On Community Structure in Complex Networks: Challenges and Opportunities
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Networks in Nature: Dynamics, Evolution, and Modularity
Networks in Nature: Dynamics, Evolution, and Modularity Sumeet Agarwal Merton College University of Oxford A thesis submitted for the degree of Doctor of Philosophy Hilary 2012 2 To my entire social network; for no man is an island Acknowledgements Primary thanks go to my supervisors, Nick Jones, Charlotte Deane, and Mason Porter, whose ideas and guidance have of course played a major role in shaping this thesis. I would also like to acknowledge the very useful sug- gestions of my examiners, Mark Fricker and Jukka-Pekka Onnela, which have helped improve this work. I am very grateful to all the members of the three Oxford groups I have had the fortune to be associated with: Sys- tems and Signals, Protein Informatics, and the Systems Biology Doctoral Training Centre. Their companionship has served greatly to educate and motivate me during the course of my time in Oxford. In particular, Anna Lewis and Ben Fulcher, both working on closely related D.Phil. projects, have been invaluable throughout, and have assisted and inspired my work in many different ways. Gabriel Villar and Samuel Johnson have been col- laborators and co-authors who have helped me to develop some of the ideas and methods used here. There are several other people who have gener- ously provided data, code, or information that has been directly useful for my work: Waqar Ali, Binh-Minh Bui-Xuan, Pao-Yang Chen, Dan Fenn, Katherine Huang, Patrick Kemmeren, Max Little, Aur´elienMazurie, Aziz Mithani, Peter Mucha, George Nicholson, Eli Owens, Stephen Reid, Nico- las Simonis, Dave Smith, Ian Taylor, Amanda Traud, and Jeffrey Wrana. -
Modularity in Static and Dynamic Networks
Modularity in static and dynamic networks Sarah F. Muldoon University at Buffalo, SUNY OHBM – Brain Graphs Workshop June 25, 2017 Outline 1. Introduction: What is modularity? 2. Determining community structure (static networks) 3. Comparing community structure 4. Multilayer networks: Constructing multitask and temporal multilayer dynamic networks 5. Dynamic community structure 6. Useful references OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Introduction: What is Modularity? OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon What is Modularity? Modularity (Community Structure) • A module (community) is a subset of vertices in a graph that have more connections to each other than to the rest of the network • Example social networks: groups of friends Modularity in the brain: • Structural networks: communities are groups of brain areas that are more highly connected to each other than the rest of the brain • Functional networks: communities are groups of brain areas with synchronous activity that is not synchronous with other brain activity OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Findings: The Brain is Modular Structural networks: cortical thickness correlations sensorimotor/spatial strategic/executive mnemonic/emotion olfactocentric auditory/language visual processing Chen et al. (2008) Cereb Cortex OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Findings: The Brain is Modular • Functional networks: resting state fMRI He et al. (2009) PLOS One OHBM 2017 – Brain Graphs Workshop – Sarah F. Muldoon Findings: The -
A Python Library to Model and Analyze Diffusion Processes Over Complex Networks
International Journal of Data Science and Analytics (2018) 5:61–79 https://doi.org/10.1007/s41060-017-0086-6 APPLICATIONS NDlib: a python library to model and analyze diffusion processes over complex networks Giulio Rossetti2 · Letizia Milli1,2 · Salvatore Rinzivillo2 · Alina Sîrbu1 · Dino Pedreschi1 · Fosca Giannotti2 Received: 19 October 2017 / Accepted: 11 December 2017 / Published online: 20 December 2017 © Springer International Publishing AG, part of Springer Nature 2017 Abstract Nowadays the analysis of dynamics of and on networks represents a hot topic in the social network analysis playground. To support students, teachers, developers and researchers, in this work we introduce a novel framework, namely NDlib,an environment designed to describe diffusion simulations. NDlib is designed to be a multi-level ecosystem that can be fruitfully used by different user segments. For this reason, upon NDlib, we designed a simulation server that allows remote execution of experiments as well as an online visualization tool that abstracts its programmatic interface and makes available the simulation platform to non-technicians. Keywords Social network analysis software · Epidemics · Opinion dynamics 1 Introduction be modeled as networks and, as such, analyzed. Undoubt- edly, such pervasiveness has produced an amplification in the In the last decades, social network analysis, henceforth SNA, visibility of network analysis studies thus making this com- has received increasing attention from several heterogeneous plex and interesting field one of the most widespread among fields of research. Such popularity was certainly due to the higher education centers, universities and academies. Given flexibility offered by graph theory: a powerful tool that the exponential diffusion reached by SNA, several tools were allows reducing countless phenomena to a common ana- developed to make it approachable to the wider audience pos- lytical framework whose basic bricks are nodes and their sible. -
