Basic Graph Properties
|
|
|
- Clare Burke
- 5 years ago
- Views:
Transcription
1 Network Analysis Basic Graph Properties Michele Coscia & Luca Rossi ITU København
2
3 Background:
4 Background: Real world networks have surprising properties
5 Stanley Milgram ( )
6
7
8
9
10
11
12
13 ~5.5 hops on average (Six Degrees of Separation)
14 ~5.5 hops on average (Six Degrees of Separation)
15 465 Sent ~5.5 hops on average 88 Arrived! (Six Degrees of Separation) < 20%
16
17
18 You
19 You Friend
20 You Friend
21 You Friend
22 You Friend
23 Trump You Friend
24 You Friend Trump Messi
25 You Friend Trump Messi Obama
26 You Me Trump Messi Obama
27 You Me Obama Trump Messi
28 2016 You Me Obama Trump Messi
29 2016 You Me Obama Trump Messi 2011
30 2016 You Me Obama Trump Messi 2011
31 Degree Distribution
32 Degree
33 Degree # of node connections
34 Degree # of node connections Each node has one!
35 Degree # of node connections Each node has one! Any patterns?
36 Degree Histogram
37 Degree Histogram Degree
38 Degree Histogram # Nodes Degree
39 Degree Histogram # Nodes Degree
40 Degree Histogram # Nodes Degree
41 Degree Histogram # Nodes Degree
42 Commonly... p(k) k
43 Commonly... p(k) k Normalize yaxis
44 Commonly... p(k) k Normalize yaxis For comparison
45 Let s Look at Some Real Distributions
46 Let s Look at Some Real Distributions
47 Let s Look at Some Real Distributions
48 Let s Look at Some Real Distributions Lots of info...
49 Let s Look at Some Real Distributions Lots of info......in a tight space
50 Real Degree Distributions
51 Real Degree Distributions log log
52 Real Degree Distributions
53 Real Degree Distributions
54 Real Degree Distributions
55 Real Degree Distributions
56 Still...
57 Still... Again lot of info in a tight space
58 p(k) Cumulative Degree Distribution k
59 Cumulative Degree Distribution p(k>=x) x
60 Cumulative Degree Distribution p(k>=x) x
61 Cumulative Degree Distribution p(k>=x) x
62 Cumulative Degree Distribution
63 Cumulative Degree Distribution
64 Cumulative Degree Distribution
65 Power Law
66 Power Law Relative change in one quantity
67 Power Law Relative change in one quantity Proportional relative change in the other
68 Power Law Relative change in one quantity Proportional relative change in the other Independent of their initial size
69 Power Law Relative change in one quantity Proportional relative change in the other Independent of their initial size
70 Power Law Relative change in one quantity Proportional relative change in the other Independent of their initial size Scale invariance = Scale free networks
