Overview of Standard Graph File Formats
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Networkx Tutorial
5.03.2020 tutorial NetworkX tutorial Source: https://github.com/networkx/notebooks (https://github.com/networkx/notebooks) Minor corrections: JS, 27.02.2019 Creating a graph Create an empty graph with no nodes and no edges. In [1]: import networkx as nx In [2]: G = nx.Graph() By definition, a Graph is a collection of nodes (vertices) along with identified pairs of nodes (called edges, links, etc). In NetworkX, nodes can be any hashable object e.g. a text string, an image, an XML object, another Graph, a customized node object, etc. (Note: Python's None object should not be used as a node as it determines whether optional function arguments have been assigned in many functions.) Nodes The graph G can be grown in several ways. NetworkX includes many graph generator functions and facilities to read and write graphs in many formats. To get started though we'll look at simple manipulations. You can add one node at a time, In [3]: G.add_node(1) add a list of nodes, In [4]: G.add_nodes_from([2, 3]) or add any nbunch of nodes. An nbunch is any iterable container of nodes that is not itself a node in the graph. (e.g. a list, set, graph, file, etc..) In [5]: H = nx.path_graph(10) file:///home/szwabin/Dropbox/Praca/Zajecia/Diffusion/Lectures/1_intro/networkx_tutorial/tutorial.html 1/18 5.03.2020 tutorial In [6]: G.add_nodes_from(H) Note that G now contains the nodes of H as nodes of G. In contrast, you could use the graph H as a node in G. -
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 -
Graphprism: Compact Visualization of Network Structure
GraphPrism: Compact Visualization of Network Structure Sanjay Kairam, Diana MacLean, Manolis Savva, Jeffrey Heer Stanford University Computer Science Department {skairam, malcdi, msavva, jheer}@cs.stanford.edu GraphPrism Connectivity ABSTRACT nodeRadius 7.9 strokeWidth 1.12 charge -242 Visual methods for supporting the characterization, com- gravity 0.65 linkDistance 20 parison, and classification of large networks remain an open Transitivity updateGraph Close Controls challenge. Ideally, such techniques should surface useful 0 node(s) selected. structural features { such as effective diameter, small-world properties, and structural holes { not always apparent from Density either summary statistics or typical network visualizations. In this paper, we present GraphPrism, a technique for visu- Conductance ally summarizing arbitrarily large graphs through combina- tions of `facets', each corresponding to a single node- or edge- specific metric (e.g., transitivity). We describe a generalized Jaccard approach for constructing facets by calculating distributions of graph metrics over increasingly large local neighborhoods and representing these as a stacked multi-scale histogram. MeetMin Evaluation with paper prototypes shows that, with minimal training, static GraphPrism diagrams can aid network anal- ysis experts in performing basic analysis tasks with network Created by Sanjay Kairam. Visualization using D3. data. Finally, we contribute the design of an interactive sys- Figure 1: GraphPrism and node-link diagrams for tem using linked selection between GraphPrism overviews the largest component of a co-authorship graph. and node-link detail views. Using a case study of data from a co-authorship network, we illustrate how GraphPrism fa- compactly summarizing networks of arbitrary size. Graph- cilitates interactive exploration of network data. -
Graph Simplification and Interaction
Graph Clarity, Simplification, & Interaction http://i.imgur.com/cW19IBR.jpg https://www.reddit.com/r/CableManagement/ Today • Today’s Reading: Lombardi Graphs – Bezier Curves • Today’s Reading: Clustering/Hierarchical edge Bundling – Definition of Betweenness Centrality • Emergency Management Graph Visualization – Sean Kim’s masters project • Reading for Tuesday & Homework 3 • Graph Interaction Brainstorming Exercise "Lombardi drawings of graphs", Duncan, Eppstein, Goodrich, Kobourov, Nollenberg, Graph Drawing 2010 • Circular arcs • Perfect angular resolution (edges for equal angles at vertices) • Arcs only intersect 2 vertices (at endpoints) • (not required to be crossing free) • Vertices may be constrained to lie on circle or concentric circles • People are more patient with aesthetically pleasing graphs (will spend longer studying to learn/draw conclusions) • What about relaxing the circular arc requirement and allowing Bezier arcs? • How does it scale to larger data? • Long curved arcs can be much harder to follow • Circular layout of nodes is often very good! • Would like more pseudocode Cubic Bézier Curve • 4 control points • Curve passes through first & last control point • Curve is tangent at P0 to (P1-P0) and at P3 to (P3-P2) http://www.e-cartouche.ch/content_reg/carto http://www.webreference.com/dla uche/graphics/en/html/Curves_learningObject b/9902/bezier.html 2.html “Force-directed Lombardi-style graph drawing”, Chernobelskiy et al., Graph Drawing 2011. • Relaxation of the Lombardi Graph requirements • “straight-line segments -
