# UNIVERSITA DEGLI STUDI DI CATANIA FACOLTA DI INGEGNERIA

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 UNIVERSITA DEGLI STUDI DI CATANIA FACOLTA DI INGEGNERIA PhD course in Electronics, Automation and Complex Systems Control-XXIV Cycle DIPARTIMENTO DI INGEGNERIA ELETTRICA ELETTRONICA E DEI SISTEMI ing. Angelo Sarra Fiore Tutor: prof. ing. Luigi Fortuna ing. Mattia Frasca

2 Outline Networks Theory Friends Network How a friends network grows? Courses

3 A network is a system consisting of many entities, called nodes, linked to each other and interacting through connections (edges). A general network may be represented as a graph G = (N, E), where N is the set of nodes and E the set of edges = = {(,2),(,5),(2,3),(2,5),(3,6),(4,5)} {,2,3,4,5,6} ) :, ( E edges N nodes E N G Networks Theory WHAT IS A NETWORK? = A Mathematically a graph G (N, E) can be represented by a matrix (called adjacency matrix A) that has nodes as elements of rows and columns and the elements are different from zero (if different from it is a weight" of the link: cost, velocity, energy etc.) if the two nodes are connected.

4 Networks Theory EXAMPLES Many complex systems can be represented as networks of interacting elements. -Social Networks Coauthors Networks Actors Networks /IM Networks -Technological Networks Telephone Networks Internet Transport Networks -Knowledge (Information) Networks References Network World Wide Web -Biological Networks Proteins Networks Neural Networks

5 Networks Theory CHARACTERISTIC PARAMETERS OF NETWORKS Node degree: number of the edge of a node k i = a ij j N Shortest path length: the average of the shortest paths connecting each pair of nodes L = N( N ) d ij i, j N, i j where d ij is the element of the D matrix which contains the shortest paths connecting each pair of nodes Clustering coefficient of a node: quantifies the importance of a node by evaluating the number of connections that remain if the node was removed c i = 2 arcs' number k ( k ) i i of G i

6 Networks Theory HISTORY The classical network theory goes back to 736 with Eulero's study to solve the Koningsberg Bridges Problem. In 959 P. Erdos and A. Rényi, two Hungarian mathematicians, introduced random network In 998 S. Strogatz e D. Watts, studying actors' networks, energy distribution network and the neural network of the worm C.elegans, saw a deviation from random networks and introduced the small world networks In 999 Barabási e R. Albert saw that many networks had a power law degree distribution N(k) ~ k - γ and defined the scale-free networks and very popular is the sentence "the rich get richer"

7 Friends Network We re analyzing the friends networks of some user of the popular social network Facebook (originally known as Thefacebook) is the most popular social network site today and was founded on 4 February 24 by Mark Zuckerberg, a nineteen student of the Harvard s University, with the help of Andrew McCollum and Eduardo Saverino. In April 29 the number of active users has reached 2 million and the average number of friends per user is 2.

8 Friends Network Start with a star network where the user is the central node

9 Friends Network Remove the central node to obtain the friend s network

10 Friends Network Remove isolated nodes and Extract the Main Component

11 Friends Network Analysis of this network

12 Friends Network Comparison with other network topologies

13 Degree Distribution of Four Different Networks L=3,488 C=,4528 K=8,398 nodes: 75 edges: L=2,5534 C=,5993 K=,2745 nodes: 3 edges: k k L=2,273 C=,436 K=24,292 nodes: 37 edges: L=2,639 C=,574 K=2,37 nodes: 262 edges: k k

14 Power Law Degree Distribution 6 Erdos L=2,28 C=,493 K=25,8824 Random L=2,944 C=,52 K=26,7324 Real L=3,2683 C=,422 K=26,7324 nodes: 528 edges: P(k)=a*k -γ a=48 γ= k k

15 Results of the Analysis L C networks erdos random real,8,7,6,5,4,3,2, networks erdos random real K networks In comparison with the random and the Erdos-Renyi networks friends networks present an higher clustering coefficient and a lower path length, typical characteristics of small-world networks, but the degree distributions aren t power law erdos random real

