UNIVERSITA DEGLI STUDI DI CATANIA FACOLTA DI INGEGNERIA

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "UNIVERSITA DEGLI STUDI DI CATANIA FACOLTA DI INGEGNERIA"

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

CS-E5740. Complex Networks. Scale-free networks

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

More information

Properties of Biological Networks

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

More information

CAIM: Cerca i Anàlisi d Informació Massiva

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

More information

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

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

More information

A Generating Function Approach to Analyze Random Graphs

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

More information

Characteristics of Preferentially Attached Network Grown from. Small World

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

More information

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

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

More information

1 Degree Distributions

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

More information

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 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

More information

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. 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

More information

Eciency of scale-free networks: error and attack tolerance

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

More information

Using! to Teach Graph Theory

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

More information

1 Random Graph Models for Networks

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

More information

Overlay (and P2P) Networks

Overlay (and P2P) Networks Overlay (and P2P) Networks Part II Recap (Small World, Erdös Rényi model, Duncan Watts Model) Graph Properties Scale Free Networks Preferential Attachment Evolving Copying Navigation in Small World Samu

More information

Simplicial Complexes of Networks and Their Statistical Properties

Simplicial Complexes of Networks and Their Statistical Properties Simplicial Complexes of Networks and Their Statistical Properties Slobodan Maletić, Milan Rajković*, and Danijela Vasiljević Institute of Nuclear Sciences Vinča, elgrade, Serbia *milanr@vin.bg.ac.yu bstract.

More information

Estrada Index. Bo Zhou. Augest 5, Department of Mathematics, South China Normal University

Estrada Index. Bo Zhou. Augest 5, Department of Mathematics, South China Normal University Outline 1. Introduction 2. Results for 3. References Bo Zhou Department of Mathematics, South China Normal University Augest 5, 2010 Outline 1. Introduction 2. Results for 3. References Outline 1. Introduction

More information

EFFECT OF VARYING THE DELAY DISTRIBUTION IN DIFFERENT CLASSES OF NETWORKS: RANDOM, SCALE-FREE, AND SMALL-WORLD. A Thesis BUM SOON JANG

EFFECT OF VARYING THE DELAY DISTRIBUTION IN DIFFERENT CLASSES OF NETWORKS: RANDOM, SCALE-FREE, AND SMALL-WORLD. A Thesis BUM SOON JANG EFFECT OF VARYING THE DELAY DISTRIBUTION IN DIFFERENT CLASSES OF NETWORKS: RANDOM, SCALE-FREE, AND SMALL-WORLD A Thesis by BUM SOON JANG Submitted to the Office of Graduate Studies of Texas A&M University

More information

Towardsunderstanding: Astudy ofthe SourceForge.net community using modeling and simulation

Towardsunderstanding: Astudy ofthe SourceForge.net community using modeling and simulation Towardsunderstanding: Astudy ofthe SourceForge.net community using modeling and simulation YongqinGao,GregMadey DepartmentofComputerScience and Engineering UniversityofNotreDame ygao,gmadey@nd.edu Keywords:

More information

OPERATIONS RESEARCH. Transportation and Assignment Problems

OPERATIONS RESEARCH. Transportation and Assignment Problems OPERATIONS RESEARCH Chapter 2 Transportation and Assignment Problems Prof Bibhas C Giri Professor of Mathematics Jadavpur University West Bengal, India E-mail : bcgirijumath@gmailcom MODULE-3: Assignment

More information

NDIA 19th Annual System Engineering Conference, Springfield, Virginia October 24-27, 2016

NDIA 19th Annual System Engineering Conference, Springfield, Virginia October 24-27, 2016 NDIA 19th Annual System Engineering Conference, Springfield, Virginia October 24-27, 2016 Caesar S. Benipayo, PhD Student Under advisement of Dr. Michael Grenn and Dr. Blake Roberts Department of Engineering

More information

V 1 Introduction! Mon, Oct 15, 2012! Bioinformatics 3 Volkhard Helms!