Constraint Graph Drawing
Constrained Graph Drawing Dissertation zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften vorgelegt von Barbara Pampel, geb. Schlieper an der Universit¨at Konstanz Mathematisch-Naturwissenschaftliche Sektion Fachbereich Informatik und Informationswissenschaft Tag der mundlichen¨ Prufung:¨ 14. Juli 2011 1. Referent: Prof. Dr. Ulrik Brandes 2. Referent: Prof. Dr. Michael Kaufmann II Teile dieser Arbeit basieren auf Ver¨offentlichungen, die aus der Zusammenar- beit mit anderen Wissenschaftlerinnen und Wissenschaftlern entstanden sind. Zu allen diesen Inhalten wurden wesentliche Beitr¨age geleistet. Kapitel 3 (Bachmaier, Brandes, and Schlieper, 2005; Brandes and Schlieper, 2009) Kapitel 4 (Brandes and Pampel, 2009) Kapitel 6 (Brandes, Cornelsen, Pampel, and Sallaberry, 2010b) Zusammenfassung Netzwerke werden in den unterschiedlichsten Forschungsgebieten zur Repr¨asenta- tion relationaler Daten genutzt. Durch geeignete mathematische Methoden kann man diese Netzwerke als Graphen darstellen. Ein Graph ist ein Gebilde aus Kno- ten und Kanten, welche die Knoten verbinden. Hierbei k¨onnen sowohl die Kan- ten als auch die Knoten weitere Informationen beinhalten. Diese Informationen k¨onnen den einzelnen Elementen zugeordnet sein, sich aber auch aus Anordnung und Verteilung der Elemente ergeben. Mit Algorithmen (strukturierten Reihen von Arbeitsanweisungen) aus dem Gebiet des Graphenzeichnens kann man die unterschiedlichsten Informationen aus verschiedenen Forschungsbereichen visualisieren. Graphische Darstellungen k¨onnen das -
Chapter 18 Spectral Graph Drawing
Chapter 18 Spectral Graph Drawing 18.1 Graph Drawing and Energy Minimization Let G =(V,E)besomeundirectedgraph.Itisoftende- sirable to draw a graph, usually in the plane but possibly in 3D, and it turns out that the graph Laplacian can be used to design surprisingly good methods. n Say V = m.Theideaistoassignapoint⇢(vi)inR to the vertex| | v V ,foreveryv V ,andtodrawaline i 2 i 2 segment between the points ⇢(vi)and⇢(vj). Thus, a graph drawing is a function ⇢: V Rn. ! 821 822 CHAPTER 18. SPECTRAL GRAPH DRAWING We define the matrix of a graph drawing ⇢ (in Rn) as a m n matrix R whose ith row consists of the row vector ⇥ n ⇢(vi)correspondingtothepointrepresentingvi in R . Typically, we want n<m;infactn should be much smaller than m. Arepresentationisbalanced i↵the sum of the entries of every column is zero, that is, 1>R =0. If a representation is not balanced, it can be made bal- anced by a suitable translation. We may also assume that the columns of R are linearly independent, since any basis of the column space also determines the drawing. Thus, from now on, we may assume that n m. 18.1. GRAPH DRAWING AND ENERGY MINIMIZATION 823 Remark: Agraphdrawing⇢: V Rn is not required to be injective, which may result in! degenerate drawings where distinct vertices are drawn as the same point. For this reason, we prefer not to use the terminology graph embedding,whichisoftenusedintheliterature. This is because in di↵erential geometry, an embedding always refers to an injective map. The term graph immersion would be more appropriate. -
Graph Drawing by Stochastic Gradient Descent
1 Graph Drawing by Stochastic Gradient Descent Jonathan X. Zheng, Samraat Pawar, Dan F. M. Goodman Abstract—A popular method of force-directed graph drawing is multidimensional scaling using graph-theoretic distances as input. We present an algorithm to minimize its energy function, known as stress, by using stochastic gradient descent (SGD) to move a single pair of vertices at a time. Our results show that SGD can reach lower stress levels faster and more consistently than majorization, without needing help from a good initialization. We then show how the unique properties of SGD make it easier to produce constrained layouts than previous approaches. We also show how SGD can be directly applied within the sparse stress approximation of Ortmann et al. [1], making the algorithm scalable up to