16 How a Friends Network Grows? Study of a social network that evolves in time A dynamic network is a particular network in which the topology changes in time for the variations in the sets of edges and nodes

17 How a Friends Network Grows? Edges number Nodes number sample sample

18 How a Friends Network Grows? L = C = sample sample 25 2 K 5 5 K = sample

19 How a Friends Network Grows? 9 DEGREE DISTRIBUTION k

20 How a Friends Network Grows? 62 nodes 4354 edges

21 Courses Fondamenti di Bioingegneria Elettronica Misure Elettroniche

### Erdős-Rényi Model for network formation

Network Science: Erdős-Rényi Model for network formation Ozalp Babaoglu Dipartimento di Informatica Scienza e Ingegneria Università di Bologna www.cs.unibo.it/babaoglu/ Why model? Simpler representation

### Lesson 4. Random graphs. Sergio Barbarossa. UPC - Barcelona - July 2008

Lesson 4 Random graphs Sergio Barbarossa Graph models 1. Uncorrelated random graph (Erdős, Rényi) N nodes are connected through n edges which are chosen randomly from the possible configurations 2. Binomial

### (Social) Networks Analysis III. Prof. Dr. Daning Hu Department of Informatics University of Zurich

(Social) Networks Analysis III Prof. Dr. Daning Hu Department of Informatics University of Zurich Outline Network Topological Analysis Network Models Random Networks Small-World Networks Scale-Free Networks

### On the impact of small-world on local search

On the impact of small-world on local search Andrea Roli andrea.roli@unibo.it DEIS Università degli Studi di Bologna Campus of Cesena p. 1 Motivation The impact of structure whatever it is on search algorithms

### Introduction to Networks and Business Intelligence

Introduction to Networks and Business Intelligence Prof. Dr. Daning Hu Department of Informatics University of Zurich Sep 16th, 2014 Outline n Network Science A Random History n Network Analysis Network

### Summary: What We Have Learned So Far

Summary: What We Have Learned So Far small-world phenomenon Real-world networks: { Short path lengths High clustering Broad degree distributions, often power laws P (k) k γ Erdös-Renyi model: Short path

### CS-E5740. Complex Networks. Scale-free networks

CS-E5740 Complex Networks Scale-free networks Course outline 1. Introduction (motivation, definitions, etc. ) 2. Static network models: random and small-world networks 3. Growing network models: scale-free

### Nick Hamilton Institute for Molecular Bioscience. Essential Graph Theory for Biologists. Image: Matt Moores, The Visible Cell

Nick Hamilton Institute for Molecular Bioscience Essential Graph Theory for Biologists Image: Matt Moores, The Visible Cell Outline Core definitions Which are the most important bits? What happens when

### CAIM: Cerca i Anàlisi d Informació Massiva

1 / 72 CAIM: Cerca i Anàlisi d Informació Massiva FIB, Grau en Enginyeria Informàtica Slides by Marta Arias, José Balcázar, Ricard Gavaldá Department of Computer Science, UPC Fall 2016 http://www.cs.upc.edu/~caim

### Wednesday, March 8, Complex Networks. Presenter: Jirakhom Ruttanavakul. CS 790R, University of Nevada, Reno

Wednesday, March 8, 2006 Complex Networks Presenter: Jirakhom Ruttanavakul CS 790R, University of Nevada, Reno Presented Papers Emergence of scaling in random networks, Barabási & Bonabeau (2003) Scale-free

### Properties of Biological Networks

Properties of Biological Networks presented by: Ola Hamud June 12, 2013 Supervisor: Prof. Ron Pinter Based on: NETWORK BIOLOGY: UNDERSTANDING THE CELL S FUNCTIONAL ORGANIZATION By Albert-László Barabási

### On Complex Dynamical Networks. G. Ron Chen Centre for Chaos Control and Synchronization City University of Hong Kong

On Complex Dynamical Networks G. Ron Chen Centre for Chaos Control and Synchronization City University of Hong Kong 1 Complex Networks: Some Typical Examples 2 Complex Network Example: Internet (William

