Block-Approximated Exponential Random Graphs

An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions, while being able to meaningfully model both local information of the graph (e.g., degrees) as well as global information (e.g., clustering coefficient, assortativity, etc.) if desired. This allows one to efficiently generate random networks with similar properties as an observed network, and the models can be used for several downstream tasks such as link prediction. Our methods are scalable to sparse graphs consisting of millions of nodes. Empirical evaluation demonstrates competitiveness in terms of both speed and accuracy with state-of-the-art methods -- which are typically based on embedding the graph into some low-dimensional space -- for link prediction, showcasing the potential of a more direct and interpretable probabalistic model for this task.Comment: Accepted for DSAA 2020 conferenc

A framework to generate hypergraphs with community structure

In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the standardized evaluation of algorithms and the statistical study of real-world networked data, these are scarcely available in the context of hypergraphs. Here we propose a flexible and efficient framework for the generation of hypergraphs with many nodes and large hyperedges, which allows specifying general community structures and tune different local statistics. We illustrate how to use our model to sample synthetic data with desired features (assortative or disassortative communities, mixed or hard community assignments, etc.), analyze community detection algorithms, and generate hypergraphs structurally similar to real-world data. Overcoming previous limitations on the generation of synthetic hypergraphs, our work constitutes a substantial advancement in the statistical modeling of higher-order systems.Comment: 18 pages, 8 figures, revised versio

Fairness in Social Networks

In professional and other social settings, networks play an important role in people\u27s lives. The communication between individuals and their positions in the network, may have a large impact on many aspects of their lives.In this work, I evaluate fairness from different perspectives.First,tomeasurefairnessfromgroupperspective,Iproposethenovelinformation unfairness criterion, which measures whether information spreads fairly to different groups in a network. Using this criterion, I perform a case study and measure fairness in information flow in different computer science co-authorship networks with respect to gender. Then, I consider two applications and show how to increase fairness with respect to a fairness metric. The first application is increasing fairness in information flow by adding a set of edges. I propose two algorithms- MaxFair and MinIUF- which are based on detecting those pairs of nodes whose connection would increase flow to disadvantaged groups. The second application is increasing fairness in organizational networks through employee hiring and assignment. I propose FairEA, a novel algorithm that allows organizations to gauge their success in achieving a diverse network. Next,Iexaminefairnessfromanindividualperspective.Iproposestratification assortativity, a novel metric that evaluates the tendency of the network to be divided into ordered classes. Then, I perform a case study on several co-authorship networks and examine the evolution of these networks over time and show that networks evolve into a highly stratified state. Finally, I introduce an agent-based model for network evolution to explain why social stratification emerges in a network

Proclivity or Popularity? Exploring Agent Heterogeneity in Network Formation

The Barabasi-Albert model (BA model) is the standard algorithm used to describe the emergent mechanism of a scale-free network. This dissertation argues that the BA model, and its variants, rarely take agent heterogeneity into account in the analysis of network formation. In social networks, however, people\u27s decisions to connect are strongly affected by the extent of similarity. In this dissertation, the author applies an agent-based modeling (ABM) approach to reassess the Barabasi-Albert model. This study proposes that, in forming social networks, agents are constantly balancing between instrumental and intrinsic preferences. After systematic simulation and subsequent analysis, this study finds that agents\u27 preference of popularity and proclivity strongly shapes various attributes of simulated social networks. Moreover, this analysis of simulated networks investigates potential ways to detect this balance within real-world networks. Particularly, the scale parameter of the power-distribution is found sensitive solely to agents\u27 preference popularity. Finally, this study employs the social media data (i.e., diffusion of different emotions) for Sina Weibo—a Chinese version Tweet—to valid the findings, and results suggest that diffusion of anger is more popularity-driven