large graphs. Index Terms—Graph drawing, multidimensional scaling, constraints, relaxation, stochastic gradient descent F 1 INTRODUCTION RAPHS are a common data structure, used to describe to the shortest path distance between vertices i and j, with w = d−2 G everything from social networks to food webs, from ij ij to offset the extra weight given to longer paths metabolic pathways to internet traffic. Any set of pairwise due to squaring the difference [3]. relationships between entities can be described by a graph, This definition was popularized for graph layout by and the ever increasing amount of data being collected Kamada and Kawai [4] who minimized the function using means that visualizing graphs for exploratory analysis has a localized 2D Newton-Raphson method, while within the become an important task. MDS community Kruskal [5] originally used gradient de- Node-link diagrams are an intuitive representation of scent [6]. -
The Hitchhiker's Guide to Graph Exchange Formats
The Hitchhiker’s Guide to Graph Exchange Formats Prof. Matthew Roughan [email protected] http://www.maths.adelaide.edu.au/matthew.roughan/ Work with Jono Tuke UoA June 4, 2015 M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 1 / 31 Graphs Graph: G(N; E) I N = set of nodes (vertices) I E = set of edges (links) Often we have additional information, e.g., I link distance I node type I graph name M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 2 / 31 Why? To represent data where “connections” are 1st class objects in their own right I storing the data in the right format improves access, processing, ... I it’s natural, elegant, efficient, ... Many, many datasets M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 3 / 31 ISPs: Internode: layer 3 http: //www.internode.on.net/pdf/network/internode-domestic-ip-network.pdf M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 4 / 31 ISPs: Level 3 (NA) http://www.fiberco.org/images/Level3-Metro-Fiber-Map4.jpg M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 5 / 31 Telegraph submarine cables http://en.wikipedia.org/wiki/File:1901_Eastern_Telegraph_cables.png M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 6 / 31 Electricity grid M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 7 / 31 Bus network (Adelaide CBD) M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 8 / 31 French Rail http://www.alleuroperail.com/europe-map-railways.htm M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 9 / 31 Protocol relationships M.Roughan (UoA) Hitch Hikers Guide June 4, 2015 10 / 31 Food web M.Roughan (UoA) Hitch Hikers -
Comm 645 Handout – Nodexl Basics
COMM 645 HANDOUT – NODEXL BASICS NodeXL: Network Overview, Discovery and Exploration for Excel. Download from nodexl.codeplex.com Plugin for social media/Facebook import: socialnetimporter.codeplex.com Plugin for Microsoft Exchange import: exchangespigot.codeplex.com Plugin for Voson hyperlink network import: voson.anu.edu.au/node/13#VOSON-NodeXL Note that NodeXL requires MS Office 2007 or 2010. If your system does not support those (or you do not have them installed), try using one of the computers in the PhD office. Major sections within NodeXL: • Edges Tab: Edge list (Vertex 1 = source, Vertex 2 = destination) and attributes (Fig.1→1a) • Vertices Tab: Nodes and attribute (nodes can be imported from the edge list) (Fig.1→1b) • Groups Tab: Groups of nodes defined by attribute, clusters, or components (Fig.1→1c) • Groups Vertices Tab: Nodes belonging to each group (Fig.1→1d) • Overall Metrics Tab: Network and node measures & graphs (Fig.1→1e) Figure 1: The NodeXL Interface 3 6 8 2 7 9 13 14 5 12 4 10 11 1 1a 1b 1c 1d 1e Download more network handouts at www.kateto.net / www.ognyanova.net 1 After you install the NodeXL template, a new NodeXL tab will appear in your Excel interface. The following features will be available in it: Fig.1 → 1: Switch between different data tabs. The most important two tabs are "Edges" and "Vertices". Fig.1 → 2: Import data into NodeXL. The formats you can use include GraphML, UCINET DL files, and Pajek .net files, among others. You can also import data from social media: Flickr, YouTube, Twitter, Facebook (requires a plugin), or a hyperlink networks (requires a plugin). -
2 Graphs and Graph Theory