### CSCI5070 Advanced Topics in Social Computing

CSCI5070 Advanced Topics in Social Computing Irwin King The Chinese University of Hong Kong king@cse.cuhk.edu.hk!! 2012 All Rights Reserved. Outline Graphs Origins Definition Spectral Properties Type of

### Critical Phenomena in Complex Networks

Critical Phenomena in Complex Networks Term essay for Physics 563: Phase Transitions and the Renormalization Group University of Illinois at Urbana-Champaign Vikyath Deviprasad Rao 11 May 2012 Abstract

### Basics of Network Analysis

Basics of Network Analysis Hiroki Sayama sayama@binghamton.edu Graph = Network G(V, E): graph (network) V: vertices (nodes), E: edges (links) 1 Nodes = 1, 2, 3, 4, 5 2 3 Links = 12, 13, 15, 23,

### Complex networks Phys 682 / CIS 629: Computational Methods for Nonlinear Systems

Complex networks Phys 682 / CIS 629: Computational Methods for Nonlinear Systems networks are everywhere (and always have been) - relationships (edges) among entities (nodes) explosion of interest in network

### Chapter 1. Social Media and Social Computing. October 2012 Youn-Hee Han

Chapter 1. Social Media and Social Computing October 2012 Youn-Hee Han http://link.koreatech.ac.kr 1.1 Social Media A rapid development and change of the Web and the Internet Participatory web application

### An Investigation into the Free/Open Source Software Phenomenon using Data Mining, Social Network Theory, and Agent-Based

An Investigation into the Free/Open Source Software Phenomenon using Data Mining, Social Network Theory, and Agent-Based Greg Madey Computer Science & Engineering University of Notre Dame UIUC - NSF Workshop

### Networks in economics and finance. Lecture 1 - Measuring networks

Networks in economics and finance Lecture 1 - Measuring networks What are networks and why study them? A network is a set of items (nodes) connected by edges or links. Units (nodes) Individuals Firms Banks

### Algorithmic and Economic Aspects of Networks. Nicole Immorlica

Algorithmic and Economic Aspects of Networks Nicole Immorlica Syllabus 1. Jan. 8 th (today): Graph theory, network structure 2. Jan. 15 th : Random graphs, probabilistic network formation 3. Jan. 20 th

### Networks and Discrete Mathematics

Aristotle University, School of Mathematics Master in Web Science Networks and Discrete Mathematics Small Words-Scale-Free- Model Chronis Moyssiadis Vassilis Karagiannis 7/12/2012 WS.04 Webscience: lecture

### Introduction to network metrics

Universitat Politècnica de Catalunya Version 0.5 Complex and Social Networks (2018-2019) Master in Innovation and Research in Informatics (MIRI) Instructors Argimiro Arratia, argimiro@cs.upc.edu, http://www.cs.upc.edu/~argimiro/

### Complex Networks. Structure and Dynamics

Complex Networks Structure and Dynamics Ying-Cheng Lai Department of Mathematics and Statistics Department of Electrical Engineering Arizona State University Collaborators! Adilson E. Motter, now at Max-Planck

### A Generating Function Approach to Analyze Random Graphs

A Generating Function Approach to Analyze Random Graphs Presented by - Vilas Veeraraghavan Advisor - Dr. Steven Weber Department of Electrical and Computer Engineering Drexel University April 8, 2005 Presentation

### L Modelling and Simulating Social Systems with MATLAB

851-0585-04L Modelling and Simulating Social Systems with MATLAB Lesson 6 Graphs (Networks) Anders Johansson and Wenjian Yu (with S. Lozano and S. Wehrli) ETH Zürich 2010-03-29 Lesson 6 Contents History:

### Some Graph Theory for Network Analysis. CS 249B: Science of Networks Week 01: Thursday, 01/31/08 Daniel Bilar Wellesley College Spring 2008

