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Social networks play a key role in studying various individual and social behaviors. To use social networks in a study, their structural properties must be measured. For offline social networks, the conventional procedure is surveying/interviewing a set of randomly-selected respondents. In many practical applications, inferring the network structure via sampling is too prohibitively costly. There are also applications in which it simply fails. For example, for optimal vaccination or employing influential spreaders for public health interventions, we need to efficiently and quickly target well-connected individuals, which random sampling does not accomplish. In a few studies, an alternative sampling scheme (which we dub `alter sampling') has proven useful. This method simply targets randomly-chosen neighbors of the randomly-selected respondents. A natural question that arises is: to what extent does this method generalize? Is the method suitable for every social network or only the very few ones considered so far? In this paper, we demonstrate the robustness of this method across a wide range of networks with diverse structural properties. The method outperforms random sampling by a large margin for a vast majority of cases. We then propose an estimator to assess the advantage of choosing alter sampling over random sampling in practical scenarios, and demonstrate its accuracy via Monte Carlo simulations on diverse synthetic networks.

Cooperation is a major factor in the evolution of human societies. The structure of human social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these signatures is the tendency to organize as groups. Among the generative models that network theorists use to emulate this feature is the Stochastic Block Model (SBM). In this paper, we study evolutionary game dynamics on SBM networks. Using a recently-discovered duality between evolutionary games and coalescing random walks, we obtain analytical conditions such that natural selection favors cooperation over defection. We calculate the transition point for each community to favor cooperation. We find that a critical inter-community link creation probability exists for given group density, such that the overall network supports cooperation even if individual communities inhibit it. As a byproduct, we present mean-field solutions for the critical benefit-to-cost ratio which perform with remarkable accuracy for diverse generative network models, including those with community structure and heavy-tailed degree distributions. We also demonstrate the generalizability of the results to arbitrary two-player games.

Social structure affects the emergence and maintenance of cooperation. Here we study the evolutionary dynamics of cooperation in fragmented societies, and show that conjoining segregated cooperation-inhibiting groups, if done properly, rescues the fate of collective cooperation. We highlight the essential role of inter-group ties, that sew the patches of the social network together and facilitate cooperation. We point out several examples of this phenomenon in actual settings. We explore random and non-random graphs, as well as empirical networks. In many cases we find a marked reduction of the critical benefit-to-cost ratio needed for sustaining cooperation. Our finding gives hope that the increasing worldwide connectivity, if managed properly, can promote global cooperation.

Knowing the structure of an offline social network facilitates a variety of analyses, including studying the rate at which infectious diseases may spread and identifying a subset of actors to immunize in order to reduce, as much as possible, the rate of spread. Offline social network topologies are typically estimated by surveying actors and asking them to list their neighbours. While identifying close friends and family (i.e., strong ties) can typically be done reliably, listing all of one's acquaintances (i.e., weak ties) is subject to error due to respondent fatigue. This issue is commonly circumvented through the use of so-called "fixed choice" surveys where respondents are asked to name a fixed, small number of their weak ties (e.g., two or ten). Of course, the resulting crude observed network will omit many ties, and using this crude network to infer properties of the network, such as its degree distribution or clustering coefficient, will lead to biased estimates. This paper develops estimators, based on the method of moments, for a number of network characteristics including those related to the first and second moments of the degree distribution as well as the network size, using fixed-choice survey data. Experiments with simulated data illustrate that the proposed estimators perform well across a variety of network topologies and measurement scenarios, and the resulting estimates are significantly more accurate than those obtained directly using the crude observed network, which are commonly used in the literature. We also describe a variation of the Jackknife procedure that can be used to obtain an estimate of the estimator variance., Comment: 24 pages, 13 figures

In this paper we propose a mechanistic model that links micro social interactions to macro observables in the case of diffusion of film-going decisions. We devise a generalized epidemic model to capture the temporal evolution of box office revenues. The model adds social influence and memory effects to conventional epidemic models. Fitting the model to a temporal data set containing domestic weekly revenue of the 5000 top US-grossing films of all time, we find that a two-parameter model can capture a remarkable portion of the observed variance in the data. Using the distribution of the estimated parameters for different genres, we then present a predictive model which provides reasonable a-priori estimates of future sale as a function of time.

Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class which suggests there is no efficient algorithm. Whether there exists a simple solution for weak selection was unanswered. Here we provide, surprisingly, a general formula for weak selection that applies to any graph or social network. Our method uses coalescent theory and relies on calculating the meeting times of random walks. We can now evaluate large numbers of diverse and heterogeneous population structures for their propensity to favor cooperation. We can also study how small changes in population structure---graph surgery---affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties., Comment: 68 pages, 10 figures

The friendship paradox is the phenomenon that in social networks, people on average have fewer friends than their friends do. The generalized friendship paradox is an extension to attributes other than the number of friends. The friendship paradox and its generalized version have gathered recent attention due to the information they provide about network structure and local inequalities. In this paper, we propose several measures of nodal qualities which capture different aspects of their activities and influence in online social networks. Using these measures we analyse the prevalence of the generalized friendship paradox over Twitter and we report high levels of prevalence (up to over 90\% of nodes). We contend that this prevalence of the friendship paradox and its generalized version arise because of the hierarchical nature of the connections in the network. This hierarchy is nested as opposed to being star-like. We conclude that these paradoxes are collective phenomena not created merely by a minority of well-connected or high-attribute nodes. Moreover, our results show that a large fraction of individuals can experience the generalized friendship paradox even in the absence of a significant correlation between degrees and attributes.

This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the special case of homogeneous growth, and are limited to the state state (that is, the limit of infinite size). In the present paper, we obtain closed-form solutions for the joint degree distribution of heterogeneously growing multiplex networks with arbitrary number of layers in the steady state. Heterogeneous growth means that each incoming node establishes different numbers of links in different layers. We consider both uniform and preferential growth. We then extend the analysis of the uniform growth mechanism to arbitrary times. We obtain a closed-form solution for the time-dependent joint degree distribution of a growing multiplex network with arbitrary initial conditions. Throughout, theoretical findings are corroborated with Monte Carlo simulations. The results shed light on the effects of the initial network on the transient dynamics of growing multiplex networks, and takes a step towards characterizing the temporal variations of the connectivity of growing multiplex networks, as well as predicting their future structural properties.

We consider the problem of growing multiplex networks with intrinsic fitness and inter-layer coupling. The model comprises two layers; one that incorporates fitness and another in which attachments are preferential. In the first layer, attachment probabilities are proportional to fitness values, and in the second layer, proportional to the sum of degrees in both layers. We provide analytical closed-form solutions for the joint distributions of fitness and degrees. We also derive closed-form expressions for the expected value of the degree as a function of fitness. The model alleviates two shortcomings that are present in the current models of growing multiplex networks: homogeneity of connections, and homogeneity of fitness. In this paper, we posit and analyze a growth model that is heterogeneous in both senses.

The friendship paradox is a sociological phenomenon stating that most people have fewer friends than their friends do. The generalized friendship paradox refers to the same observation for attributes other than degree, and it has been observed in Twitter and scientific collaboration networks. This paper takes an analytical approach to model this phenomenon. We consider a preferential attachment-like network growth mechanism governed by both node degrees and `qualities'. We introduce measures to quantify paradoxes, and contrast the results obtained in our model to those obtained for an uncorrelated network, where the degrees and qualities of adjacent nodes are uncorrelated. We shed light on the effect of the distribution of node qualities on the friendship paradox. We consider both the mean and the median to measure paradoxes, and compare the results obtained by using these two statistics.

The multiplex network growth literature has been confined to homogeneous growth hitherto, where the number of links that each new incoming node establishes is the same across layers. This paper focuses on heterogeneous growth. We first analyze the case of two preferentially growing layers and find a closed-form expression for the inter-layer degree distribution, and demonstrate that non-trivial inter-layer degree correlations emerge in the steady state. Then we focus on the case of uniform growth. Surprisingly, inter-layer correlations arise in the random case, too. Also, we observe that the expression for the average layer-2 degree of nodes whose layer-1 degree is k, is identical for the uniform and preferential schemes. Throughout, theoretical predictions are corroborated using Monte Carlo simulations.

The friendship paradox refers to the sociological observation that, while the people's assessment of their own popularity is typically self-aggrandizing, in reality they are less popular than their friends. The generalized friendship paradox is the average alter superiority observed empirically in social settings, scientific collaboration networks, as well as online social media. We posit a quality-based network growth model in which the chance for a node to receive new links depends both on its degree and a quality parameter. Nodes are assigned qualities the first time they join the network, and these do not change over time. We analyse the model theoretically, finding expressions for the joint degree-quality distribution and nearest-neighbor distribution. We then demonstrate that this model exhibits both the friendship paradox and the generalized friendship paradox at the network level, regardless of the distribution of qualities. We also show that, in the proposed model, the degree and quality of each node are positively correlated regardless of how node qualities are distributed.