V 1 Introduction! Mon, Oct 15, 2012! Bioinformatics 3 Volkhard Helms! V 1 Introduction! Mon, Oct 15, 2012! Bioinformatics 3 Volkhard Helms! How Does a Cell Work?! A cell is a crowded environment! => many different proteins,! metabolites, compartments,! On a microscopic level!

More information

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes Commun. Theor. Phys. (Beijing, China) 45 (2006) pp. 950 954 c International Academic Publishers Vol. 45, No. 5, May 15, 2006 Small World Properties Generated by a New Algorithm Under Same Degree of All

More information

Evolving Complex Neural Networks

Evolving Complex Neural Networks Evolving Complex Neural Networks Mauro Annunziato, Ilaria Bertini, Matteo De Felice, Stefano Pizzuti Energy, New technology and Environment Agency (ENEA) Via Anguillarese 30, 003 Rome, Italy {mauro.annunziato,

More information

Nested (2, r)-regular Graphs and Their Network Properties. A thesis. presented to. the faculty of the Department of Mathematics

Nested (2, r)-regular Graphs and Their Network Properties. A thesis. presented to. the faculty of the Department of Mathematics Nested (, r-regular Graphs and Their Network Properties A thesis presented to the faculty of the Department of Mathematics East Tennessee State University In partial fulfillment of the requirements for

More information

On the relationship between the algebraic connectivity and graph s robustness to node and link failures

On the relationship between the algebraic connectivity and graph s robustness to node and link failures On the relationship between the algebraic connectivity and graph s robustness to node and link failures A. Jamakovic, S. Uhlig Delft University of Technology Electrical Engineering, Mathematics and Computer

More information

Agent and Object Technology Lab Dipartimento di Ingegneria dell Informazione Università degli Studi di Parma. Computer Network.

Agent and Object Technology Lab Dipartimento di Ingegneria dell Informazione Università degli Studi di Parma. Computer Network. Agent and Object Technology Lab Dipartimento di Ingegneria dell Informazione Università degli Studi di Parma Computer Network Introduction Prof. Agostino Poggi Summary Theory Data Transmission Packet Transmission

More information

Graph Algorithms using Map-Reduce. Graphs are ubiquitous in modern society. Some examples: The hyperlink structure of the web

Graph Algorithms using Map-Reduce. Graphs are ubiquitous in modern society. Some examples: The hyperlink structure of the web Graph Algorithms using Map-Reduce Graphs are ubiquitous in modern society. Some examples: The hyperlink structure of the web Graph Algorithms using Map-Reduce Graphs are ubiquitous in modern society. Some

More information

Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows arxiv: v1 [physics.soc-ph] 12 May 2008

Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows arxiv: v1 [physics.soc-ph] 12 May 2008 Statistical Analysis of the Metropolitan Seoul Subway System: Network Structure and Passenger Flows arxiv:0805.1712v1 [physics.soc-ph] 12 May 2008 Keumsook Lee a,b Woo-Sung Jung c Jong Soo Park d M. Y.

More information

Exploiting the Scale-free Structure of the WWW

Exploiting the Scale-free Structure of the WWW Exploiting the Scale-free Structure of the WWW Niina Päivinen Department of Computer Science, University of Kuopio P.O. Box 1627, FIN-70211 Kuopio, Finland email niina.paivinen@cs.uku.fi tel. +358-17-16

More information

Onset of traffic congestion in complex networks

Onset of traffic congestion in complex networks Onset of traffic congestion in complex networks Liang Zhao, 1,2 Ying-Cheng Lai, 1,3 Kwangho Park, 1 and Nong Ye 4 1 Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287,

More information

Power Grid Modeling Using Graph Theory and Machine Learning Techniques. by Daniel Duncan A PROJECT. submitted to. Oregon State University

Power Grid Modeling Using Graph Theory and Machine Learning Techniques. by Daniel Duncan A PROJECT. submitted to. Oregon State University Power Grid Modeling Using Graph Theory and Machine Learning Techniques by Daniel Duncan A PROJECT submitted to Oregon State University University Honors College in partial fulfillment of the requirements

