Emergence of scale-free leadership structure in social recommender systems

True scale-free networks hidden by finite size effects

The generalized scale invariance of complex networks, whose trademark feature is the power law distributions of key structural properties like node degree, has recently been questioned on the basis of statistical testing of samples from model and real data. This has important implications on the dynamic origins of network self-organization and consequently, on the general interpretation of their function and resilience. However, a well-known mechanism of departure from scale invariance is the presence of finite size effects. Developed for critical phenomena, finite size scaling analysis assesses whether an underlying scale invariance is clouded by a sample limited in size. Our approach sorts out when we may reject the hypothesis that the inherent structure of networks is scale invariant.

We analyze about 200 naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees. Specifically, we analyze by finite size scaling analysis the datasets of real networks to check whether the purported departures from power law behavior are due to the finiteness of sample size. We find that a large number of the networks follows a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially involving infrastructure and transportation but also in social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite size effects due to the nature of the sample data.

Detecting the Influencer on Social Networks Using Passion Point and Measures of Information Propagation †

Influencer marketing is a modern method that uses influential users to approach goal customers easily and quickly. An online social network is a useful platform to detect the most effective influencer for a brand. Thus, we have an issue: how can we extract user data to determine an influencer? In this paper, a model for representing a social network based on users, tags, and the relationships among them, called the SNet model, is presented. A graph-based approach for computing the impact of users and the speed of information propagation, and measuring the favorite brand of a user and sharing the similar brand characteristics, called a passion point, is proposed. Therefore, we consider two main influential measures, including the extent of the influence on other people by the relationships between users and the concern to user’s tags, and the tag propagation through social pulse on the social network. Based on these, the problem of determining the influencer of a specific brand on a social network is solved. The results of this method are used to run the influencer marketing strategy in practice and have obtained positive results.

Subnormal Distribution Derived From Evolving Networks With Variable Elements

During the past decades, power-law distributions have played a significant role in analyzing the topology of scale-free networks. However, in the observation of degree distributions in practical networks and other nonuniform distributions such as the wealth distribution, we discover that, there exists a peak at the beginning of most real distributions, which cannot be accurately described by a monotonic decreasing power-law distribution. To better describe the real distributions, in this paper, we propose a subnormal distribution derived from evolving networks with variable elements and study its statistical properties for the first time. By utilizing this distribution, we can precisely describe those distributions commonly existing in the real world, e.g., distributions of degree in social networks and personal wealth. Additionally, we fit connectivity in evolving networks and the data observed in the real world by the proposed subnormal distribution, resulting in a better performance of fitness.

Dense power-law networks and simplicial complexes

There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e., their degree distributions follow P(k)∝k^{-γ} with γ∈(1,2]. Models of growing networks have been successfully employed to produce scale-free networks using preferential attachment, however these models can only produce sparse networks as the numbers of links and nodes being added at each time step is constant. Here we present a modeling framework which produces networks that are both dense and scale-free. The mechanism by which the networks grow in this model is based on the Pitman-Yor process. Variations on the model are able to produce undirected scale-free networks with exponent γ=2 or directed networks with power-law out-degree distribution with tunable exponent γ∈(1,2). We also extend the model to that of directed two-dimensional simplicial complexes. Simplicial complexes are generalization of networks that can encode the many body interactions between the parts of a complex system and as such are becoming increasingly popular to characterize different data sets ranging from social interacting systems to the brain. Our model produces dense directed simplicial complexes with power-law distribution of the generalized out-degrees of the nodes.

Emergence of opinion leaders in reference networks

Individuals often refer to opinions of others when they make decisions in the real world. Our question is how the people’s reference structure self-organizes when people try to provide correct answers by referring to more accurate agents. We constructed an adaptive network model, in which each node represents an agent and each directed link represents a reference. In every iteration round within our model, each agent makes a decision sequentially by following the majority of the reference partners’ opinions and rewires a reference link to a partner if the partner’s performance falls below a given threshold. The value of this threshold is common for all agents and represents the performance assessment severity of the population. We found that the reference network self-organizes into a heterogeneous one with a nearly exponential in-degree (the number of followers) distribution, where reference links concentrate around agents with high intrinsic ability. In this heterogeneous network, the decision-making accuracy of agents improved on average. However, the proportion of agents who provided correct answers showed strong temporal fluctuation compared to that observed in the case in which each agent refers to randomly selected agents. We also found a counterintuitive phenomenon in which reference links concentrate more around high-ability agents and the population became smarter on average when the rewiring threshold was set lower than when it was set higher.