Some Graph Theory for Network Analysis CS 9B: Science of Networks Week 0: Thursday, 0//08 Daniel Bilar Wellesley College Spring 008 Goals this lecture Introduce you to some jargon what we call things in

### Resilient Networking. Thorsten Strufe. Module 3: Graph Analysis. Disclaimer. Dresden, SS 15

Resilient Networking Thorsten Strufe Module 3: Graph Analysis Disclaimer Dresden, SS 15 Module Outline Why bother with theory? Graphs and their representations Important graph metrics Some graph generators

### Characteristics of Preferentially Attached Network Grown from. Small World

Characteristics of Preferentially Attached Network Grown from Small World Seungyoung Lee Graduate School of Innovation and Technology Management, Korea Advanced Institute of Science and Technology, Daejeon

### CS 6824: The Small World of the Cerebral Cortex

CS 6824: The Small World of the Cerebral Cortex T. M. Murali September 1, 2016 Motivation The Watts-Strogatz paper set off a storm of research. It has nearly 30,000 citations. Even in 2004, it had more

### Hyperbolic Geometry of Complex Network Data

Hyperbolic Geometry of Complex Network Data Konstantin Zuev http://www.its.caltech.edu/~zuev/ Joint work with D. Krioukov, M. Boguñá, and G. Bianconi CMX seminar, Caltech May 24, 2017 How do complex networks

### An Exploratory Journey Into Network Analysis A Gentle Introduction to Network Science and Graph Visualization

An Exploratory Journey Into Network Analysis A Gentle Introduction to Network Science and Graph Visualization Pedro Ribeiro (DCC/FCUP & CRACS/INESC-TEC) Part 1 Motivation and emergence of Network Science

### Networks and stability

Networks and stability Part 1A. Network topology www.weaklink.sote.hu csermelypeter@yahoo.com Peter Csermely 1. network topology 2. network dynamics 3. examples for networks 4. synthesis (complex equilibria,

### Volume 2, Issue 11, November 2014 International Journal of Advance Research in Computer Science and Management Studies

Volume 2, Issue 11, November 2014 International Journal of Advance Research in Computer Science and Management Studies Research Article / Survey Paper / Case Study Available online at: www.ijarcsms.com

### Social, Information, and Routing Networks: Models, Algorithms, and Strategic Behavior

Social, Information, and Routing Networks: Models, Algorithms, and Strategic Behavior Who? Prof. Aris Anagnostopoulos Prof. Luciana S. Buriol Prof. Guido Schäfer What will We Cover? Topics: Network properties

### Advanced Algorithms and Models for Computational Biology -- a machine learning approach

Advanced Algorithms and Models for Computational Biology -- a machine learning approach Biological Networks & Network Evolution Eric Xing Lecture 22, April 10, 2006 Reading: Molecular Networks Interaction

### Case Studies in Complex Networks

Case Studies in Complex Networks Introduction to Scientific Modeling CS 365 George Bezerra 08/27/2012 The origin of graph theory Königsberg bridge problem Leonard Euler (1707-1783) The Königsberg Bridge

### Graph Theory. Graph Theory. COURSE: Introduction to Biological Networks. Euler s Solution LECTURE 1: INTRODUCTION TO NETWORKS.

Graph Theory COURSE: Introduction to Biological Networks LECTURE 1: INTRODUCTION TO NETWORKS Arun Krishnan Koenigsberg, Russia Is it possible to walk with a route that crosses each bridge exactly once,

### Machine Learning and Modeling for Social Networks

Machine Learning and Modeling for Social Networks Olivia Woolley Meza, Izabela Moise, Nino Antulov-Fatulin, Lloyd Sanders 1 Introduction to Networks Computational Social Science D-GESS Olivia Woolley Meza

### Models of Network Formation. Networked Life NETS 112 Fall 2017 Prof. Michael Kearns

Models of Network Formation Networked Life NETS 112 Fall 2017 Prof. Michael Kearns Roadmap Recently: typical large-scale social and other networks exhibit: giant component with small diameter sparsity