More information

KNOWLEDGE ARCHITECTURE FOR ENVIRONMENT REPRESENTATION IN AUTONOMOUS AGENTS

KNOWLEDGE ARCHITECTURE FOR ENVIRONMENT REPRESENTATION IN AUTONOMOUS AGENTS KNOWLEDGE ARCHITECTURE FOR ENVIRONMENT REPRESENTATION IN AUTONOMOUS AGENTS Dario Maio, Stefano Rizzi DEIS - Facoltà di Ingegneria, Università di Bologna, Italy dmaio@deis.unibo.it, srizzi@deis.unibo.it

More information

Collaboration networks and innovation in Canada s ICT Hardware Cluster. Catherine Beaudry and Melik Bouhadra Polytechnique Montréal

Collaboration networks and innovation in Canada s ICT Hardware Cluster. Catherine Beaudry and Melik Bouhadra Polytechnique Montréal Collaboration networks and innovation in Canada s ICT Hardware Cluster Catherine Beaudry and Melik Bouhadra Polytechnique Montréal CDO Third Annual Network Conference April 26 th 2016 2 Agenda Research

More information

Mining and Analyzing Online Social Networks

Mining and Analyzing Online Social Networks The 5th EuroSys Doctoral Workshop (EuroDW 2011) Salzburg, Austria, Sunday 10 April 2011 Mining and Analyzing Online Social Networks Emilio Ferrara eferrara@unime.it Advisor: Prof. Giacomo Fiumara PhD School

More information

The Evolution of the Mathematical Research Collaboration Graph

The Evolution of the Mathematical Research Collaboration Graph The Evolution of the Mathematical Research Collaboration Graph Jerrold W. Grossman Department of Mathematics and Statistics Oakland University Rochester, MI 48309-4485 e-mail: grossman@oakland.edu Abstract

More information

A Topological Network Analysis of Greek Firms

A Topological Network Analysis of Greek Firms A Topological Network Analysis of Greek Firms Kydros Dimitrios, Lecturer 1 * Notopoulos Panagiotis, Assoc. Professor* Kaparis Anastasios, Visiting Lecturer* *TEI of Serres School of Economics and Administration

More information

arxiv:cond-mat/ v3 [cond-mat.dis-nn] 30 Jun 2005

arxiv:cond-mat/ v3 [cond-mat.dis-nn] 30 Jun 2005 arxiv:cond-mat/0505185v3 [cond-mat.dis-nn] 30 Jun 2005 Characterization of Complex Networks: A Survey of measurements L. da F. Costa F. A. Rodrigues G. Travieso P. R. Villas Boas Instituto de Física de

More information

Random Graphs CS224W

Random Graphs CS224W Random Graphs CS224W Network models Why model? simple representation of complex network can derive properties mathematically predict properties and outcomes Also: to have a strawman In what ways is your

More information

Research on Community Structure in Bus Transport Networks

Research on Community Structure in Bus Transport Networks Commun. Theor. Phys. (Beijing, China) 52 (2009) pp. 1025 1030 c Chinese Physical Society and IOP Publishing Ltd Vol. 52, No. 6, December 15, 2009 Research on Community Structure in Bus Transport Networks

More information

Lesson 18. Laura Ricci 08/05/2017

Lesson 18. Laura Ricci 08/05/2017 Lesson 18 WATTS STROGATZ AND KLEINBERG MODELS 08/05/2017 1 SMALL WORLD NETWORKS Many real networks are characterized by a diameter very low. In several social networks, individuals tend to group in clusters

More information

Research Article Small-World and Scale-Free Network Models for IoT Systems

Research Article Small-World and Scale-Free Network Models for IoT Systems Hindawi Mobile Information Systems Volume 2017, Article ID 6752048, 9 pages https://doi.org/10.1155/2017/6752048 Research Article Small-World and Scale-Free Network Models for IoT Systems Insoo Sohn Division

More information

Engineering shortest-path algorithms for dynamic networks

Engineering shortest-path algorithms for dynamic networks Engineering shortest-path algorithms for dynamic networks Mattia D Emidio and Daniele Frigioni Department of Information Engineering, Computer Science and Mathematics, University of L Aquila, Via Gronchi