Modeling Periodic Impulsive Effects on Online TV Series Diffusion

BACKGROUND

Online broadcasting substantially affects the production, distribution, and profit of TV series. In addition, online word-of-mouth significantly affects the diffusion of TV series. Because on-demand streaming rates are the most important factor that influences the earnings of online video suppliers, streaming statistics and forecasting trends are valuable. In this paper, we investigate the effects of periodic impulsive stimulation and pre-launch promotion on on-demand streaming dynamics. We consider imbalanced audience feverish distribution using an impulsive susceptible-infected-removed(SIR)-like model. In addition, we perform a correlation analysis of online buzz volume based on Baidu Index data.

METHODS

We propose a PI-SIR model to evolve audience dynamics and translate them into on-demand streaming fluctuations, which can be observed and comprehended by online video suppliers. Six South Korean TV series datasets are used to test the model. We develop a coarse-to-fine two-step fitting scheme to estimate the model parameters, first by fitting inter-period accumulation and then by fitting inner-period feverish distribution.

RESULTS

We find that audience members display similar viewing habits. That is, they seek new episodes every update day but fade away. This outcome means that impulsive intensity plays a crucial role in on-demand streaming diffusion. In addition, the initial audience size and online buzz are significant factors. On-demand streaming fluctuation is highly correlated with online buzz fluctuation.

CONCLUSION

To stimulate audience attention and interpersonal diffusion, it is worthwhile to invest in promotion near update days. Strong pre-launch promotion is also a good marketing tool to improve overall performance. It is not advisable for online video providers to promote several popular TV series on the same update day. Inter-period accumulation is a feasible forecasting tool to predict the future trend of the on-demand streaming amount. The buzz in public social communities also represents a highly correlated analysis tool to evaluate the advertising value of TV series.

OLFinder: Finding opinion leaders in online social networks

Opinion leaders are the influential people who are able to shape the minds and thoughts of other people in their society. Finding opinion leaders is an important task in various domains ranging from marketing to politics. In this paper, a new effective algorithm for finding opinion leaders in a given domain in online social networks is introduced. The proposed algorithm, named OLFinder, detects the main topics of discussion in a given domain, calculates a competency and a popularity score for each user in the given domain, then calculates a probability for being an opinion leader in that domain by using the competency and the popularity scores and finally ranks the users of the social network based on their probability of being an opinion leader. Our experimental results show that OLFinder outperforms other methods based on precision-recall, average precision and P@N measures.

Personal Health Record Use in the United States: Forecasting Future Adoption Levels

Background

Personal health records (PHRs) offer a tremendous opportunity to generate consumer support in pursing the triple aim of reducing costs, increasing access, and improving care quality. Moreover, surveys in the United States indicate that consumers want Web-based access to their medical records. However, concerns that consumers’ low health information literacy levels and physicians’ resistance to sharing notes will limit PHRs’ utility to a relatively small portion of the population have reduced both the product innovation and policy imperatives.

Objective

The purpose of our study was 3-fold: first, to report on US consumers’ current level of PHR activity; second, to describe the roles of imitation and innovation influence factors in determining PHR adoption rates; and third, to forecast future PHR diffusion uptake among US consumers under 3 scenarios.

Methods

We used secondary data from the Health Information National Trends Survey (HINTS) of US citizens for the survey years 2008, 2011, and 2013. Applying technology diffusion theory and Bass modeling, we evaluated 3 future PHR adoption scenarios by varying the introduction dates.

