scale dataset which comprehensively captures the diffusion of a mobile service product over a social network for 5 months after its launch date. A key challenge in identifying true contagions in such data is to distinguish peer-topeer influence, in which a node influences or causes outcomes in its neighbors, from homophily, in which dyadic similarities between nodes create correlated outcome patterns among neighbors that merely mimic viral contagions without direct causal influence (19). Although the diffusion patterns created by peer influence-driven contagions and homophilous diffusion are similar, they are likely to result in significantly different dynamics. Influence-driven contagions are self-reinforcing and display rapid, exponential, and less predictable diffusion as they evolve (18...

Our society is increasingly relying on the digitized, aggregated opinions of others to make decisions. We therefore designed and analyzed a large-scale randomized experiment on a social news aggregation Web site to investigate whether knowledge of such aggregates distorts decision-making. Prior ratings created significant bias in individual rating behavior, and positive and negative social influences created asymmetric herding effects. Whereas negative social influence inspired users to correct manipulated ratings, positive social influence increased the likelihood of positive ratings by 32% and created accumulating positive herding that increased final ratings by 25% on average. This positive herding was topic-dependent and affected by whether individuals were viewing the opinions of friends or enemies. A mixture of changing opinion and greater turnout under both manipulations together with a natural tendency to up-vote on the site combined to create the herding effects. Such findings will help interpret collective judgment accurately and avoid social influence bias in collective intelligence in the future.