More information

Discovery of Community Structure in Complex Networks Based on Resistance Distance and Center Nodes

Discovery of Community Structure in Complex Networks Based on Resistance Distance and Center Nodes Journal of Computational Information Systems 8: 23 (2012) 9807 9814 Available at http://www.jofcis.com Discovery of Community Structure in Complex Networks Based on Resistance Distance and Center Nodes

More information

Guest Editorial GEOFFREY S CANRIGHT, KENTH ENGØ-MONSEN. graph), and a variety of interesting applications of this concept.

Guest Editorial GEOFFREY S CANRIGHT, KENTH ENGØ-MONSEN. graph), and a variety of interesting applications of this concept. Guest Editorial GEOFFREY S CANRIGHT, KENTH ENGØ-MONSEN Geoffrey S. Canright is senior researcher in Telenor R&I This issue of Telektronikk is devoted to network analysis. You, the reader, may immediately

More information

Research on Social Network Structure and Public Opinions Dissemination of Micro-blog Based on Complex Network Analysis

Research on Social Network Structure and Public Opinions Dissemination of Micro-blog Based on Complex Network Analysis JOURNAL OF NETWORKS, VOL. 8, NO. 7, JULY 2013 1543 Research on Social Network Structure and Public Opinions Dissemination of Micro-blog Based on Complex Network Analysis Xin Jin and Yaohua Wang School

More information

Evolutionary Complex Neural Networks

Evolutionary Complex Neural Networks Evolutionary Complex Neural Networks Mauro Annunziato, Ilaria Bertini, Matteo De Felice, Stefano Pizzuti ENEA Energy, New technologies and Environment Agency Casaccia R.C. - Via Anguillarese 301, 00123

More information

Rumour spreading in the spatial preferential attachment model

Rumour spreading in the spatial preferential attachment model Rumour spreading in the spatial preferential attachment model Abbas Mehrabian University of British Columbia Banff, 2016 joint work with Jeannette Janssen The push&pull rumour spreading protocol [Demers,

More information

NETWORK LITERACY. Essential Concepts and Core Ideas

NETWORK LITERACY. Essential Concepts and Core Ideas NETWORK LITERACY Essential Concepts and Core Ideas As our world becomes increasingly connected through the use of networks that allow instantaneous communication and the spread of information, the degree

More information

Graph Data Management Systems in New Applications Domains. Mikko Halin

Graph Data Management Systems in New Applications Domains. Mikko Halin Graph Data Management Systems in New Applications Domains Mikko Halin Introduction Presentation is based on two papers Graph Data Management Systems for New Application Domains - Philippe Cudré-Mauroux,

More information

Sampling Large Graphs for Anticipatory Analysis

Sampling Large Graphs for Anticipatory Analysis Sampling Large Graphs for Anticipatory Analysis Lauren Edwards*, Luke Johnson, Maja Milosavljevic, Vijay Gadepally, Benjamin A. Miller IEEE High Performance Extreme Computing Conference September 16, 2015

More information

Introduction To Graphs and Networks. Fall 2013 Carola Wenk

Introduction To Graphs and Networks. Fall 2013 Carola Wenk Introduction To Graphs and Networks Fall 2013 Carola Wenk What is a Network? We have thought of a computer as a single entity, but they can also be connected to one another. Internet What are the advantages

More information

Reply Networks on Bulletin Board System

Reply Networks on Bulletin Board System APS/123-QED Reply Networks on Bulletin Board System Kou Zhongbao and Zhang Changshui State Key Laboratory of Intelligent Technology and Systems Department of Automation, Tsinghua University Beijing, 100084,

More information

Task Assignment Problem in Camera Networks

Task Assignment Problem in Camera Networks Task Assignment Problem in Camera Networks Federico Cerruti Mirko Fabbro Chiara Masiero Corso di laurea in Ingegneria dell Automazione Università degli Studi di Padova Progettazione di sistemi di controllo

