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Networkx: Network Analysis with Python
NetworkX: Network Analysis with Python Salvatore Scellato Full tutorial presented at the XXX SunBelt Conference “NetworkX introduction: Hacking social networks using the Python programming language” by Aric Hagberg & Drew Conway Outline 1. Introduction to NetworkX 2. Getting started with Python and NetworkX 3. Basic network analysis 4. Writing your own code 5. You are ready for your project! 1. Introduction to NetworkX. Introduction to NetworkX - network analysis Vast amounts of network data are being generated and collected • Sociology: web pages, mobile phones, social networks • Technology: Internet routers, vehicular flows, power grids How can we analyze this networks? Introduction to NetworkX - Python awesomeness Introduction to NetworkX “Python package for the creation, manipulation and study of the structure, dynamics and functions of complex networks.” • Data structures for representing many types of networks, or graphs • Nodes can be any (hashable) Python object, edges can contain arbitrary data • Flexibility ideal for representing networks found in many different fields • Easy to install on multiple platforms • Online up-to-date documentation • First public release in April 2005 Introduction to NetworkX - design requirements • Tool to study the structure and dynamics of social, biological, and infrastructure networks • Ease-of-use and rapid development in a collaborative, multidisciplinary environment • Easy to learn, easy to teach • Open-source tool base that can easily grow in a multidisciplinary environment with non-expert users -
Introduction to Network Science & Visualisation
IFC – Bank Indonesia International Workshop and Seminar on “Big Data for Central Bank Policies / Building Pathways for Policy Making with Big Data” Bali, Indonesia, 23-26 July 2018 Introduction to network science & visualisation1 Kimmo Soramäki, Financial Network Analytics 1 This presentation was prepared for the meeting. The views expressed are those of the author and do not necessarily reflect the views of the BIS, the IFC or the central banks and other institutions represented at the meeting. FNA FNA Introduction to Network Science & Visualization I Dr. Kimmo Soramäki Founder & CEO, FNA www.fna.fi Agenda Network Science ● Introduction ● Key concepts Exposure Networks ● OTC Derivatives ● CCP Interconnectedness Correlation Networks ● Housing Bubble and Crisis ● US Presidential Election Network Science and Graphs Analytics Is already powering the best known AI applications Knowledge Social Product Economic Knowledge Payment Graph Graph Graph Graph Graph Graph Network Science and Graphs Analytics “Goldman Sachs takes a DIY approach to graph analytics” For enhanced compliance and fraud detection (www.TechTarget.com, Mar 2015). “PayPal relies on graph techniques to perform sophisticated fraud detection” Saving them more than $700 million and enabling them to perform predictive fraud analysis, according to the IDC (www.globalbankingandfinance.com, Jan 2016) "Network diagnostics .. may displace atomised metrics such as VaR” Regulators are increasing using network science for financial stability analysis. (Andy Haldane, Bank of England Executive -
Jump Bifurcation and Hysteresis in an Infinite-Dimensional Dynamical System of Coupled Spins*
SIAM J. APPL. MATH. (C) 1990 Society for Industrial and Applied Mathematics Vol. 50, No. 1, pp. 108-124, February 1990 008 JUMP BIFURCATION AND HYSTERESIS IN AN INFINITE-DIMENSIONAL DYNAMICAL SYSTEM OF COUPLED SPINS* RENATO E. MIROLLOt AND STEVEN H. STROGATZ: Abstract. This paper studies an infinite-dimensional dynamical system that models a collection of coupled spins in a random magnetic field. A state of the system is given by a self-map of the unit circle. Critical states for the dynamical system correspond to equilibrium configurations of the spins. Exact solutions are obtained for all the critical states and their stability is characterized by analyzing the second variation of the system's potential function at those states. It is proven rigorously that the system exhibits a jump bifurcation and hysteresis as the coupling between spins is varied. Key words, bifurcation, dynamical system, phase transition, spin system AMS(MOS) subject classifications. 58F14, 82A57, 34F05 1. Introduction. There is currently a great deal of interest in the collective behavior of dynamical systems with many interacting subunits [2]. Such systems are very difficult to analyze rigorously unless some simplifying assumptions are made. "Phase models," in which each subunit is characterized by a single phase angle Oi, provide an analytically tractable class of many-body systems. Phase models have been used in a wide variety of scientific contexts, including charge-density wave transport [8], [9], [23], [24], magnetic spin systems [3], [26], oscillating chemical reactions 15], 18], [28], networks of biological oscillators [4], [7], [14], [27], [28], and arrays of Josephson junctions [11], [25]. -