### ECS 253 / MAE 253, Lecture 8 April 21, Web search and decentralized search on small-world networks

ECS 253 / MAE 253, Lecture 8 April 21, 2016 Web search and decentralized search on small-world networks Search for information Assume some resource of interest is stored at the vertices of a network: Web

### NETWORK ANALYSIS. Duygu Tosun-Turgut, Ph.D. Center for Imaging of Neurodegenerative Diseases Department of Radiology and Biomedical Imaging

NETWORK ANALYSIS Duygu Tosun-Turgut, Ph.D. Center for Imaging of Neurodegenerative Diseases Department of Radiology and Biomedical Imaging duygu.tosun@ucsf.edu What is a network? - Complex web-like structures

### 1 Degree Distributions

Lecture Notes: Social Networks: Models, Algorithms, and Applications Lecture 3: Jan 24, 2012 Scribes: Geoffrey Fairchild and Jason Fries 1 Degree Distributions Last time, we discussed some graph-theoretic

### Structured prediction using the network perceptron

Structured prediction using the network perceptron Ta-tsen Soong Joint work with Stuart Andrews and Prof. Tony Jebara Motivation A lot of network-structured data Social networks Citation networks Biological

### M.E.J. Newman: Models of the Small World

A Review Adaptive Informatics Research Centre Helsinki University of Technology November 7, 2007 Vocabulary N number of nodes of the graph l average distance between nodes D diameter of the graph d is

### An Introduction to Complex Systems Science

DEIS, Campus of Cesena Alma Mater Studiorum Università di Bologna andrea.roli@unibo.it Disclaimer The field of Complex systems science is wide and it involves numerous themes and disciplines. This talk

### Topic II: Graph Mining

Topic II: Graph Mining Discrete Topics in Data Mining Universität des Saarlandes, Saarbrücken Winter Semester 2012/13 T II.Intro-1 Topic II Intro: Graph Mining 1. Why Graphs? 2. What is Graph Mining 3.

### Distances in power-law random graphs

Distances in power-law random graphs Sander Dommers Supervisor: Remco van der Hofstad February 2, 2009 Where innovation starts Introduction There are many complex real-world networks, e.g. Social networks

### RANDOM-REAL NETWORKS

RANDOM-REAL NETWORKS 1 Random networks: model A random graph is a graph of N nodes where each pair of nodes is connected by probability p: G(N,p) Random networks: model p=1/6 N=12 L=8 L=10 L=7 The number

### Modeling and Simulating Social Systems with MATLAB

Modeling and Simulating Social Systems with MATLAB Lecture 8 Introduction to Graphs/Networks Olivia Woolley, Stefano Balietti, Lloyd Sanders, Dirk Helbing Chair of Sociology, in particular of Modeling

### The Establishment Game. Motivation

Motivation Motivation The network models so far neglect the attributes, traits of the nodes. A node can represent anything, people, web pages, computers, etc. Motivation The network models so far neglect

### arxiv: v2 [physics.soc-ph] 23 Jul 2018

arxiv:1804.02350v2 [physics.soc-ph] 23 Jul 2018 ABSTRACT Marco Alberto Javarone nchain London, UK School of Computing, University of Kent Medway, UK marcojavarone@gmail.com Bitcoins and Blockchain technologies

### Example 1: An algorithmic view of the small world phenomenon

Lecture Notes: Social Networks: Models, Algorithms, and Applications Lecture 1: Jan 17, 2012 Scribes: Preethi Ambati and Azar Aliyev Example 1: An algorithmic view of the small world phenomenon The story

### Complex-Network Modelling and Inference

Complex-Network Modelling and Inference Lecture 8: Graph features (2) Matthew Roughan http://www.maths.adelaide.edu.au/matthew.roughan/notes/ Network_Modelling/ School

### Network Thinking. Complexity: A Guided Tour, Chapters 15-16

Network Thinking Complexity: A Guided Tour, Chapters 15-16 Neural Network (C. Elegans) http://gephi.org/wp-content/uploads/2008/12/screenshot-celegans.png Food Web http://1.bp.blogspot.com/_vifbm3t8bou/sbhzqbchiei/aaaaaaaaaxk/rsc-pj45avc/