Evolving Networks and Social Network Analysis Methods And
DOI: 10.5772/intechopen.79041 ProvisionalChapter chapter 7 Evolving Networks andand SocialSocial NetworkNetwork AnalysisAnalysis Methods and Techniques Mário Cordeiro, Rui P. Sarmento,Sarmento, PavelPavel BrazdilBrazdil andand João Gama Additional information isis available atat thethe endend ofof thethe chapterchapter http://dx.doi.org/10.5772/intechopen.79041 Abstract Evolving networks by definition are networks that change as a function of time. They are a natural extension of network science since almost all real-world networks evolve over time, either by adding or by removing nodes or links over time: elementary actor-level network measures like network centrality change as a function of time, popularity and influence of individuals grow or fade depending on processes, and events occur in net- works during time intervals. Other problems such as network-level statistics computation, link prediction, community detection, and visualization gain additional research impor- tance when applied to dynamic online social networks (OSNs). Due to their temporal dimension, rapid growth of users, velocity of changes in networks, and amount of data that these OSNs generate, effective and efficient methods and techniques for small static networks are now required to scale and deal with the temporal dimension in case of streaming settings. This chapter reviews the state of the art in selected aspects of evolving social networks presenting open research challenges related to OSNs. The challenges suggest that significant further research is required in evolving social networks, i.e., existent methods, techniques, and algorithms must be rethought and designed toward incremental and dynamic versions that allow the efficient analysis of evolving networks. Keywords: evolving networks, social network analysis 1. -
Homophily and Long-Run Integration in Social Networks∗
Homophily and Long-Run Integration in Social Networks∗ Yann Bramoulléy Sergio Currariniz Matthew O. Jacksonx Paolo Pin{ Brian W. Rogersk January 19, 2012 Abstract We study network formation in which nodes enter sequentially and form connections through a combination of random meetings and network-based search, as in Jackson and Rogers (2007). We focus on the impact of agents' heterogeneity on link patterns when connections are formed under type-dependent biases. In particular, we are concerned with how the local neighborhood of a node evolves as the node ages. We provide a surprising general result on long-run in- tegration whereby the composition of types in a node's neighborhood approaches the global type distribution, provided that the search part of the meeting process is unbiased. Integration, however, occurs only for suciently old nodes, while the aggregate distribution of connections still reects the bias of the random process. For a special case of the model, we analyze the form of these biases with regard to type-based degree distributions and group-level homophily patterns. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals. JEL Codes: A14, D85, I21. ∗Following the suggestion of JET editors, this paper draws from two working papers developed independently: Bramoullé and Rogers (2010) and Currarini, Jackson and Pin (2010b). We gratefully acknowledge nancial support from the NSF under grant SES-0961481 and we thank Vincent Boucher for his research assistance. We also thank Habiba Djebbari, Andrea Galeotti, Sanjeev Goyal, James Moody, Betsy Sinclair, Bruno Strulovici, and Adrien Vigier, as well as numerous seminar participants. -
Arxiv:1705.10225V8 [Stat.ML] 6 Feb 2020
Bayesian stochastic blockmodelinga Tiago P. Peixotoy Department of Mathematical Sciences and Centre for Networks and Collective Behaviour, University of Bath, United Kingdom and ISI Foundation, Turin, Italy This chapter provides a self-contained introduction to the use of Bayesian inference to ex- tract 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 non- parametric 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. arXiv:1705.10225v8 [stat.ML] 6 Feb 2020 aTo appear in “Advances in Network Clustering and Blockmodeling,” edited by P. Doreian, V. Batagelj, A. Ferligoj, (Wiley, New York, 2019 [forthcoming]). y [email protected] 2 CONTENTS I. Introduction 3 II. Structure versus randomness in networks 3 III. The stochastic blockmodel (SBM) 5 IV. Bayesian inference: the posterior probability of partitions 7 V. Microcanonical models and the minimum description length principle (MDL) 11 VI. The “resolution limit” underfitting problem, and the nested SBM 13 VII. Model variations 17 A. Model selection 18 B. Degree correction 18 C. -
Multidimensional Network Analysis