More information

Cooperative Computing for Autonomous Data Centers

Cooperative Computing for Autonomous Data Centers Cooperative Computing for Autonomous Data Centers Jared Saia (U. New Mexico) Joint with: Jon Berry, Cindy Phillips (Sandia Labs), Aaron Kearns (U. New Mexico) Outline 1) Bounding clustering coefficients

More information

Dynamic modelling and network optimization

Dynamic modelling and network optimization Dynamic modelling and network optimization Risto Lahdelma Aalto University Energy Technology Otakaari 4, 25 Espoo, Finland risto.lahdelma@aalto.fi Risto Lahdelma Feb 4, 26 Outline Dynamic systems Dynamic

More information

1 Comparing networks, and why social networks are different

1 Comparing networks, and why social networks are different 1 Comparing networks, and why social networks are different The various measures of network structure that we have encountered so far allow us mainly to understand the structure of a single particular

More information

Social Network Analysis as Knowledge Discovery process: a case study on Digital Bibliography

Social Network Analysis as Knowledge Discovery process: a case study on Digital Bibliography Social etwork Analysis as Knowledge Discovery process: a case study on Digital Bibliography Michele Coscia, Fosca Giannotti, Ruggero Pensa ISTI-CR Pisa, Italy Email: name.surname@isti.cnr.it Abstract Today

More information

.. Spring 2009 CSC 466: Knowledge Discovery from Data Alexander Dekhtyar..

.. Spring 2009 CSC 466: Knowledge Discovery from Data Alexander Dekhtyar.. .. Spring 2009 CSC 466: Knowledge Discovery from Data Alexander Dekhtyar.. Link Analysis in Graphs: PageRank Link Analysis Graphs Recall definitions from Discrete math and graph theory. Graph. A graph

More information

2. CONNECTIVITY Connectivity

2. CONNECTIVITY Connectivity 2. CONNECTIVITY 70 2. Connectivity 2.1. Connectivity. Definition 2.1.1. (1) A path in a graph G = (V, E) is a sequence of vertices v 0, v 1, v 2,..., v n such that {v i 1, v i } is an edge of G for i =

More information

NETWORK BASICS OUTLINE ABSTRACT ORGANIZATION NETWORK MEASURES. 1. Network measures 2. Small-world and scale-free networks 3. Connectomes 4.

NETWORK BASICS OUTLINE ABSTRACT ORGANIZATION NETWORK MEASURES. 1. Network measures 2. Small-world and scale-free networks 3. Connectomes 4. NETWORK BASICS OUTLINE 1. Network measures 2. Small-world and scale-free networks 3. Connectomes 4. Motifs ABSTRACT ORGANIZATION In systems/mechanisms in the real world Entities have distinctive properties

More information

Performance Analysis of A Feed-Forward Artifical Neural Network With Small-World Topology

Performance Analysis of A Feed-Forward Artifical Neural Network With Small-World Topology Available online at www.sciencedirect.com Procedia Technology (202 ) 29 296 INSODE 20 Performance Analysis of A Feed-Forward Artifical Neural Network With Small-World Topology Okan Erkaymaz a, Mahmut Özer

More information

Study of Data Mining Algorithm in Social Network Analysis

Study of Data Mining Algorithm in Social Network Analysis 3rd International Conference on Mechatronics, Robotics and Automation (ICMRA 2015) Study of Data Mining Algorithm in Social Network Analysis Chang Zhang 1,a, Yanfeng Jin 1,b, Wei Jin 1,c, Yu Liu 1,d 1

More information

University of the Basque Country UPV/EHU Department of Computer Science and Artificial Intelligence. Communities in complex networks

University of the Basque Country UPV/EHU Department of Computer Science and Artificial Intelligence. Communities in complex networks Technical Report University of the Basque Country UPV/EHU Department of Computer Science and Artificial Intelligence Communities in complex networks Abdelmalik Moujahid January 2013 San Sebastian, Spain

More information

EuroSymphony Solver. The Simplex Algorithm

EuroSymphony Solver. The Simplex Algorithm EuroSymphony Solver After opening Lotus Symphony Spreadsheet EuroSymphony Solver can be reached in Tools menu EuroSymphony Solver submenu. It provides four algorithms to solve optimization problems, namly

More information

The DataBridge: A Social Network for Long Tail Science Data!