Graph-theoretic Approach To Modeling Propagation And Control Of Network Worms

In today\u27s network-dependent society, cyber attacks with network worms have become the predominant threat to confidentiality, integrity, and availability of network computing resources. Despite ongoing research efforts, there is still no comprehensive network-security solution aimed at controling large-scale worm propagation. The aim of this work is fivefold: (1) Developing an accurate combinatorial model of worm propagation that can facilitate the analysis of worm control strategies, (2) Building an accurate epidemiological model for the propagation of a worm employing local strategies, (3) Devising distributed architecture and algorithms for detection of worm scanning activities, (4) Designing effective control strategies against the worm, and (5) Simulation of the developed models and strategies on large, scale-free graphs representing real-world communication networks. The proposed pair-approximation model uses the information about the network structure--order, size, degree distribution, and transitivity. The empirical study of propagation on large scale-free graphs is in agreement with the theoretical analysis of the proposed pair-approximation model. We, then, describe a natural generalization of the classical cops-and-robbers game--a combinatorial model of worm propagation and control. With the help of this game on graphs, we show that the problem of containing the worm is NP-hard. Six novel near-optimal control strategies are devised: combination of static and dynamic immunization, reactive dynamic and invariant dynamic immunization, soft quarantining, predictive traffic-blocking, and contact-tracing. The analysis of the predictive dynamic traffic-blocking, employing only local information, shows that the worm can be contained so that 40\% of the network nodes are not affected. Finally, we develop the Detection via Distributed Blackholes architecture and algorithm which reflect the propagation strategy used by the worm and the salient properties of the network. Our distributed detection algorithm can detect the worm scanning activity when only 1.5% of the network has been affected by the propagation. The proposed models and algorithms are analyzed with an individual-based simulation of worm propagation on realistic scale-free topologies

Different roles of nodes in networks

The 'complex network' has been studied in many disciplines. In this thesis, we use an economic network to study the heterogeneity of the networks. Networks of shareholders in Turkey and the Netherlands are constructed from raw data. The nodes are shareholders and an edge between shareholders exists if they have invested in the same company. The general analysis of network has shown that this type of network has characteristics similar to other types of real-world networks: power-law like degree distributions, small-world phenomenon and scaling of community size distributions. Furthermore, we introduce the 'type' of shareholders and analyse the different behaviour of shareholder types by comparing with a randomised null model. The results are that different types of shareholders are parts of different topological structures in the networks. Based on the economic behaviours, we propose a random walk model to mimic the different roles of shareholders in the networks. The model starts with a directed random graph of shareholders with assigned labels/types mimicing the raw data, and companies, showing which companies shareholders have invested in. A biased random walker model is introduced to model, on an abstract level, how shareholders' investments evolve. We then extract the associated shareholder network. This evolving model can qualitatively explain general characteristics and heterogeneity of the real-world shareholder networks: the scaling of community size distributions, percolation behaviour and the average shortest paths between different types. When we focus on the emergence of features from local interactions and higher-order interactions. We propose a new framework for this analysis. For a more general analysis, we design a simple transition matrix of temporal triplets. By comparing the transition matrix of higher-order interactions with the transition matrix of a pairwise interaction toy model, we can quantify the interactions of triplets. Moreover, we create an algorithm based on the transition matrix to make link predictions. We apply this framework to real-world networks and show that this new framework is successful in making predictions.Open Acces

Strain Elevation Tension Spring embedding and Cascading failures on the power-grid

Understanding the dynamics and properties of networks is of great importance in our highly connected data-driven society. When the networks relate to infrastructure, such understanding can have a substantial impact on public welfare. As such, there is a need for algorithms that can provide insights into the observable and latent properties of these structures. This thesis presents a novel embedding algorithm: the Strain Elevation Tension Spring embedding (SETSe), as a method of understanding complex networks. The algorithm is a deterministic physics model that incorporates both node and edge features into the final embedding. SETSe distinguishes itself from most embeddings methods by not having a loss function in the conventional sense and by not trying to place similar nodes close together. Instead, SETSe acts as a smoothing function for node features across the network topology. This approach produces embeddings that are intuitive and interpretable. In this thesis, I demonstrate how SETSe outperforms alternative embedding methods on node level and graph level tasks using networks made from stochastic block models and social networks with over 40,000 nodes and over 1 million edges. I also highlight a weakness of traditional methods to analysing cascading failures on power grids and demonstrate that SETSe is not susceptible to such issues. I then show how SETSe can be used as a measure of robustness in addition to providing a means to create interpretable maps in the geographical space given its smoothing embedding method. The framework has been made widely available through two open source R packages contributions, 1) the implementation of SETSe ("rsetse" on CRAN), and 2) a package for analysing cascading failures on power grids