Universita` degli Studi di Pisa Dipartimento di Informatica Dottorato di Ricerca in Informatica Ph.D. Thesis Multidimensional Network Analysis Michele Coscia Supervisor Supervisor Fosca Giannotti Dino Pedreschi May 9, 2012 Abstract This thesis is focused on the study of multidimensional networks. A multidimensional network is a network in which among the nodes there may be multiple different qualitative and quantitative relations. Traditionally, complex network analysis has focused on networks with only one kind of relation. Even with this constraint, monodimensional networks posed many analytic challenges, being representations of ubiquitous complex systems in nature. However, it is a matter of common experience that the constraint of considering only one single relation at a time limits the set of real world phenomena that can be represented with complex networks. When multiple different relations act at the same time, traditional complex network analysis cannot provide suitable an- alytic tools. To provide the suitable tools for this scenario is exactly the aim of this thesis: the creation and study of a Multidimensional Network Analysis, to extend the toolbox of complex network analysis and grasp the complexity of real world phenomena. The urgency and need for a multidimensional network analysis is here presented, along with an empirical proof of the ubiquity of this multifaceted reality in different complex networks, and some related works that in the last two years were proposed in this novel setting, yet to be systematically defined. Then, we tackle the foundations of the multidimensional setting at different levels, both by looking at the basic exten- sions of the known model and by developing novel algorithms and frameworks for well-understood and useful problems, such as community discovery (our main case study), temporal analysis, link prediction and more. -
A Network Approach to Define Modularity of Components In
A Network Approach to Define Modularity of Components Manuel E. Sosa1 Technology and Operations Management Area, in Complex Products INSEAD, 77305 Fontainebleau, France Modularity has been defined at the product and system levels. However, little effort has e-mail: [email protected] gone into defining and quantifying modularity at the component level. We consider com- plex products as a network of components that share technical interfaces (or connections) Steven D. Eppinger in order to function as a whole and define component modularity based on the lack of Sloan School of Management, connectivity among them. Building upon previous work in graph theory and social net- Massachusetts Institute of Technology, work analysis, we define three measures of component modularity based on the notion of Cambridge, Massachusetts 02139 centrality. Our measures consider how components share direct interfaces with adjacent components, how design interfaces may propagate to nonadjacent components in the Craig M. Rowles product, and how components may act as bridges among other components through their Pratt & Whitney Aircraft, interfaces. We calculate and interpret all three measures of component modularity by East Hartford, Connecticut 06108 studying the product architecture of a large commercial aircraft engine. We illustrate the use of these measures to test the impact of modularity on component redesign. Our results show that the relationship between component modularity and component redesign de- pends on the type of interfaces connecting product components. We also discuss direc- tions for future work. ͓DOI: 10.1115/1.2771182͔ 1 Introduction The need to measure modularity has been highlighted implicitly by Saleh ͓12͔ in his recent invitation “to contribute to the growing Previous research on product architecture has defined modular- field of flexibility in system design” ͑p. -
Task-Dependent Evolution of Modularity in Neural Networks1
Task-dependent evolution of modularity in neural networks1 Michael Husk¨ en, Christian Igel, and Marc Toussaint Institut fur¨ Neuroinformatik, Ruhr-Universit¨at Bochum, 44780 Bochum, Germany Telephone: +49 234 32 25558, Fax: +49 234 32 14209 fhuesken,igel,[email protected] Connection Science Vol 14, No 3, 2002, p. 219-229 Abstract. There exist many ideas and assumptions about the development and meaning of modu- larity in biological and technical neural systems. We empirically study the evolution of connectionist models in the context of modular problems. For this purpose, we define quantitative measures for the degree of modularity and monitor them during evolutionary processes under different constraints. It turns out that the modularity of the problem is reflected by the architecture of adapted systems, although learning can counterbalance some imperfection of the architecture. The demand for fast learning systems increases the selective pressure towards modularity. 1 Introduction The performance of biological as well as technical neural systems crucially depends on their ar- chitectures. In case of a feed-forward neural network (NN), architecture may be defined as the underlying graph constituting the number of neurons and the way these neurons are connected. Particularly one property of architectures, modularity, has raised a lot of interest among researchers dealing with biological and technical aspects of neural computation. It appears to be obvious to emphasise modularity in neural systems because the vertebrate brain is highly modular both in an anatomical and in a functional sense. It is important to stress that there are different concepts of modules. `When a neuroscientist uses the word \module", s/he is usually referring to the fact that brains are structured, with cells, columns, layers, and regions which divide up the labour of information processing in various ways' 1This paper is a revised and extended version of the GECCO 2001 Late-Breaking Paper by Husk¨ en, Igel, & Toussaint (2001). -
Analyzing Social Media Network for Students in Presidential Election 2019 with Nodexl