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. -
Network Science, Homophily and Who Reviews Who in the Linux Kernel? Working Paper[+] Open-Access at ECIS2020-Arxiv.Pdf
Network Science, Homophily and Who Reviews Who in the Linux Kernel? Working paper[P] Open-access at http://users.abo.fi/jteixeir/pub/linuxsna/ ECIS2020-arxiv.pdf José Apolinário Teixeira Åbo Akademi University Finland # jteixeira@abo. Ville Leppänen University of Turku Finland Sami Hyrynsalmi arXiv:2106.09329v1 [cs.SE] 17 Jun 2021 LUT University Finland [P]As presented at 2020 European Conference on Information Systems (ECIS 2020), held Online, June 15-17, 2020. The ocial conference proceedings are available at the AIS eLibrary (https://aisel.aisnet.org/ecis2020_rp/). Page ii of 24 ? Copyright notice ? The copyright is held by the authors. The same article is available at the AIS Electronic Library (AISeL) with permission from the authors (see https://aisel.aisnet.org/ ecis2020_rp/). The Association for Information Systems (AIS) can publish and repro- duce this article as part of the Proceedings of the European Conference on Information Systems (ECIS 2020). ? Archiving information ? The article was self-archived by the rst author at its own personal website http:// users.abo.fi/jteixeir/pub/linuxsna/ECIS2020-arxiv.pdf dur- ing June 2021 after the work was presented at the 28th European Conference on Informa- tion Systems (ECIS 2020). Page iii of 24 ð Funding and Acknowledgements ð The rst author’s eorts were partially nanced by Liikesivistysrahasto - the Finnish Foundation for Economic Education, the Academy of Finland via the DiWIL project (see http://abo./diwil) project. A research companion website at http://users.abo./jteixeir/ECIS2020cw supports the paper with additional methodological details, additional data visualizations (plots, tables, and networks), as well as high-resolution versions of the gures embedded in the paper. -
Network Science
This is a preprint of Katy Börner, Soma Sanyal and Alessandro Vespignani (2007) Network Science. In Blaise Cronin (Ed) Annual Review of Information Science & Technology, Volume 41. Medford, NJ: Information Today, Inc./American Society for Information Science and Technology, chapter 12, pp. 537-607. Network Science Katy Börner School of Library and Information Science, Indiana University, Bloomington, IN 47405, USA [email protected] Soma Sanyal School of Library and Information Science, Indiana University, Bloomington, IN 47405, USA [email protected] Alessandro Vespignani School of Informatics, Indiana University, Bloomington, IN 47406, USA [email protected] 1. Introduction.............................................................................................................................................2 2. Notions and Notations.............................................................................................................................4 2.1 Graphs and Subgraphs .........................................................................................................................5 2.2 Graph Connectivity..............................................................................................................................7 3. Network Sampling ..................................................................................................................................9 4. Network Measurements........................................................................................................................11 -
Processes on Complex Networks. Percolation
Chapter 5 Processes on complex networks. Percolation 77 Up till now we discussed the structure of the complex networks. The actual reason to study this structure is to understand how this structure influences the behavior of random processes on networks. I will talk about two such processes. The first one is the percolation process. The second one is the spread of epidemics. There are a lot of open problems in this area, the main of which can be innocently formulated as: How the network topology influences the dynamics of random processes on this network. We are still quite far from a definite answer to this question. 