Results

All models displayed the characteristic diffusion S-curve indicating that the PHR technology is likely to achieve significant market penetration ahead of meaningful use goals. The best-performing model indicates that PHR adoption will exceed 75% by 2020. Therefore, the meaningful use program targets for PHR adoption are below the rates likely to occur without an intervention.

Conclusions

The promise of improved care quality and cost savings through better consumer engagement prompted the US Institute of Medicine to call for universal PHR adoption in 1999. The PHR products available as of 2014 are likely to meet and exceed meaningful use stage 3 targets before 2020 without any incentive. Therefore, more ambitious uptake and functionality availability should be incorporated into future goals.

PhysarumSpreader: A New Bio-Inspired Methodology for Identifying Influential Spreaders in Complex Networks

Identifying influential spreaders in networks, which contributes to optimizing the use of available resources and efficient spreading of information, is of great theoretical significance and practical value. A random-walk-based algorithm LeaderRank has been shown as an effective and efficient method in recognizing leaders in social network, which even outperforms the well-known PageRank method. As LeaderRank is initially developed for binary directed networks, further extensions should be studied in weighted networks. In this paper, a generalized algorithm PhysarumSpreader is proposed by combining LeaderRank with a positive feedback mechanism inspired from an amoeboid organism called Physarum Polycephalum. By taking edge weights into consideration and adding the positive feedback mechanism, PhysarumSpreader is applicable in both directed and undirected networks with weights. By taking two real networks for examples, the effectiveness of the proposed method is demonstrated by comparing with other standard centrality measures.

Item Anomaly Detection Based on Dynamic Partition for Time Series in Recommender Systems

In recent years, recommender systems have become an effective method to process information overload. However, recommendation technology still suffers from many problems. One of the problems is shilling attacks-attackers inject spam user profiles to disturb the list of recommendation items. There are two characteristics of all types of shilling attacks: 1) Item abnormality: The rating of target items is always maximum or minimum; and 2) Attack promptness: It takes only a very short period time to inject attack profiles. Some papers have proposed item anomaly detection methods based on these two characteristics, but their detection rate, false alarm rate, and universality need to be further improved. To solve these problems, this paper proposes an item anomaly detection method based on dynamic partitioning for time series. This method first dynamically partitions item-rating time series based on important points. Then, we use chi square distribution (χ²) to detect abnormal intervals. The experimental results on MovieLens 100K and 1M indicate that this approach has a high detection rate and a low false alarm rate and is stable toward different attack models and filler sizes.

Shilling Attacks Detection in Recommender Systems Based on Target Item Analysis

Recommender systems are highly vulnerable to shilling attacks, both by individuals and groups. Attackers who introduce biased ratings in order to affect recommendations, have been shown to negatively affect collaborative filtering (CF) algorithms. Previous research focuses only on the differences between genuine profiles and attack profiles, ignoring the group characteristics in attack profiles. In this paper, we study the use of statistical metrics to detect rating patterns of attackers and group characteristics in attack profiles. Another question is that most existing detecting methods are model specific. Two metrics, Rating Deviation from Mean Agreement (RDMA) and Degree of Similarity with Top Neighbors (DegSim), are used for analyzing rating patterns between malicious profiles and genuine profiles in attack models. Building upon this, we also propose and evaluate a detection structure called RD-TIA for detecting shilling attacks in recommender systems using a statistical approach. In order to detect more complicated attack models, we propose a novel metric called DegSim’ based on DegSim. The experimental results show that our detection model based on target item analysis is an effective approach for detecting shilling attacks.

Empirical Studies on the Network of Social Groups: The Case of Tencent QQ

BACKGROUND

Participation in social groups are important but the collective behaviors of human as a group are difficult to analyze due to the difficulties to quantify ordinary social relation, group membership, and to collect a comprehensive dataset. Such difficulties can be circumvented by analyzing online social networks.

METHODOLOGY/PRINCIPAL FINDINGS

In this paper, we analyze a comprehensive dataset released from Tencent QQ, an instant messenger with the highest market share in China. Specifically, we analyze three derivative networks involving groups and their members-the hypergraph of groups, the network of groups and the user network-to reveal social interactions at microscopic and mesoscopic level.