The DataBridge: A Social Network for Long Tail Science Data! The DataBridge: A Social Network for Long Tail Science Data Howard Lander howard@renci.org Renaissance Computing Institute The University of North Carolina at Chapel Hill Outline of This Talk The DataBridge

More information

From Objects to Agents: The Java Agent Middleware (JAM)

From Objects to Agents: The Java Agent Middleware (JAM) From Objects to Agents: The Java Agent Middleware (JAM) Laboratory of Multiagent Systems LM Laboratorio di Sistemi Multiagente LM Elena Nardini elena.nardini@unibo.it Ingegneria Due Alma Mater Studiorum

More information

Mobile Wireless Sensor Network enables convergence of ubiquitous sensor services

Mobile Wireless Sensor Network enables convergence of ubiquitous sensor services 1 2005 Nokia V1-Filename.ppt / yyyy-mm-dd / Initials Mobile Wireless Sensor Network enables convergence of ubiquitous sensor services Dr. Jian Ma, Principal Scientist Nokia Research Center, Beijing 2 2005

More information

Smallest small-world network

Smallest small-world network Smallest small-world network Takashi Nishikawa, 1, * Adilson E. Motter, 1, Ying-Cheng Lai, 1,2 and Frank C. Hoppensteadt 1,2 1 Department of Mathematics, Center for Systems Science and Engineering Research,

More information

G(B)enchmark GraphBench: Towards a Universal Graph Benchmark. Khaled Ammar M. Tamer Özsu

G(B)enchmark GraphBench: Towards a Universal Graph Benchmark. Khaled Ammar M. Tamer Özsu G(B)enchmark GraphBench: Towards a Universal Graph Benchmark Khaled Ammar M. Tamer Özsu Bioinformatics Software Engineering Social Network Gene Co-expression Protein Structure Program Flow Big Graphs o

More information

Attack Vulnerability of Network with Duplication-Divergence Mechanism

Attack Vulnerability of Network with Duplication-Divergence Mechanism Commun. Theor. Phys. (Beijing, China) 48 (2007) pp. 754 758 c International Academic Publishers Vol. 48, No. 4, October 5, 2007 Attack Vulnerability of Network with Duplication-Divergence Mechanism WANG

More information

Data mining --- mining graphs

Data mining --- mining graphs Data mining --- mining graphs University of South Florida Xiaoning Qian Today s Lecture 1. Complex networks 2. Graph representation for networks 3. Markov chain 4. Viral propagation 5. Google s PageRank

More information

Diffusion in Networks

Diffusion in Networks Paper Diffusion in Networks Rafał Kasprzyk Faculty of Cybernetics, Military University of Technology, Warsaw, Poland Abstract In this paper a concept of method and its application examining a dynamic of

More information

Complex Network Metrology

Complex Network Metrology Complex Network Metrology Jean-Loup Guillaume and Matthieu Latapy liafa cnrs Université Paris 7 2 place Jussieu, 755 Paris, France. (guillaume,latapy)@liafa.jussieu.fr Abstract In order to study some complex

More information

Online Social Networks and Media

Online Social Networks and Media Online Social Networks and Media Absorbing Random Walks Link Prediction Why does the Power Method work? If a matrix R is real and symmetric, it has real eigenvalues and eigenvectors: λ, w, λ 2, w 2,, (λ

More information

Hierarchical Clustering of Process Schemas

Hierarchical Clustering of Process Schemas Hierarchical Clustering of Process Schemas Claudia Diamantini, Domenico Potena Dipartimento di Ingegneria Informatica, Gestionale e dell'automazione M. Panti, Università Politecnica delle Marche - via

More information

The physics of the Web

The physics of the Web 1 of 9 physics world The internet appears to have taken on a life of its own ever since the National Science Foundation in the US gave up stewardship of the network in 1995. New lines and routers are added