5.1 Percolation 5.1.1 Introduction to percolation Percolation is one of the simplest processes that exhibit the critical phenomena or phase transition. This means that there is a parameter in the system, whose small change yields a large change in the system behavior. To define the percolation process, consider a graph, that has a large connected component. In the classical settings, percolation was actually studied on infinite graphs, whose vertices constitute the set Zd, and edges connect each vertex with nearest neighbors, but we consider general random graphs. We have parameter ϕ, which is the probability that any edge present in the underlying graph is open or closed (an event with probability 1 − ϕ) independently of the other edges. Actually, if we talk about edges being open or closed, this means that we discuss bond percolation. It is also possible to talk about the vertices being open or closed, and this is called site percolation. -
Correlation in Complex Networks
Correlation in Complex Networks by George Tsering Cantwell A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the University of Michigan 2020 Doctoral Committee: Professor Mark Newman, Chair Professor Charles Doering Assistant Professor Jordan Horowitz Assistant Professor Abigail Jacobs Associate Professor Xiaoming Mao George Tsering Cantwell [email protected] ORCID iD: 0000-0002-4205-3691 © George Tsering Cantwell 2020 ACKNOWLEDGMENTS First, I must thank Mark Newman for his support and mentor- ship throughout my time at the University of Michigan. Further thanks are due to all of the people who have worked with me on projects related to this thesis. In alphabetical order they are Eliz- abeth Bruch, Alec Kirkley, Yanchen Liu, Benjamin Maier, Gesine Reinert, Maria Riolo, Alice Schwarze, Carlos Serván, Jordan Sny- der, Guillaume St-Onge, and Jean-Gabriel Young. ii TABLE OF CONTENTS Acknowledgments .................................. ii List of Figures ..................................... v List of Tables ..................................... vi List of Appendices .................................. vii Abstract ........................................ viii Chapter 1 Introduction .................................... 1 1.1 Why study networks?...........................2 1.1.1 Example: Modeling the spread of disease...........3 1.2 Measures and metrics...........................8 1.3 Models of networks............................ 11 1.4 Inference................................. -
Question-And-Answer-Physics-Today
Questions and answers with Steven Strogatz An applied mathematician notes that for many physics topics, including general relativity and climate science, the whole is often not equal to the sum of the parts. By Jeremy N. A. Matthews April 2015 Bookends: Questions and answers with Steven Strogatz Questions and answers with Peter Pesic Questions and answers with Marcelo Gleiser Questions and answers with Amit Hagar Questions and answers with A. Douglas Stone Steven Strogatz is the Jacob Schurman Professor of Applied Mathematics at Cornell University in Ithaca, New York. He conducts research on dynamical systems in physics, biology, and social science. His 1998 Nature article “Collective dynamics of ‘small-world’ networks” is considered a seminal contribution to complexity research. Strogatz is also an active communicator of mathematics and related topics to the public. He frequently appears on public radio and writes for The New Yorker and other publications. A 2015 recipient of the Lewis Thomas Prize for Writing About Science, he has written books that include Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life (Hyperion, 2003) and The Joy of x: A Guided Tour of Math, from One to Infinity (Houghton Mifflin Harcourt, 2012). Strogatz recently published the second edition of a text he wrote more than two decades ago. The new edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, 2015) contains new exercises on such topics as protein dynamics and superconductivity and covers applications in such emerging fields as sociophysics and systems biology. Physics Today reviewed the book in the April issue. -
Social Network Analysis and Information Propagation: a Case Study Using Flickr and Youtube Networks