CONCLUSIONS/SIGNIFICANCE

Our results uncover interesting behaviors on the growth of user groups, the interactions between groups, and their relationship with member age and gender. These findings lead to insights which are difficult to obtain in social networks based on personal contacts.

Measuring multiple evolution mechanisms of complex networks

Numerous concise models such as preferential attachment have been put forward to reveal the evolution mechanisms of real-world networks, which show that real-world networks are usually jointly driven by a hybrid mechanism of multiplex features instead of a single pure mechanism. To get an accurate simulation for real networks, some researchers proposed a few hybrid models by mixing multiple evolution mechanisms. Nevertheless, how a hybrid mechanism of multiplex features jointly influence the network evolution is not very clear. In this study, we introduce two methods (link prediction and likelihood analysis) to measure multiple evolution mechanisms of complex networks. Through tremendous experiments on artificial networks, which can be controlled to follow multiple mechanisms with different weights, we find the method based on likelihood analysis performs much better and gives very accurate estimations. At last, we apply this method to some real-world networks which are from different domains (including technology networks and social networks) and different countries (e.g., USA and China), to see how popularity and clustering co-evolve. We find most of them are affected by both popularity and clustering, but with quite different weights.

Network-driven reputation in online scientific communities

The ever-increasing quantity and complexity of scientific production have made it difficult for researchers to keep track of advances in their own fields. This, together with growing popularity of online scientific communities, calls for the development of effective information filtering tools. We propose here an algorithm which simultaneously computes reputation of users and fitness of papers in a bipartite network representing an online scientific community. Evaluation on artificially-generated data and real data from the Econophysics Forum is used to determine the method's best-performing variants. We show that when the input data is extended to a multilayer network including users, papers and authors and the algorithm is correspondingly modified, the resulting performance improves on multiple levels. In particular, top papers have higher citation count and top authors have higher h-index than top papers and top authors chosen by other algorithms. We finally show that our algorithm is robust against persistent authors (spammers) which makes the method readily applicable to the existing online scientific communities.

Similarity from multi-dimensional scaling: solving the accuracy and diversity dilemma in information filtering

Recommender systems are designed to assist individual users to navigate through the rapidly growing amount of information. One of the most successful recommendation techniques is the collaborative filtering, which has been extensively investigated and has already found wide applications in e-commerce. One of challenges in this algorithm is how to accurately quantify the similarities of user pairs and item pairs. In this paper, we employ the multidimensional scaling (MDS) method to measure the similarities between nodes in user-item bipartite networks. The MDS method can extract the essential similarity information from the networks by smoothing out noise, which provides a graphical display of the structure of the networks. With the similarity measured from MDS, we find that the item-based collaborative filtering algorithm can outperform the diffusion-based recommendation algorithms. Moreover, we show that this method tends to recommend unpopular items and increase the global diversification of the networks in long term.

Influence of reciprocal links in social networks

How does reciprocal links affect the function of real social network? Does reciprocal link and non-reciprocal link play the same role? Previous researches haven't displayed a clear picture to us until now according to the best of our knowledge. Motivated by this, in this paper, we empirically study the influence of reciprocal links in two representative real datasets, Sina Weibo and Douban. Our results demonstrate that the reciprocal links play a more important role than non-reciprocal ones in information diffusion process. In particular, not only coverage but also the speed of the information diffusion can be significantly enhanced by considering the reciprocal effect. We give some possible explanations from the perspectives of network connectivity and efficiency. This work may shed some light on the in-depth understanding and application of the reciprocal effect in directed online social networks.

Diversity of individual mobility patterns and emergence of aggregated scaling laws

Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries of volunteers, we show the absence of scaling properties in the displacement distribution at the individual level,while the aggregated displacement distribution follows a power law with an exponential cutoff. Given the constraint on total travelling cost, this aggregated scaling law can be analytically predicted by the mixture nature of human travel under the principle of maximum entropy. A direct corollary of such theory is that the displacement distribution of a single mode of transportation should follow an exponential law, which also gets supportive evidences in known data. We thus conclude that the travelling cost shapes the displacement distribution at the aggregated level.