71 Power Laws in Nature
72 Power Laws in Nature
73 Power Laws in Nature
74 Power Laws in Nature
75 Power Laws in Nature
76 Power Laws in Nature
77 Power Laws in Networks
78 Power Laws in Networks p(k) ~ k -α
79 Power Laws in Networks p(k) ~ k -α
80 Power Laws in Networks p(k) ~ k -α
81 Power Laws in Networks p(k) ~ k -α
82 Average Degree?
83 Average Degree?
84 Average Degree?
85 Average Degree?
86 Average Degree?
87 Power Laws Everywhere?
88 Power Laws Everywhere?
89 Power Laws Everywhere?
90 Power Laws Everywhere?
91 Power Laws Everywhere?
92 Power Laws Everywhere?
93 The Power Law Craze
94 The Power Law Craze
95 The Power Law Craze
96 The Power Law Craze???
97 Testing for Power Laws
98 Testing for Power Laws Option #1: Linear Fit in log-log space
99 Testing for Power Laws Option #1: Linear Fit in log-log space Very good R2 and p-value
100 Testing for Power Laws Option #1: Linear Fit in log-log space Very good R2 and p-value Because of log-log scale!
101 Testing for Power Laws
102 Testing for Power Laws Option #2: Log-Likelihood
103 Testing for Power Laws Option #2: Log-Likelihood How likely is funtion f to fit the data?
104 Testing for Power Laws Option #2: Log-Likelihood How likely is funtion f to fit the data? Allows p-value estimation between two alternatives
105 Testing for Power Laws Option #2: Log-Likelihood How likely is funtion f to fit the data? Allows p-value estimation between two alternatives Power Law
106 Testing for Power Laws Option #2: Log-Likelihood How likely is funtion f to fit the data? Allows p-value estimation between two alternatives Power Law Lognormal
107 Power Laws in the Wild
108 Power Laws in the Wild Shifted
109 Power Laws in the Wild Shifted Exponential Cutoff
110 Shifted Power Law
111 Shifted Power Law A power law excluding the head
112 Shifted Power Law A power law excluding the head
113 Shifted Power Law A power law excluding the head Power law with a warm up
114 Shifted Power Law A power law excluding the head Power law with a warm up
115 Shifted Power Law A power law excluding the head Power law with a warm up p(k) ~ k -α
116 Shifted Power Law A power law excluding the head Power law with a warm up p(k) ~ f(k)k -α
117 Shifted Power Law
118 Shifted Power Law
119 Shifted Power Law
120 Exponential Cutoff
121 Exponential Cutoff A power law excluding the tail
122 Exponential Cutoff A power law excluding the tail
123 Exponential Cutoff A power law excluding the tail Truncated Power law
124 Exponential Cutoff A power law excluding the tail Truncated Power law
125 Exponential Cutoff A power law excluding the tail Truncated Power law p(k) ~ k -α
126 Exponential Cutoff A power law excluding the tail Truncated Power law p(k) ~ k e -α -λk
127 Exponential Cutoff
128 Exponential Cutoff
129 Exponential Cutoff
130 Exponential Cutoff
131 Broad Distribution
132 Broad Distribution
133 Broad Distribution ~70%
134 Broad Distribution ~70%
135 Broad Distribution ~70% ~24x average
136 Pareto s 80/20
137 Pareto s 80/20
138 Pareto s 80/20
139 Pareto s 80/20
140 Pareto s 80/20
141 Pareto s 80/20
142 Zipf
143 Frequency Zipf
144 Frequency Zipf Rank
145 Zipf Frequency The Rank
146 Zipf Frequency The Of Rank
147 Zipf Frequency The Of And Rank
148 Zipf Frequency The Of And A Rank
149 Zipf Frequency The Of And A Rank In
150 Clustering
151 Disambiguation
152 Disambiguation Communities Clusters
153 Disambiguation Communities Clusters Only mildly related to clustering and clustering coefficient!
154 Disambiguation Communities Clusters Only mildly related to clustering and clustering coefficient! Communities ~ High Clustering
