One-step Estimation of Networked Population Size: Respondent-Driven Capture-Recapture with Anonymity

Population size estimates for hidden and hard-to-reach populations are particularly important when members are known to suffer from disproportion health issues or to pose health risks to the larger ambient population in which they are embedded. Efforts to derive size estimates are often frustrated by a range of factors that preclude conventional survey strategies, including social stigma associated with group membership or members' involvement in illegal activities. This paper extends prior research on the problem of network population size estimation, building on established survey/sampling methodologies commonly used with hard-to-reach groups. Three novel one-step, network-based population size estimators are presented, to be used in the context of uniform random sampling, respondent-driven sampling, and when networks exhibit significant clustering effects. Provably sufficient conditions for the consistency of these estimators (in large configuration networks) are given. Simulation experiments across a wide range of synthetic network topologies validate the performance of the estimators, which are seen to perform well on a real-world location-based social networking data set with significant clustering. Finally, the proposed schemes are extended to allow them to be used in settings where participant anonymity is required. Systematic experiments show favorable tradeoffs between anonymity guarantees and estimator performance. Taken together, we demonstrate that reasonable population estimates can be derived from anonymous respondent driven samples of 250-750 individuals, within ambient populations of 5,000-40,000. The method thus represents a novel and cost-effective means for health planners and those agencies concerned with health and disease surveillance to estimate the size of hidden populations. Limitations and future work are discussed in the concluding section

Graphlet and Orbit Computation on Heterogeneous Graphs

Many applications, ranging from natural to social sciences, rely on graphlet analysis for the intuitive and meaningful characterization of networks employing micro-level structures as building blocks. However, it has not been thoroughly explored in heterogeneous graphs, which comprise various types of nodes and edges. Finding graphlets and orbits for heterogeneous graphs is difficult because of the heterogeneity and abundance of semantic information. We consider heterogeneous graphs, which can be treated as colored graphs. By applying the canonical label technique, we determine the graph isomorphism problem with multiple states on nodes and edges. With minimal parameters, we build all non-isomorphic graphs and associated orbits. We provide a Python package that can be used to generate orbits for colored directed graphs and determine the frequency of orbit occurrence. Finally, we provide four examples to illustrate the use of the Python package.Comment: 13 pages, 7 figure

Group-size dependent synergy in heterogeneous populations

When people collaborate, they expect more in return than a simple sum of their efforts. This observation is at the heart of the so-called public goods game, where the participants' contributions are multiplied by an $r$ synergy factor before they are distributed among group members. However, a larger group could be more effective, which can be described by a larger synergy factor. To elaborate on the possible consequences, in this study, we introduce a model where the population has different sizes of groups, and the applied synergy factor depends on the size of the group. We examine different options when the increment of $r$ is linear, slow, or sudden, but in all cases, the cooperation level is higher than that in a population where the homogeneous $r$ factor is used. In the latter case, smaller groups perform better; however, this behavior is reversed when synergy increases for larger groups. Hence, the entire community benefits because larger groups are rewarded better. Notably, a similar qualitative behavior can be observed for other heterogeneous topologies, including scale-free interaction graphs.Comment: 9 pages, 6 figures, accepted by Chaos, Solitons and Fractals: the Interdisciplinary Journal of Nonlinear Science, and Nonequilibrium and Complex Phenomen

Dynamics and Social Clustering on Coevolving Networks

Complex networks offer a powerful conceptual framework for the description and analysis of many real world systems. Many processes have been formed into networks in the area of random graphs, and the dynamics of networks have been studied. These two mechanisms combined creates an adaptive or coevolving network -- a network whose edges change adaptively with respect to its states, bringing a dynamical interaction between the state of nodes and the topology of the network. We study three binary-state dynamics in the context of opinion formation, disease propagation and evolutionary games of networks. We try to understand how the network structure affects the status of individuals, and how the behavior of individuals, in turn, affects the overall network structure. We focus our investigation on social clustering, since this is one of the central properties of social networks, arising due to the ubiquitous tendency among individuals to connect to friends of a friend, and can significantly impact a coevolving network system. Introducing rewiring models with transitivity reinforcement, we investigate how the mechanism affects network dynamics and the clustering structure of the networks. We perform Monte Carlo simulations to explore the parameter space of each model. By applying improved compartmental formalism methods, including approximate master equations, our semi-analytical approximation generally provide accurate predictions of the final states of the networks, degree distributions, and evolution of fundamental quantities. Different levels of semi-analytical estimation are compared.Doctor of Philosoph

Restoring spatial cooperation with myopic agents in a three-strategy social dilemma

Introducing strategy complexity into the basic conflict of cooperation and defection is a natural response to avoid the tragedy of the common state. As an intermediate approach, quasi-cooperators were recently suggested to address the original problem. In this study, we test its vitality in structured populations where players have fixed partners. Naively, the latter condition should support cooperation unambiguously via enhanced network reciprocity. However, the opposite is true because the spatial structure may provide a humbler cooperation level than a well-mixed population. This unexpected behavior can be understood if we consider that at a certain parameter interval the original prisoner's dilemma game is transformed into a snow-drift game. If we replace the original imitating strategy protocol by assuming myopic players, the spatial population becomes a friendly environment for cooperation. This observation is valid in a huge region of parameter space. This study highlights that spatial structure can reveal a new aspect of social dilemmas when strategy complexity is introduced.Comment: 9 pages, 4 figures, accepted by Applied Mathematics and Computatio

A method for assessing the success and failure of community-level interventions in the presence of network diffusion, social reinforcement, and related social effects

Prevention and intervention work done within community settings often face unique analytic challenges for rigorous evaluations. Since community prevention work (often geographically isolated) cannot be controlled in the same way other prevention programs and these communities have an increased level of interpersonal interactions, rigorous evaluations are needed. Even when the `gold standard' randomized control trials are implemented within community intervention work, the threats to internal validity can be called into question given informal social spread of information in closed network settings. A new prevention evaluation method is presented here to disentangle the social influences assumed to influence prevention effects within communities. We formally introduce the method and it's utility for a suicide prevention program implemented in several Alaska Native villages. The results show promise to explore eight sociological measures of intervention effects in the face of social diffusion, social reinforcement, and direct treatment. Policy and research implication are discussed.Comment: 18 pages, 5 figure