Optimizing online social networks for information propagation

Online users nowadays are facing serious information overload problem. In recent years, recommender systems have been widely studied to help people find relevant information. Adaptive social recommendation is one of these systems in which the connections in the online social networks are optimized for the information propagation so that users can receive interesting news or stories from their leaders. Validation of such adaptive social recommendation methods in the literature assumes uniform distribution of users' activity frequency. In this paper, our empirical analysis shows that the distribution of online users' activity is actually heterogenous. Accordingly, we propose a more realistic multi-agent model in which users' activity frequency are drawn from a power-law distribution. We find that previous social recommendation methods lead to serious delay of information propagation since many users are connected to inactive leaders. To solve this problem, we design a new similarity measure which takes into account users' activity frequencies. With this similarity measure, the average delay is significantly shortened and the recommendation accuracy is largely improved.

Information filtering in sparse online systems: recommendation via semi-local diffusion

With the rapid growth of the Internet and overwhelming amount of information and choices that people are confronted with, recommender systems have been developed to effectively support users' decision-making process in the online systems. However, many recommendation algorithms suffer from the data sparsity problem, i.e. the user-object bipartite networks are so sparse that algorithms cannot accurately recommend objects for users. This data sparsity problem makes many well-known recommendation algorithms perform poorly. To solve the problem, we propose a recommendation algorithm based on the semi-local diffusion process on the user-object bipartite network. The simulation results on two sparse datasets, Amazon and Bookcross, show that our method significantly outperforms the state-of-the-art methods especially for those small-degree users. Two personalized semi-local diffusion methods are proposed which further improve the recommendation accuracy. Finally, our work indicates that sparse online systems are essentially different from the dense online systems, so it is necessary to reexamine former algorithms and conclusions based on dense data in sparse systems.

How Twitter Is Studied in the Medical Professions: A Classification of Twitter Papers Indexed in PubMed

Background

Since their inception, Twitter and related microblogging systems have provided a rich source of information for researchers and have attracted interest in their affordances and use. Since 2009 PubMed has included 123 journal articles on medicine and Twitter, but no overview exists as to how the field uses Twitter in research.

Objective

This paper aims to identify published work relating to Twitter within the fields indexed by PubMed, and then to classify it. This classification will provide a framework in which future researchers will be able to position their work, and to provide an understanding of the current reach of research using Twitter in medical disciplines.

Methods

Papers on Twitter and related topics were identified and reviewed. The papers were then qualitatively classified based on the paper’s title and abstract to determine their focus. The work that was Twitter focused was studied in detail to determine what data, if any, it was based on, and from this a categorization of the data set size used in the studies was developed. Using open coded content analysis additional important categories were also identified, relating to the primary methodology, domain, and aspect.

Results

As of 2012, PubMed comprises more than 21 million citations from biomedical literature, and from these a corpus of 134 potentially Twitter related papers were identified, eleven of which were subsequently found not to be relevant. There were no papers prior to 2009 relating to microblogging, a term first used in 2006. Of the remaining 123 papers which mentioned Twitter, thirty were focused on Twitter (the others referring to it tangentially). The early Twitter focused papers introduced the topic and highlighted the potential, not carrying out any form of data analysis. The majority of published papers used analytic techniques to sort through thousands, if not millions, of individual tweets, often depending on automated tools to do so. Our analysis demonstrates that researchers are starting to use knowledge discovery methods and data mining techniques to understand vast quantities of tweets: the study of Twitter is becoming quantitative research.

Conclusions

This work is to the best of our knowledge the first overview study of medical related research based on Twitter and related microblogging. We have used 5 dimensions to categorize published medical related research on Twitter. This classification provides a framework within which researchers studying development and use of Twitter within medical related research, and those undertaking comparative studies of research, relating to Twitter in the area of medicine and beyond, can position and ground their work.