### Response Network Emerging from Simple Perturbation

Journal of the Korean Physical Society, Vol 44, No 3, March 2004, pp 628 632 Response Network Emerging from Simple Perturbation S-W Son, D-H Kim, Y-Y Ahn and H Jeong Department of Physics, Korea Advanced

### CS249: SPECIAL TOPICS MINING INFORMATION/SOCIAL NETWORKS

CS249: SPECIAL TOPICS MINING INFORMATION/SOCIAL NETWORKS Overview of Networks Instructor: Yizhou Sun yzsun@cs.ucla.edu January 10, 2017 Overview of Information Network Analysis Network Representation Network

### arxiv:cond-mat/ v1 21 Oct 1999

Emergence of Scaling in Random Networks Albert-László Barabási and Réka Albert Department of Physics, University of Notre-Dame, Notre-Dame, IN 46556 arxiv:cond-mat/9910332 v1 21 Oct 1999 Systems as diverse

### Package fastnet. February 12, 2018

Type Package Title Large-Scale Social Network Analysis Version 0.1.4 Package fastnet February 12, 2018 We present an implementation of the algorithms required to simulate largescale social networks and

### Small-World Models and Network Growth Models. Anastassia Semjonova Roman Tekhov

Small-World Models and Network Growth Models Anastassia Semjonova Roman Tekhov Small world 6 billion small world? 1960s Stanley Milgram Six degree of separation Small world effect Motivation Not only friends:

### Network models and graph theory

Network models and graph theory G. Ferrari Trecate Dipartimento di Ingegneria Industriale e dell Informazione (DIII) Università degli Studi di Pavia Industrial Automation Ferrari Trecate (DII) Network

### NETWORKS. David J Hill Research School of Information Sciences and Engineering The Australian National University

Lab Net Con 网络控制 Short-course: Complex Systems Beyond the Metaphor UNSW, February 2007 NETWORKS David J Hill Research School of Information Sciences and Engineering The Australian National University 8/2/2007

### 1 Random Graph Models for Networks

Lecture Notes: Social Networks: Models, Algorithms, and Applications Lecture : Jan 6, 0 Scribes: Geoffrey Fairchild and Jason Fries Random Graph Models for Networks. Graph Modeling A random graph is a

### Web 2.0 Social Data Analysis

Web 2.0 Social Data Analysis Ing. Jaroslav Kuchař jaroslav.kuchar@fit.cvut.cz Structure(1) Czech Technical University in Prague, Faculty of Information Technologies Software and Web Engineering 2 Contents

### Examples of Complex Networks

Examples of Complex Networks Neural Network (C. Elegans) http://gephi.org/wp-content/uploads/2008/12/screenshot-celegans.png Food Web http://1.bp.blogspot.com/_vifbm3t8bou/sbhzqbchiei/aaaaaaaaaxk/rsc-

### Graph similarity. Laura Zager and George Verghese EECS, MIT. March 2005

Graph similarity Laura Zager and George Verghese EECS, MIT March 2005 Words you won t hear today impedance matching thyristor oxide layer VARs Some quick definitions GV (, E) a graph G V the set of vertices

### Mathematics of networks. Artem S. Novozhilov

Mathematics of networks Artem S. Novozhilov August 29, 2013 A disclaimer: While preparing these lecture notes, I am using a lot of different sources for inspiration, which I usually do not cite in the

### 6.207/14.15: Networks Lecture 5: Generalized Random Graphs and Small-World Model

6.207/14.15: Networks Lecture 5: Generalized Random Graphs and Small-World Model Daron Acemoglu and Asu Ozdaglar MIT September 23, 2009 1 Outline Generalized random graph models Graphs with prescribed

### Constructing a G(N, p) Network

Random Graph Theory Dr. Natarajan Meghanathan Associate Professor Department of Computer Science Jackson State University, Jackson, MS E-mail: natarajan.meghanathan@jsums.edu Introduction At first inspection,