ANALYZING SOCIAL MEDIA NETWORK FOR STUDENTS IN PRESIDENTIAL ELECTION 2019 WITH NODEXL Irwan Dwi Arianto Doctoral Candidate of Communication Sciences, Airlangga University Corresponding Authors: [email protected] Abstract. Twitter is widely used in digital political campaigns. Twitter as a social media that is useful for building networks and even connecting political participants with the community. Indonesia will get a demographic bonus starting next year until 2030. The number of productive ages that will become a demographic bonus if not recognized correctly can be a problem. The election organizer must seize this opportunity for the benefit of voter participation. This study aims to describe the network structure of students in the 2019 presidential election. The first debate was held on January 17, 2019 as a starting point for data retrieval on Twitter social media. This study uses data sources derived from Twitter talks from 17 January 2019 to 20 August 2019 with keywords “#pilpres2019 OR #mahasiswa since: 2019-01-17”. The data obtained were analyzed by the communication network analysis method using NodeXL software. Our Analysis found that Top Influencer is @jokowi, as well as Top, Mentioned also @jokowi while Top Tweeters @okezonenews and Top Replied-To @hasmi_bakhtiar. Jokowi is incumbent running for re-election with Ma’ruf Amin (Senior Muslim Cleric) as his running mate against Prabowo Subianto (a former general) and Sandiaga Uno as his running mate (former vice governor). This shows that the more concentrated in the millennial generation in this case students are presidential candidates @jokowi. @okezonenews, the official twitter account of okezone.com (MNC Media Group). -
Evolving Neural Networks Using Behavioural Genetic Principles
Evolving Neural Networks Using Behavioural Genetic Principles Maitrei Kohli A dissertation submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy Department of Computer Science & Information Systems Birkbeck, University of London United Kingdom March 2017 0 Declaration This thesis is the result of my own work, except where explicitly acknowledged in the text. Maitrei Kohli …………………. 1 ABSTRACT Neuroevolution is a nature-inspired approach for creating artificial intelligence. Its main objective is to evolve artificial neural networks (ANNs) that are capable of exhibiting intelligent behaviours. It is a widely researched field with numerous successful methods and applications. However, despite its success, there are still open research questions and notable limitations. These include the challenge of scaling neuroevolution to evolve cognitive behaviours, evolving ANNs capable of adapting online and learning from previously acquired knowledge, as well as understanding and synthesising the evolutionary pressures that lead to high-level intelligence. This thesis presents a new perspective on the evolution of ANNs that exhibit intelligent behaviours. The novel neuroevolutionary approach presented in this thesis is based on the principles of behavioural genetics (BG). It evolves ANNs’ ‘general ability to learn’, combining evolution and ontogenetic adaptation within a single framework. The ‘general ability to learn’ was modelled by the interaction of artificial genes, encoding the intrinsic properties of the ANNs, and the environment, captured by a combination of filtered training datasets and stochastic initialisation weights of the ANNs. Genes shape and constrain learning whereas the environment provides the learning bias; together, they provide the ability of the ANN to acquire a particular task. -
Albert-László Barabási with Emma K
Network Science Class 5: BA model Albert-László Barabási With Emma K. Towlson, Sebastian Ruf, Michael Danziger and Louis Shekhtman www.BarabasiLab.com Section 1 Introduction Section 1 Hubs represent the most striking difference between a random and a scale-free network. Their emergence in many real systems raises several fundamental questions: • Why does the random network model of Erdős and Rényi fail to reproduce the hubs and the power laws observed in many real networks? • Why do so different systems as the WWW or the cell converge to a similar scale-free architecture? Section 2 Growth and preferential attachment BA MODEL: Growth ER model: the number of nodes, N, is fixed (static models) networks expand through the addition of new nodes Barabási & Albert, Science 286, 509 (1999) BA MODEL: Preferential attachment ER model: links are added randomly to the network New nodes prefer to connect to the more connected nodes Barabási & Albert, Science 286, 509 (1999) Network Science: Evolving Network Models Section 2: Growth and Preferential Sttachment The random network model differs from real networks in two important characteristics: Growth: While the random network model assumes that the number of nodes is fixed (time invariant), real networks are the result of a growth process that continuously increases. Preferential Attachment: While nodes in random networks randomly choose their interaction partner, in real networks new nodes prefer to link to the more connected nodes. Barabási & Albert, Science 286, 509 (1999) Network Science: Evolving Network Models Section 3 The Barabási-Albert model Origin of SF networks: Growth and preferential attachment (1) Networks continuously expand by the GROWTH: addition of new nodes add a new node with m links WWW : addition of new documents PREFERENTIAL ATTACHMENT: (2) New nodes prefer to link to highly the probability that a node connects to a node connected nodes.