A bio-inspired methodology of identifying influential nodes in complex networks

How to identify influential nodes is a key issue in complex networks. The degree centrality is simple, but is incapable to reflect the global characteristics of networks. Betweenness centrality and closeness centrality do not consider the location of nodes in the networks, and semi-local centrality, leaderRank and pageRank approaches can be only applied in unweighted networks. In this paper, a bio-inspired centrality measure model is proposed, which combines the Physarum centrality with the K-shell index obtained by K-shell decomposition analysis, to identify influential nodes in weighted networks. Then, we use the Susceptible-Infected (SI) model to evaluate the performance. Examples and applications are given to demonstrate the adaptivity and efficiency of the proposed method. In addition, the results are compared with existing methods.

Potential theory for directed networks

Uncovering factors underlying the network formation is a long-standing challenge for data mining and network analysis. In particular, the microscopic organizing principles of directed networks are less understood than those of undirected networks. This article proposes a hypothesis named potential theory, which assumes that every directed link corresponds to a decrease of a unit potential and subgraphs with definable potential values for all nodes are preferred. Combining the potential theory with the clustering and homophily mechanisms, it is deduced that the Bi-fan structure consisting of 4 nodes and 4 directed links is the most favored local structure in directed networks. Our hypothesis receives strongly positive supports from extensive experiments on 15 directed networks drawn from disparate fields, as indicated by the most accurate and robust performance of Bi-fan predictor within the link prediction framework. In summary, our main contribution is twofold: (i) We propose a new mechanism for the local organization of directed networks; (ii) We design the corresponding link prediction algorithm, which can not only testify our hypothesis, but also find out direct applications in missing link prediction and friendship recommendation.

Emergence of scale-free close-knit friendship structure in online social networks

Although the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properties. It is found that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. The degree correlation is very weak over a wide range of the degrees. We propose a simple directed network model that captures the observed properties. The model incorporates two mechanisms: reciprocation and preferential attachment. Through rate equation analysis of our model, the local-scale and mesoscale structural properties are derived. In the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear relationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlations. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only on one global parameter, the mean in/outdegree, while both the mean in/outdegree and the reciprocity together determine the ratio of the reciprocal degree of a node to its in/outdegree. Structural properties of numerical simulated networks are analyzed and compared with each of the four real networks. This work helps understand the interplay between structures on different scales in online social networks.

Instability in evolutionary games

Background

Phenomena of instability are widely observed in many dissimilar systems, with punctuated equilibrium in biological evolution and economic crises being noticeable examples. Recent studies suggested that such instabilities, quantified by the abrupt changes of the composition of individuals, could result within the framework of a collection of individuals interacting through the prisoner's dilemma and incorporating three mechanisms: (i) imitation and mutation, (ii) preferred selection on successful individuals, and (iii) networking effects.

Methodology/Principal Findings

We study the importance of each mechanism using simplified models. The models are studied numerically and analytically via rate equations and mean-field approximation. It is shown that imitation and mutation alone can lead to the instability on the number of cooperators, and preferred selection modifies the instability in an asymmetric way. The co-evolution of network topology and game dynamics is not necessary to the occurrence of instability and the network topology is found to have almost no impact on instability if new links are added in a global manner. The results are valid in both the contexts of the snowdrift game and prisoner's dilemma.

Conclusions/Significance

The imitation and mutation mechanism, which gives a heterogeneous rate of change in the system's composition, is the dominating reason of the instability on the number of cooperators. The effects of payoffs and network topology are relatively insignificant. Our work refines the understanding on the driving forces of system instability.

Enhancing topology adaptation in information-sharing social networks

The advent of the Internet and World Wide Web has led to unprecedent growth of the information available. People usually face the information overload by following a limited number of sources which best fit their interests. It has thus become important to address issues like who gets followed and how to allow people to discover new and better information sources. In this paper we conduct an empirical analysis of different online social networking sites and draw inspiration from its results to present different source selection strategies in an adaptive model for social recommendation. We show that local search rules which enhance the typical topological features of real social communities give rise to network configurations that are globally optimal. These rules create networks which are effective in information diffusion and resemble structures resulting from real social systems.