### Graph theoretic concepts. Devika Subramanian Comp 140 Fall 2008

Graph theoretic concepts Devika Subramanian Comp 140 Fall 2008 The small world phenomenon The phenomenon is surprising because Size of graph is very large (> 6 billion for the planet). Graph is sparse

### Package fastnet. September 11, 2018

Type Package Title Large-Scale Social Network Analysis Version 0.1.6 Package fastnet September 11, 2018 We present an implementation of the algorithms required to simulate largescale social networks and

### - relationships (edges) among entities (nodes) - technology: Internet, World Wide Web - biology: genomics, gene expression, proteinprotein

Complex networks Phys 7682: Computational Methods for Nonlinear Systems networks are everywhere (and always have been) - relationships (edges) among entities (nodes) explosion of interest in network structure,

### 6. Overview. L3S Research Center, University of Hannover. 6.1 Section Motivation. Investigation of structural aspects of peer-to-peer networks

, University of Hannover Random Graphs, Small-Worlds, and Scale-Free Networks Wolf-Tilo Balke and Wolf Siberski 05.12.07 * Original slides provided by K.A. Lehmann (University Tübingen, Germany) 6. Overview

### On Reshaping of Clustering Coefficients in Degreebased Topology Generators

On Reshaping of Clustering Coefficients in Degreebased Topology Generators Xiafeng Li, Derek Leonard, and Dmitri Loguinov Texas A&M University Presented by Derek Leonard Agenda Motivation Statement of

### Specific Communication Network Measure Distribution Estimation

Baller, D., Lospinoso, J. Specific Communication Network Measure Distribution Estimation 1 Specific Communication Network Measure Distribution Estimation Daniel P. Baller, Joshua Lospinoso United States

### How Do Real Networks Look? Networked Life NETS 112 Fall 2014 Prof. Michael Kearns

How Do Real Networks Look? Networked Life NETS 112 Fall 2014 Prof. Michael Kearns Roadmap Next several lectures: universal structural properties of networks Each large-scale network is unique microscopically,

### Girls Talk Math Summer Camp

From Brains and Friendships to the Stock Market and the Internet -Sanjukta Krishnagopal 10 July 2018 Girls Talk Math Summer Camp Some real networks Social Networks Networks of acquaintances Collaboration

### NEW CHALLENGES IN NETWORK RELIABILITY ANALYSIS

NEW CHALLENGES IN NETWORK RELIABILITY ANALYSIS Andrea Bobbio, Caterina Ferraris, Roberta Terruggia Dipartimento di Informatica Università del Piemonte Orientale, A. Avogadro 15100 Alessandria (Italy) Alessandria

### An introduction to the physics of complex networks

An introduction to the physics of complex networks Alain Barrat CPT, Marseille, France ISI, Turin, Italy http://www.cpt.univ-mrs.fr/~barrat http://www.cxnets.org http://www.sociopatterns.org REVIEWS: Statistical

### An Evolving Network Model With Local-World Structure

The Eighth International Symposium on Operations Research and Its Applications (ISORA 09) Zhangjiajie, China, September 20 22, 2009 Copyright 2009 ORSC & APORC, pp. 47 423 An Evolving Network odel With

### Math/Stat 2300 Modeling using Graph Theory (March 23/25) from text A First Course in Mathematical Modeling, Giordano, Fox, Horton, Weir, 2009.

Math/Stat 2300 Modeling using Graph Theory (March 23/25) from text A First Course in Mathematical Modeling, Giordano, Fox, Horton, Weir, 2009. Describing Graphs (8.2) A graph is a mathematical way of describing

### Using! to Teach Graph Theory

!! Using! to Teach Graph Theory Todd Abel Mary Elizabeth Searcy Appalachian State University Why Graph Theory? Mathematical Thinking (Habits of Mind, Mathematical Practices) Accessible to students at a