More information

Graph Theory: Applications and Algorithms

Graph Theory: Applications and Algorithms Graph Theory: Applications and Algorithms CIS008-2 Logic and Foundations of Mathematics David Goodwin david.goodwin@perisic.com 11:00, Tuesday 21 st February 2012 Outline 1 n-cube 2 Gray Codes 3 Shortest-Path

More information

An Algorithm of Parking Planning for Smart Parking System

An Algorithm of Parking Planning for Smart Parking System An Algorithm of Parking Planning for Smart Parking System Xuejian Zhao Wuhan University Hubei, China Email: xuejian zhao@sina.com Kui Zhao Zhejiang University Zhejiang, China Email: zhaokui@zju.edu.cn

More information

Smart and Resilient Energy Systems: Metrics and Evaluation

Smart and Resilient Energy Systems: Metrics and Evaluation Smart and Resilient Energy Systems: Metrics and Evaluation Igor Linkov and Matthew Bates Risk and Decision Sciences Team, US Army 6172339869 Igor.Linkov@usace.army.mil 1 Smart Resilient 2 Smart vs Resilient

More information

Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure

Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure Research on Invulnerability of Wireless Sensor Networks Based on Complex Network Topology Structure https://doi.org/10.3991/ijoe.v13i03.6863 Zhigang Zhao Zhejiang University of Media and Communications,

More information

PART III. GPU Cards and Architectures. Dr. Christian Napoli, M.Sc.! Dpt. Mathematics and Informatics, University of Catania!

PART III. GPU Cards and Architectures. Dr. Christian Napoli, M.Sc.! Dpt. Mathematics and Informatics, University of Catania! Postgraduate course on Electronics and Informatics Engineering (M.Sc.) Training Course on Circuits Theory (prof. G. Capizzi)! Workshop on High performance computing and GPGPU computing Postgraduate course

More information

Optimizing Random Walk Search Algorithms in P2P Networks

Optimizing Random Walk Search Algorithms in P2P Networks Optimizing Random Walk Search Algorithms in P2P Networks Nabhendra Bisnik Rensselaer Polytechnic Institute Troy, New York bisnin@rpi.edu Alhussein A. Abouzeid Rensselaer Polytechnic Institute Troy, New

More information

Preferential attachment models and their generalizations

Preferential attachment models and their generalizations Preferential attachment models and their generalizations Liudmila Ostroumova, Andrei Raigorodskii Yandex Lomonosov Moscow State University Moscow Institute of Physics and Technology June, 2013 Experimental

More information

Algorithms after Dijkstra and Kruskal for Big Data. User Manual

Algorithms after Dijkstra and Kruskal for Big Data. User Manual Algorithms after Dijkstra and Kruskal for Big Data User Manual Ovak Technologies 2016 Contents 1. Introduction... 3 1.1. Definition and Acronyms... 3 1.2. Purpose... 3 1.3. Overview... 3 2. Algorithms...

More information

arxiv: v1 [physics.soc-ph] 13 Jan 2011

arxiv: v1 [physics.soc-ph] 13 Jan 2011 An Estimation of the Shortest and Largest Average Path Length in Graphs of Given Density László Gulyás, Gábor Horváth, Tamás Cséri and George Kampis arxiv:1101.549v1 [physics.soc-ph] 1 Jan 011 Abstract

More information

Graph Mining: Overview of different graph models

Graph Mining: Overview of different graph models Graph Mining: Overview of different graph models Davide Mottin, Konstantina Lazaridou Hasso Plattner Institute Graph Mining course Winter Semester 2016 Lecture road Anomaly detection (previous lecture)

More information

Social-Network Graphs

Social-Network Graphs Social-Network Graphs Mining Social Networks Facebook, Google+, Twitter Email Networks, Collaboration Networks Identify communities Similar to clustering Communities usually overlap Identify similarities

More information

Bipartite graphs unique perfect matching.