2 Graphs and Graph Theory chapter:graphs Graphs are the mathematical objects used to represent networks, and graph theory is the branch of mathematics that involves the study of graphs. Graph theory has a long history. The notion of graph was introduced for the first time in 1763 by Euler, to settle a famous unsolved problem of his days, the so-called “K¨onigsberg bridges” problem. It is no coin- cidence that the first paper on graph theory arose from the need to solve a problem from the real world. Also subsequent works in graph theory by Kirchhoff and Cayley had their root in the physical world. For instance, Kirchhoff’s investigations on electric circuits led to his development of a set of basic concepts and theorems concerning trees in graphs. Nowadays, graph theory is a well established discipline which is commonly used in areas as diverse as computer science, sociology, and biology. To make some examples, graph theory helps us to schedule airplane routings, and has solved problems such as finding the maximum flow per unit time from a source to a sink in a network of pipes, or coloring the regions of a map using the minimum number of different colors so that no neighbouring regions are colored the same way. In this chapter we introduce the basic definitions, set- ting up the language we will need in the following of the book. The two last sections are respectively devoted to the proof of the Euler theorem, and to the description of a graph as an array of numbers. -
Data Structures and Network Algorithms [Tarjan 1987-01-01].Pdf
CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS A series of lectures on topics of current research interest in applied mathematics under the direction of the Conference Board of the Mathematical Sciences, supported by the National Science Foundation and published by SIAM. GAKRHT BiRKiion , The Numerical Solution of Elliptic Equations D. V. LINDIY, Bayesian Statistics, A Review R S. VAR<;A. Functional Analysis and Approximation Theory in Numerical Analysis R R H:\II\DI:R, Some Limit Theorems in Statistics PXIKK K Bin I.VISLI -y. Weak Convergence of Measures: Applications in Probability .1. I.. LIONS. Some Aspects of the Optimal Control of Distributed Parameter Systems R(H;I:R PI-NROSI-:. Tecltniques of Differentia/ Topology in Relativity Hi.KM \N C'ui KNOI r. Sequential Analysis and Optimal Design .1. DI'KHIN. Distribution Theory for Tests Based on the Sample Distribution Function Soi I. Ri BINO\\, Mathematical Problems in the Biological Sciences P. D. L\x. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves I. .1. Soioi.NUiiRci. Cardinal Spline Interpolation \\.\\ SiMii.R. The Theory of Best Approximation and Functional Analysis WI-.KNI R C. RHHINBOLDT, Methods of Solving Systems of Nonlinear Equations HANS I-'. WHINBKRQKR, Variational Methods for Eigenvalue Approximation R. TYRRM.I. ROCKAI-KLI.AK, Conjugate Dtialitv and Optimization SIR JAMKS LIGHTHILL, Mathematical Biofhtiddynamics GI-.RAKD SAI.ION, Theory of Indexing C \ rnLi-:i;.N S. MORAWKTX, Notes on Time Decay and Scattering for Some Hyperbolic Problems F. Hoi'i'hNSTKAm, Mathematical Theories of Populations: Demographics, Genetics and Epidemics RK HARD ASKF;Y. -
Graphs Introduction and Depth-First Algorithm Carol Zander
Graphs Introduction and Depth‐first algorithm Carol Zander Introduction to graphs Graphs are extremely common in computer science applications because graphs are common in the physical world. Everywhere you look, you see a graph. Intuitively, a graph is a set of locations and edges connecting them. A simple example would be cities on a map that are connected by roads. Or cities connected by airplane routes. Another example would be computers in a local network that are connected to each other directly. Constellations of stars (among many other applications) can be also represented this way. Relationships can be represented as graphs. Section 9.1 has many good graph examples. Graphs can be viewed in three ways (trees, too, since they are special kind of graph): 1. A mathematical construction – this is how we will define them 2. An abstract data type – this is how we will think about interfacing with them 3. A data structure – this is how we will implement them The mathematical construction gives the definition of a graph: graph G = (V, E) consists of a set of vertices V (often called nodes) and a set of edges E (sometimes called arcs) that connect the edges. Each edge is a pair (u, v), such that u,v ∈V . Every tree is a graph, but not vice versa. There are two types of graphs, directed and undirected. In a directed graph, the edges are ordered pairs, for example (u,v), indicating that a path exists from u to v (but not vice versa, unless there is another edge.) For the edge, (u,v), v is said to be adjacent to u, but not the other way, i.e., u is not adjacent to v.