155 Clustering
156 Clustering
157 Clustering
158 Clustering The friend of my friend is my friend
159 Disambiguation B A C
160 Disambiguation B Transitivity : A C
161 Disambiguation B Transitivity : If A-B A C
162 Disambiguation B Transitivity : If A-B and B-C A C
163 Disambiguation B Transitivity : If A-B and B-C then A-C A C
164 Clustering
165 Clustering Triangle
166 Clustering Coefficient
167 Clustering Coefficient How many of these
168 Clustering Coefficient How many of these...turn into these?
169 Clustering Coefficient
170 Clustering Coefficient 3 x # Triangles CC = # of Triplets
171 Clustering Coefficient 3 x # Triangles CC = # of Triplets
172 Clustering Coefficient 3 x # Triangles CC = # of Triplets
173 Clustering Coefficient 3 x # Triangles CC = # of Triplets
174 Clustering Coefficient 3 x # Triangles CC = # of Triplets
175 Counting Triplets v
176 Counting Triplets v
177 Counting Triplets v
178 Counting Triplets v
179 Counting Triplets v
180 Counting Triplets v
181 Counting Triplets v
182 Counting Triplets v
183 Counting Triplets v
184 Counting Triplets v
185 Counting Triplets # Tripletsv = nv * (nv - 1) 2 (with nv being the number of neighbors v has) v
186 Clustering Coefficient 3 x # Triangles CC = # of Triplets
187 Clustering Coefficient 1 3 x # Triangles CC = # of Triplets
188 Clustering Coefficient 1 3 x # Triangles CC = # of Triplets 2
189 Clustering Coefficient x # Triangles CC = # of Triplets 2
190 Clustering Coefficient x # Triangles CC = # of Triplets 4 2
191 Clustering Coefficient x # Triangles CC = # of Triplets 4 2 5
192 Clustering Coefficient x # Triangles CC = # of Triplets
193 Clustering Coefficient x # Triangles CC = # of Triplets 6 7
194 Clustering Coefficient x # Triangles CC = # of Triplets 6 8 7
195 Clustering Coefficient x # Triangles CC = # of Triplets 6 8 7
196 Clustering Coefficient x # Triangles CC = # of Triplets 3x8 = =
197 Clustering Coefficient Global x # Triangles CC = # of Triplets 3x8 = =
198 Clustering Coefficient Local?
199 Clustering Coefficient Local? # Trianglesv CCv = # of Tripletsv
200 Clustering Coefficient Local? # Trianglesv CCv = # of Tripletsv
201 Clustering Coefficient Local? 1 # Trianglesv CCv = # of Tripletsv
202 Clustering Coefficient Local? 1 # Trianglesv CCv = # of Tripletsv 2
203 Clustering Coefficient Local? 1 # Trianglesv CCv = # of Tripletsv 2 3
204 Clustering Coefficient Local? 1 # Trianglesv CCv = # of Tripletsv 2 3 4
205 Clustering Coefficient Local? 1 2 # Trianglesv CCv = # of Tripletsv 3 5 4
206 Clustering Coefficient Local? 1 # Trianglesv CCv = # of Tripletsv 5 = =
207 Are We Done?
208 Are We Done? Average
209 Are We Done? Average CC =
210 Are We Done? Average CC = CCv
211 Are We Done? Average 1 CC = V Σ CC v
212 Are We Done? Average 1 CC = CCv V 5.83 = ~ Σ
213 Are We Done? Average!= Global 1 CC = CCv V 5.83 = ~ Σ
214 Complete Graphs
215 Complete Graphs Graphs with V * ( V - 1) 2 edges
216 Complete Graphs Graphs with V * ( V - 1) 2 edges Cliques
217 The Clique Zoo
218 The Clique Zoo Edge (Dyad) 2-Clique
219 The Clique Zoo Edge (Dyad) 2-Clique Triangle 3-Clique
220 The Clique Zoo Edge (Dyad) 2-Clique Triangle 3-Clique 4-Clique
221 The Clique Zoo... Edge (Dyad) 2-Clique Triangle 3-Clique 4-Clique
222 The Clique Zoo... Edge (Dyad) 2-Clique (Biclique) 3,2-Clique Triangle 3-Clique 4-Clique
223 The Clique Zoo... Edge (Dyad) 2-Clique (Biclique) 3,2-Clique Triangle 3-Clique 4-Clique
224 The Clique Zoo... Edge (Dyad) 2-Clique (Biclique) 3,2-Clique Triangle 3-Clique 4-Clique
225 The Clique Zoo... Edge (Dyad) 2-Clique Triangle 3-Clique 4-Clique Non-maximal Clique (Biclique) 3,2-Clique
226 The Clique Zoo... Edge (Dyad) 2-Clique Triangle 3-Clique 4-Clique Non-maximal Clique Maximal Clique (Biclique) 3,2-Clique
