A Triclustering Approach for Time Evolving Graphs

This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make an a priori discretization. Experiments conducted on a synthetic dataset illustrate the good behaviour of the technique, and a study of a real-life dataset shows the potential of the proposed approach for exploratory data analysis

A Graph-Theoretic Formulation of Exploratory Blockmodeling

We present a new simple graph-theoretic formulation of the exploratory blockmodeling problem on undirected and unweighted one-mode networks. Our formulation takes as input the network G and the maximum number t of blocks for the solution model. The task is to find a minimum-size set of edge insertions and deletions that transform the input graph G into a graph G\u27 with at most t neighborhood classes. Herein, a neighborhood class is a maximal set of vertices with the same neighborhood. The neighborhood classes of G\u27 directly give the blocks and block interactions of the computed blockmodel. We analyze the classic and parameterized complexity of the exploratory blockmodeling problem, provide a branch-and-bound algorithm, an ILP formulation and several heuristics. Finally, we compare our exact algorithms to previous ILP-based approaches and show that the new algorithms are faster for t ? 4

Bayesian stochastic blockmodeling

This chapter provides a self-contained introduction to the use of Bayesian inference to extract large-scale modular structures from network data, based on the stochastic blockmodel (SBM), as well as its degree-corrected and overlapping generalizations. We focus on nonparametric formulations that allow their inference in a manner that prevents overfitting, and enables model selection. We discuss aspects of the choice of priors, in particular how to avoid underfitting via increased Bayesian hierarchies, and we contrast the task of sampling network partitions from the posterior distribution with finding the single point estimate that maximizes it, while describing efficient algorithms to perform either one. We also show how inferring the SBM can be used to predict missing and spurious links, and shed light on the fundamental limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool at https://graph-tool.skewed.de . See also the HOWTO at https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference

EUSN 2021 Book of Abstracts, Fifth European Conference on Social Networks

Book of abstract of the fifth European conference on Social Networks EUSN 202

Prediction, evolution and privacy in social and affiliation networks

In the last few years, there has been a growing interest in studying online social and affiliation networks, leading to a new category of inference problems that consider the actor characteristics and their social environments. These problems have a variety of applications, from creating more effective marketing campaigns to designing better personalized services. Predictive statistical models allow learning hidden information automatically in these networks but also bring many privacy concerns. Three of the main challenges that I address in my thesis are understanding 1) how the complex observed and unobserved relationships among actors can help in building better behavior models, and in designing more accurate predictive algorithms, 2) what are the processes that drive the network growth and link formation, and 3) what are the implications of predictive algorithms to the privacy of users who share content online. The majority of previous work in prediction, evolution and privacy in online social networks has concentrated on the single-mode networks which form around user-user links, such as friendship and email communication. However, single-mode networks often co-exist with two-mode affiliation networks in which users are linked to other entities, such as social groups, online content and events. We study the interplay between these two types of networks and show that analyzing these higher-order interactions can reveal dependencies that are difficult to extract from the pair-wise interactions alone. In particular, we present our contributions to the challenging problems of collective classification, link prediction, network evolution, anonymization and preserving privacy in social and affiliation networks. We evaluate our models on real-world data sets from well-known online social networks, such as Flickr, Facebook, Dogster and LiveJournal

Visual network storytelling

We love networks! Networks are powerful conceptual tools, encapsulating in a single item multiple affordances for computation (networks as graphs), visualization (networks as maps) and manipulation of data (networks as interfaces). In the field of mathematics, graph theory has been around since Euler’s walk on Königsberg’s bridges (Euler 1736). But it is not until the end of the last century that networks acquired a multidisciplinary popularity. Graph computation is certainly powerful, but it is also very demanding and for many years its advantages remained the privilege of scholars with solid mathematical fundamentals. In the last few decades, however, networks acquired a new set of affordances and reached a larger audience, thanks to the growing availability of tools to design them. Drawn on paper or screen, networks became easier to handle and obtained properties that calculation could not express. Far from being merely aesthetic, the graphical representation of networks has an intrinsic hermeneutic value. Networks can become maps and be read as such. Combining the computation power of graphs with the visual expressivity of maps and the interactivity of computer interface, networks can be used in Exploratory Data Analysis (Tukey, 1977). Navigating through data becomes so fluid that zooming in on a single data-point and out to a landscape of a million traces is just a click away. Increasingly specialized software has been designed to support the exploration of network data. Tools like Pajek (vlado.fmf.uni-lj.si/pub/networks/pajek), NetDraw (sites.google.com/site/ netdrawsoftware), Ucinet (www.analytictech.com/ucinet), Guess (graphexploration.cond.org) and more recently Gephi (gephi.org) have progressively smoothed out the difficulties of graph mathematics, turning a complex mathematical formalism into a more user-friendly point-and-click interface (1) . If visual exploration of networks can output to confirmatory statistics, what about sharing one network exploration with others? We developed Manylines (https://github.com/medialab/manylines), a tool allowing you to share the visual analysis of a network with a wide audience by publishing it on the web. With Manylines, you can not only easily publish a network on the web but also share its exploration by describing the network’s visual key findings. Through a set of examples, we will illustrate how the narrative opportunities of Manylines can contribute to the enunciation of a visual grammar of networks. (1) A simple look at the URLs of the subsequent tools reveals the efforts deployed to make network-manipulation tools user-friendly and thereby available to a larger public

Modeling heterogeneity in random graphs through latent space models: a selective review

We present a selective review on probabilistic modeling of heterogeneity in random graphs. We focus on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the last five years