International Journal of Future Computer and Communication, Vol. 2, No. 3, June 2013 Social Network Analysis and Information Propagation: A Case Study Using Flickr and YouTube Networks Samir Akrouf, Laifa Meriem, Belayadi Yahia, and Mouhoub Nasser Eddine, Member, IACSIT 1 makes decisions based on what other people do because their Abstract—Social media and Social Network Analysis (SNA) decisions may reflect information that they have and he or acquired a huge popularity and represent one of the most she does not. This concept is called ″herding″ or ″information important social and computer science phenomena of recent cascades″. Therefore, analyzing the flow of information on years. One of the most studied problems in this research area is influence and information propagation. The aim of this paper is social media and predicting users’ influence in a network to analyze the information diffusion process and predict the became so important to make various kinds of advantages influence (represented by the rate of infected nodes at the end of and decisions. In [2]-[3], the marketing strategies were the diffusion process) of an initial set of nodes in two networks: enhanced with a word-of-mouth approach using probabilistic Flickr user’s contacts and YouTube videos users commenting models of interactions to choose the best viral marketing plan. these videos. These networks are dissimilar in their structure Some other researchers focused on information diffusion in (size, type, diameter, density, components), and the type of the relationships (explicit relationship represented by the contacts certain special cases. Given an example, the study of Sadikov links, and implicit relationship created by commenting on et.al [6], where they addressed the problem of missing data in videos), they are extracted using NodeXL tool. -
Network Science
NETWORK SCIENCE Random Networks Prof. Marcello Pelillo Ca’ Foscari University of Venice a.y. 2016/17 Section 3.2 The random network model RANDOM NETWORK MODEL Pál Erdös Alfréd Rényi (1913-1996) (1921-1970) Erdös-Rényi model (1960) Connect with probability p p=1/6 N=10 <k> ~ 1.5 SECTION 3.2 THE RANDOM NETWORK MODEL BOX 3.1 DEFINING RANDOM NETWORKS RANDOM NETWORK MODEL Network science aims to build models that reproduce the properties of There are two equivalent defini- real networks. Most networks we encounter do not have the comforting tions of a random network: Definition: regularity of a crystal lattice or the predictable radial architecture of a spi- der web. Rather, at first inspection they look as if they were spun randomly G(N, L) Model A random graph is a graph of N nodes where each pair (Figure 2.4). Random network theoryof nodes embraces is connected this byapparent probability randomness p. N labeled nodes are connect- by constructing networks that are truly random. ed with L randomly placed links. Erds and Rényi used From a modeling perspectiveTo a constructnetwork is a arandom relatively network simple G(N, object, p): this definition in their string consisting of only nodes and links. The real challenge, however, is to decide of papers on random net- where to place the links between1) the Start nodes with so thatN isolated we reproduce nodes the com- works [2-9]. plexity of a real system. In this 2)respect Select the a philosophynode pair, behindand generate a random a network is simple: We assume thatrandom this goal number is best betweenachieved by0 and placing 1. -
Fractal Network in the Protein Interaction Network Model
Journal of the Korean Physical Society, Vol. 56, No. 3, March 2010, pp. 1020∼1024 Fractal Network in the Protein Interaction Network Model Pureun Kim and Byungnam Kahng∗ Department of Physics and Astronomy, Seoul National University, Seoul 151-747 (Received 22 September 2009) Fractal complex networks (FCNs) have been observed in a diverse range of networks from the World Wide Web to biological networks. However, few stochastic models to generate FCNs have been introduced so far. Here, we simulate a protein-protein interaction network model, finding that FCNs can be generated near the percolation threshold. The number of boxes needed to cover the network exhibits a heavy-tailed distribution. Its skeleton, a spanning tree based on the edge betweenness centrality, is a scaffold of the original network and turns out to be a critical branching tree. Thus, the model network is a fractal at the percolation threshold. PACS numbers: 68.37.Ef, 82.20.-w, 68.43.-h Keywords: Fractal complex network, Percolation, Protein interaction network DOI: 10.3938/jkps.56.1020 I. INTRODUCTION consistent with that of the hub-repulsion model [2]. The fractal scaling of a FCN originates from the fractality of its skeleton underneath it [8]. The skeleton is regarded Fractal complex networks (FCNs) have been discov- as a critical branching tree: It exhibits a plateau in the ered in diverse real-world systems [1, 2]. Examples in- mean branching number functionn ¯(d), defined as the clude the co-authorship network [3], metabolic networks average number of offsprings created by nodes at a dis- [4], the protein interaction networks [5], the World-Wide tance d from the root.