Bipartite graphs unique perfect matching. Generation of graphs Bipartite graphs unique perfect matching. In this section, we assume G = (V, E) bipartite connected graph. The following theorem states that if G has unique perfect matching, then

More information

Why Do Computer Viruses Survive In The Internet?

Why Do Computer Viruses Survive In The Internet? Why Do Computer Viruses Survive In The Internet? Margarita Ifti a and Paul Neumann b a Department of Physics, Faculty of Natural Sciences, University of Tirana Bul. Zog I, Tirana, Albania b Department

More information

My favorite application using eigenvalues: partitioning and community detection in social networks

My favorite application using eigenvalues: partitioning and community detection in social networks My favorite application using eigenvalues: partitioning and community detection in social networks Will Hobbs February 17, 2013 Abstract Social networks are often organized into families, friendship groups,

More information

A Locality Model of the Evolution of Blog Networks

A Locality Model of the Evolution of Blog Networks A Locality Model of the Evolution of Blog Networs Mar Goldberg, Mali Magdon-Ismail, Stephen Kelley, Konstantin Mertsalov goldberg@cs.rpi.edu, magdon@cs.rpi.edu, elles@cs.rpi.edu, merts2@cs.rpi.edu Computer

More information

PROPERTIES OF NONUNIFORM RANDOM GRAPH MODELS

PROPERTIES OF NONUNIFORM RANDOM GRAPH MODELS Research Reports 77 Teknillisen korkeakoulun tietojenkäsittelyteorian laboratorion tutkimusraportti 77 Espoo 2003 HUT-TCS-A77 PROPERTIES OF NONUNIFORM RANDOM GRAPH MODELS Satu Virtanen ABTEKNILLINEN KORKEAKOULU

More information

Detecting and Analyzing Communities in Social Network Graphs for Targeted Marketing

Detecting and Analyzing Communities in Social Network Graphs for Targeted Marketing Detecting and Analyzing Communities in Social Network Graphs for Targeted Marketing Gautam Bhat, Rajeev Kumar Singh Department of Computer Science and Engineering Shiv Nadar University Gautam Buddh Nagar,

More information

Scalable Network Analysis

Scalable Network Analysis Inderjit S. Dhillon University of Texas at Austin COMAD, Ahmedabad, India Dec 20, 2013 Outline Unstructured Data - Scale & Diversity Evolving Networks Machine Learning Problems arising in Networks Recommender

More information

A complex network approach for identifying vulnerabilities of the medium and low voltage grid. Giuliano Andrea Pagani* and Marco Aiello

A complex network approach for identifying vulnerabilities of the medium and low voltage grid. Giuliano Andrea Pagani* and Marco Aiello 36 Int. J. Critical Infrastructures, Vol. 11, No. 1, 2015 A complex network approach for identifying vulnerabilities of the medium and low voltage grid Giuliano Andrea Pagani* and Marco Aiello Johann Bernoulli

More information

Politecnico di Torino. Porto Institutional Repository

Politecnico di Torino. Porto Institutional Repository Politecnico di Torino Porto Institutional Repository [Doctoral thesis] Power system vulnerability and performance: application from complexity scienze and complex network Original Citation: Lingen Luo

More information

Encoding Words into String Vectors for Word Categorization

Encoding Words into String Vectors for Word Categorization Int'l Conf. Artificial Intelligence ICAI'16 271 Encoding Words into String Vectors for Word Categorization Taeho Jo Department of Computer and Information Communication Engineering, Hongik University,

More information

The Mathematical Description of Networks

The Mathematical Description of Networks Feza Gürsey Institute - Imperial College International Summer School and Research Worshop on Complexity, Istanbul 5 th -10 th September 2011 Tim Evans The Mathematical Description of Networs Page 1 Feza

More information

Study on node importance evaluation of the high-speed passenger traflc complex network based on the Structural Hole Theory

Study on node importance evaluation of the high-speed passenger traflc complex network based on the Structural Hole Theory Open Phys. 2017; 15:1 11 Research Article Open Access Xu Zhang* and Bingzhi Chen Study on node importance evaluation of the high-speed passenger traflc complex network based on the Structural Hole Theory

More information