### Structural Analysis of Paper Citation and Co-Authorship Networks using Network Analysis Techniques

Structural Analysis of Paper Citation and Co-Authorship Networks using Network Analysis Techniques Kouhei Sugiyama, Hiroyuki Ohsaki and Makoto Imase Graduate School of Information Science and Technology,

### Constructing a G(N, p) Network

Random Graph Theory Dr. Natarajan Meghanathan Professor Department of Computer Science Jackson State University, Jackson, MS E-mail: natarajan.meghanathan@jsums.edu Introduction At first inspection, most

### Higher order clustering coecients in Barabasi Albert networks

Physica A 316 (2002) 688 694 www.elsevier.com/locate/physa Higher order clustering coecients in Barabasi Albert networks Agata Fronczak, Janusz A. Ho lyst, Maciej Jedynak, Julian Sienkiewicz Faculty of

### Complex networks: A mixture of power-law and Weibull distributions

Complex networks: A mixture of power-law and Weibull distributions Ke Xu, Liandong Liu, Xiao Liang State Key Laboratory of Software Development Environment Beihang University, Beijing 100191, China Abstract:

### Eciency of scale-free networks: error and attack tolerance

Available online at www.sciencedirect.com Physica A 320 (2003) 622 642 www.elsevier.com/locate/physa Eciency of scale-free networks: error and attack tolerance Paolo Crucitti a, Vito Latora b, Massimo

### Heuristics for the Critical Node Detection Problem in Large Complex Networks

Heuristics for the Critical Node Detection Problem in Large Complex Networks Mahmood Edalatmanesh Department of Computer Science Submitted in partial fulfilment of the requirements for the degree of Master

### Peer-to-Peer Data Management

Peer-to-Peer Data Management Wolf-Tilo Balke Sascha Tönnies Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tu-bs.de 10. Networkmodels 1. Introduction Motivation

### Analytical reasoning task reveals limits of social learning in networks

Electronic Supplementary Material for: Analytical reasoning task reveals limits of social learning in networks Iyad Rahwan, Dmytro Krasnoshtan, Azim Shariff, Jean-François Bonnefon A Experimental Interface

### Graph Theory. Network Science: Graph theory. Graph theory Terminology and notation. Graph theory Graph visualization

Network Science: Graph Theory Ozalp abaoglu ipartimento di Informatica Scienza e Ingegneria Università di ologna www.cs.unibo.it/babaoglu/ ranch of mathematics for the study of structures called graphs

### The Social Network of Java Classes Power-law for Dummies

The Social Network of Java Classes Power-law for Dummies Diego Puppin Institute for Information Sciences and Technology Pisa, Italy March 24, 2006 Diego Puppin (ISTI-CNR) LabDay March 24, 2006 1 / 41 Outline

### Algorithms and Applications in Social Networks. 2017/2018, Semester B Slava Novgorodov

Algorithms and Applications in Social Networks 2017/2018, Semester B Slava Novgorodov 1 Lesson #1 Administrative questions Course overview Introduction to Social Networks Basic definitions Network properties

### CSE 158 Lecture 11. Web Mining and Recommender Systems. Triadic closure; strong & weak ties

CSE 158 Lecture 11 Web Mining and Recommender Systems Triadic closure; strong & weak ties Triangles So far we ve seen (a little about) how networks can be characterized by their connectivity patterns What

### CSE 258 Lecture 11. Web Mining and Recommender Systems. Triadic closure; strong & weak ties

CSE 258 Lecture 11 Web Mining and Recommender Systems Triadic closure; strong & weak ties Triangles So far we ve seen (a little about) how networks can be characterized by their connectivity patterns What

### Signal Processing for Big Data

Signal Processing for Big Data Sergio Barbarossa 1 Summary 1. Networks 2.Algebraic graph theory 3. Random graph models 4. OperaGons on graphs 2 Networks The simplest way to represent the interaction between

### Clustering in Networks

Clustering in Networks (Spectral Clustering with the Graph Laplacian... a brief introduction) Tom Carter Computer Science CSU Stanislaus http://csustan.csustan.edu/ tom/clustering April 1, 2012 1 Our general