We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byJordan Porteus
Modified about 1 year ago
Collective Dynamics of ‘Small World’ Networks C+ Elegans: Ilhan Savut, Spencer Telford, Melody Lim 29/10/13
Networks of dynamical systems
Can be represented by points (vertices or nodes) connected with lines (edges)
Overview Different types of networks o ‘Collective Dynamics of Small World Networks’ Duncan Watts and Steven Strogatz, Nature 393: (1998) Properties of networks o New type of network! Applications
A Regular Network
A Random Network
Fine-Tuning p Changes Network Properties p - rewiring of regular network Properties depend heavily on p
Properties of Networks Path Length, L Clustering coefficient, C
Properties of Networks Path Length, L o “Degrees of separation” Clustering coefficient, C o Chances that your friends are friends with each other
Path Length for Networks LongShort
Clustering for Networks HighLow
An Example of a Regular Network
No Random Networks Exist in Nature
L and C Depend on p
New Type of Network 0 < p < 1 (not fully random, not fully regular)
Small-World Networks Short path length, highly clustered
‘Small-world’ Network in the Middle
Small World Networks Are Natural Formation of networks favors small world Most networks built from small elements Evolutionary and natural processes favor the formation of small-world networks
Many Real World Systems are Small World Networks Collaboration graph of actors (six degrees of separation study) Neural network of C. elegans Power grid of Western US
Small World Networks Have New Properties Robustness Resistant to random changes Targeted ‘attacks’
Small World Networks Model the Spread of Disease
Conclusion New class of network model Low path length High clustering coefficient Models many natural systems!
Small-world networks. What is it? Everyone talks about the small world phenomenon, but truly what is it? There are three landmark papers: Stanley Milgram.
Peer-to-Peer and Social Networks Power law graphs Small world graphs.
‘Small World’ Networks (An Introduction) Presenter : Vishal Asthana
Lecture 10: Network models CS 765: Complex Networks Slides are modified from Networks: Theory and Application by Lada Adamic.
Topology and Dynamics of Complex Networks FRES1010 Complex Adaptive Systems Eileen Kraemer Fall 2005.
Complex Networks Advanced Computer Networks: Part1.
Neural Network of C. elegans is a Small-World Network Masroor Hossain Wednesday, February 29 th, 2012 Introduction to Complex Systems.
NILOY GANGULY Complex Network Theory. Complex Networks ? Real-World Networks (as Complex Networks) Large network size Heterogeneous network elements Diverse.
CSE 522 – Algorithmic and Economic Aspects of the Internet Instructors: Nicole Immorlica Mohammad Mahdian.
Performance in Decentralized Filesharing Networks Theodore Hong Freenet Project.
Networks FIAS Summer School 6th August 2008 Complex Networks 1.
Complex Network Theory – An Introduction Niloy Ganguly.
Complex Networks: Complex Networks: Structures and Dynamics Changsong Zhou AGNLD, Institute für Physik Universität Potsdam.
It’s a Small World by Jamie Luo. Introduction Small World Networks and their place in Network Theory An application of a 1D small world network to model.
March 3, 2009 Network Analysis Valerie Cardenas Nicolson Assistant Adjunct Professor Department of Radiology and Biomedical Imaging.
Network properties Slides are modified from Networks: Theory and Application by Lada Adamic.
3. SMALL WORLDS The Watts-Strogatz model. Watts-Strogatz, Nature 1998 Small world: the average shortest path length in a real network is small Six degrees.
1 Analyzing Kleinberg’s Small-world Model Chip Martel and Van Nguyen Computer Science Department; University of California at Davis.
Netlogo demo. Complexity and Networks Melanie Mitchell Portland State University and Santa Fe Institute.
COLOR TEST COLOR TEST. Social Networks: Structure and Impact N ICOLE I MMORLICA, N ORTHWESTERN U.
Teachers Teaching With Technology 2010 Annual Meeting - Atlanta, GA Ray Barton, Olympus High, SLC, UT.
Section 8 – Ec1818 Jeremy Barofsky March 31 st and April 1 st, 2010.
Small Worlds Presented by Geetha Akula For the Faculty of Department of Computer Science, CALSTATE LA. On 8 th June 07.
Performance Evaluation Lecture 1: Complex Networks Giovanni Neglia INRIA – EPI Maestro 10 December 2012.
VL Netzwerke, WS 2007/08 Edda Klipp 1 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Networks in Metabolism.
Stanley Milgram The small-world problem. Small world poses a math problem The problem: How can a network be both very small and very clustered?
Small-World File-Sharing Communities Adriana Iamnitchi, Matei Ripeanu and Ian Foster,
1 Small Worlds and Phase Transition in Agent Based Models with Binary Choices. Denis Phan ENST de Bretagne, Département Économie et Sciences Humaines &
Emergence of Scaling in Random Networks Albert-Laszlo Barabsi & Reka Albert.
Stochastic Simulations Six degrees of Kevin Bacon.
What Is A Network? (and why do we care?). An Introduction to Network Theory | Kyle Findlay | SAMRA 2010 | 2 “A collection of objects (nodes) connected.
Graph Theory in 50 minutes. This Graph has 6 nodes (also called vertices) and 7 edges (also called links)
1 Friends and Neighbors on the Web Presentation for Web Information Retrieval Bruno Lepri.
Peer-to-Peer and Grid Computing Exercise Session 3 (TUD Student Use Only)
Six degrees: The science of a connected age By Duncan J. Watts Brian Lewis INF 385Q December 1, 2005 Brian Lewis INF 385Q December 1, 2005.
Networks. Graphs (undirected, unweighted) has a set of vertices V has a set of undirected, unweighted edges E graph G = (V, E), where.
Small Worlds and the Security of Ubiquitous Computing From ： IEEE CNF Author ： Harald Vogt Presented by Chen Shih Yu.
Class 4: It’s a Small World After All Network Science: Small World February 2012 Dr. Baruch Barzel.
Gennaro Cordasco - How Much Independent Should Individual Contacts be to Form a Small-World? - 19/12/2006 How Much Independent Should Individual Contacts.
Topics In Social Computing (67810) Module 1 Introduction & The Structure of Social Networks.
The Small World Phenomenon: An Algorithmic Perspective Speaker: Bradford Greening, Jr. Rutgers University – Camden.
Network Design IS250 Spring 2010 John Chuang. 2 Questions What does the Internet look like? -Why do we care? Are there any structural invariants?
Most of contents are provided by the website Network Models TJTSD66: Advanced Topics in Social Media (Social.
Degree A F H G B E D C. Adjacent A F H G B E D C.
Simulating the Social Processes of Science Leiden| 9 April 2014 INGENIO [CSIC-UPV] Ciudad Politécnica de la Innovación | Edif 8E 4º Camino de Vera s/n.
Data Mining - Volinsky Columbia University Topic 13 Network Models 1 Credits: C. Faloutsos and J. Leskovec Tutorial E. Kolaczyk Notes.
Scale Free Networks Robin Coope April Abert-László Barabási, Linked (Perseus, Cambridge, 2002). Réka Albert and AL Barabási,Statistical Mechanics.
© 2017 SlidePlayer.com Inc. All rights reserved.