We conclude our study with a performance analysis of the selected Mobile MECs by varying the community detection algorithms adopted. We then compare some structural properties of the communities detected, namely Similarity, Forward Stability, Cohesion and Coverage. We first measure the quality of the data set during an observation period of 1 year, during which the data set provides the 75% of the expected traces collected by approximately 170 users. Our analysis is based on the ParticipAct data set that offers real human mobility data. In particular, we study TILES, Infomap, and iLCD which are specifically designed to identify evolving communities of users in dynamic networks. In this context, our work focusses on the impact of three community detection algorithms to our edge selection strategy. The Multi-access Edge Computing (MEC) paradigm increases the computational capabilities of distributed sensing architectures, such as Mobile CrowdSensing platforms, which are designed to collect heterogeneous data from the crowd by exploiting mobile devices. Our results are verified on simulated graphs by estimating the relevant tail index parameters. We find that the distribution of number of common connections are regularly varying as well, where the tail indices of regular variation are governed by the type of graphex function used. The number being high for a fixed pair is an indicator of the original pair of vertices being connected. We also focus on a different metric for our study: the distribution of the number of common vertices (connections) shared by a pair of vertices. In this paper, we study sparse exchangeable graphs generated by graphex functions which are multivariate regularly varying. Previous work on such graphs imposes a marginal assumption of univariate regular variation (e.g., power-law tail) on the bivariate generating graphex function. In particular, these models help with investigating power-law properties of degree distributions, number of edges, and other relevant network metrics which support the scale-free structure of networks. Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. We demonstrate our approach in simulations as well as on real data applications in finance and transcriptomics. Moreover, we devise a tailored computation strategy of Bayes factors for block structure based on the Savage-Dickey ratio to test for presence of larger structure in a graph. We extend such models to consider clique-based blocks and to multiple graph settings introducing a novel prior process based on a Dependent Dirichlet process. We consider Bayesian nonparametric stochastic blockmodels as priors on the graph. A consequence of this approach is the propagation of the uncertainty in graph estimation to large-scale structure learning. We thus propose to exploit advances in random graph theory and embed them within the graphical models framework. Stochastic blockmodels offer a powerful tool to detect such structure in a network. Nonetheless, there is increasing interest in inferring more complex structures, such as communities, for multiple reasons, including more effective information retrieval and better interpretability. Inference is often focused on estimating individual edges in the latent graph. Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. The obtained model is not significantly moreĭifficult to implement than existing methods and performs well on real network We derive a simple expression for the likelihood and anĮfficient sampling method. Obtain a model which admits the inference of block-structure and edge Use of block-structure for network modelling in the new setting and thereby Latent vertex traits such as block-structure. Retaining desirable statistical properties, however this model do not capture (2009) and obtained a network model which admits power-law behaviour while Proposed the use of a different notion of exchangeability due to Kallenberg Implies quadratic scaling of the number of edges. TheseĪssumptions are fundamentally irreconcilable as the Aldous-Hoover theorem Of edges scale slower than quadratically in the number of vertices. Have a power-law distribution of the vertices which in turn implies the number Many statistical methods for network data parameterize the edge-probabilityīy attributing latent traits to the vertices such as block structure and assumeĮxchangeability in the sense of the Aldous-Hoover representation theorem.Įmpirical studies of networks indicates that many large, real-world networks
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