227 Complete Graphs
228 Complete Graphs # possible triplets: V * ( V - 1) 2
229 Complete Graphs # possible triplets: V * ( V - 1) 2 By definition: a clique s CC = 1
230 Real World Networks are Clustered
231 Real World Networks are Clustered Protein-protein network
232 Real World Networks are Clustered Protein-protein network Global cc =.0236
233 Real World Networks are Clustered Protein-protein network Global cc =.0236
234 Real World Networks are Clustered Protein-protein network Global cc =.0236 >16x as expected!
235 Real World Networks are Clustered
236 Real World Networks are Clustered Paper co-authors
237 Real World Networks are Clustered Paper co-authors Global cc =.318
238 Real World Networks are Clustered Paper co-authors Global cc =.318
239 Real World Networks are Clustered Paper co-authors Global cc =.318 >200x as expected!
240 Real World Networks are Clustered
241 Real World Networks are Clustered Power grid
242 Real World Networks are Clustered Power grid Global cc =.1032
243 Real World Networks are Clustered Power grid Global cc =.1032
244 Real World Networks are Clustered Power grid Global cc =.1032 >150x as expected!
245 Textbook Chapters Degree Distribution Section 2.3 (all) Sections 4.1 to 4.5, 4.7, 4.12 & 4.13 Clustering Sections 2.10 & 2.13
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
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,
Peer-to-Peer Networks 15 Self-Organization. Christian Schindelhauer Technical Faculty Computer-Networks and Telematics University of Freiburg
Peer-to-Peer Networks 15 Self-Organization Christian Schindelhauer Technical Faculty Computer-Networks and Telematics University of Freiburg Gnutella Connecting Protokoll - Ping Ping participants query
Example for calculation of clustering coefficient Node N 1 has 8 neighbors (red arrows) There are 12 connectivities among neighbors (blue arrows)
Example for calculation of clustering coefficient Node N 1 has 8 neighbors (red arrows) There are 12 connectivities among neighbors (blue arrows) Average clustering coefficient of a graph Overall measure
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
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/
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
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,
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
CSE 190 Lecture 16. Data Mining and Predictive Analytics. Small-world phenomena
CSE 190 Lecture 16 Data Mining and Predictive Analytics Small-world phenomena Another famous study Stanley Milgram wanted to test the (already popular) hypothesis that people in social networks are separated
Graph-theoretic Properties of Networks
Graph-theoretic Properties of Networks Bioinformatics: Sequence Analysis COMP 571 - Spring 2015 Luay Nakhleh, Rice University Graphs A graph is a set of vertices, or nodes, and edges that connect pairs
(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
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
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
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
ECE 158A - Data Networks
ECE 158A - Data Networks Homework 2 - due Tuesday Nov 5 in class Problem 1 - Clustering coefficient and diameter In this problem, we will compute the diameter and the clustering coefficient of a set of
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,
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
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
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
caution in interpreting graph-theoretic diagnostics
April 17, 2013 What is a network [1, 2, 3] What is a network [1, 2, 3] What is a network [1, 2, 3] What is a network [1, 2, 3] What is a network a collection of more or less identical agents or objects,
Why is a power law interesting? 2. it begs a question about mechanism: How do networks come to have power-law degree distributions in the first place?
you ve got the power Why is a power law interesting? 1. it is scale-free 2. it begs a question about mechanism: How do networks come to have power-law degree distributions in the first place? powerful
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
Degree Distribution: The case of Citation Networks
Network Analysis Degree Distribution: The case of Citation Networks Papers (in almost all fields) refer to works done earlier on same/related topics Citations A network can be defined as Each node is a
Community detection algorithms survey and overlapping communities. Presented by Sai Ravi Kiran Mallampati
Community detection algorithms survey and overlapping communities Presented by Sai Ravi Kiran Mallampati (sairavi5@vt.edu) 1 Outline Various community detection algorithms: Intuition * Evaluation of the
Structure of Social Networks
Structure of Social Networks Outline Structure of social networks Applications of structural analysis Social *networks* Twitter Facebook Linked-in IMs Email Real life Address books... Who Twitter #numbers
Counting Triangles & The Curse of the Last Reducer. Siddharth Suri Sergei Vassilvitskii Yahoo! Research
Counting Triangles & The Curse of the Last Reducer Siddharth Suri Yahoo! Research Why Count Triangles? 2 Why Count Triangles? Clustering Coefficient: Given an undirected graph G =(V,E) cc(v) = fraction
Network Mathematics - Why is it a Small World? Oskar Sandberg
Network Mathematics - Why is it a Small World? Oskar Sandberg 1 Networks Formally, a network is a collection of points and connections between them. 2 Networks Formally, a network is a collection of points
SI Networks: Theory and Application, Fall 2008
University of Michigan Deep Blue deepblue.lib.umich.edu 2008-09 SI 508 - Networks: Theory and Application, Fall 2008 Adamic, Lada Adamic, L. (2008, November 12). Networks: Theory and Application. Retrieved
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.
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
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
Statistics Worksheet 1 - Solutions
Statistics Worksheet 1 - Solutions Math& 146 Descriptive Statistics (Chapter 2) Data Set 1 We look at the following data set, describing hypothetical observations of voltage of as et of 9V batteries. The
Graph Model Selection using Maximum Likelihood
Graph Model Selection using Maximum Likelihood Ivona Bezáková Adam Tauman Kalai Rahul Santhanam Theory Canal, Rochester, April 7 th 2008 [ICML 2006 (International Conference on Machine Learning)] Overview
CSE 255 Lecture 13. Data Mining and Predictive Analytics. Triadic closure; strong & weak ties
CSE 255 Lecture 13 Data Mining and Predictive Analytics Triadic closure; strong & weak ties Monday Random models of networks: Erdos Renyi random graphs (picture from Wikipedia http://en.wikipedia.org/wiki/erd%c5%91s%e2%80%93r%c3%a9nyi_model)
TELCOM2125: Network Science and Analysis
School of Information Sciences University of Pittsburgh TELCOM2125: Network Science and Analysis Konstantinos Pelechrinis Spring 2015 Figures are taken from: M.E.J. Newman, Networks: An Introduction 2
CSE 158 Lecture 13. Web Mining and Recommender Systems. Triadic closure; strong & weak ties
CSE 158 Lecture 13 Web Mining and Recommender Systems Triadic closure; strong & weak ties Monday Random models of networks: Erdos Renyi random graphs (picture from Wikipedia http://en.wikipedia.org/wiki/erd%c5%91s%e2%80%93r%c3%a9nyi_model)
COMP6237 Data Mining and Networks. Markus Brede. Lecture slides available here:
COMP6237 Data Mining and Networks Markus Brede Brede.Markus@gmail.com Lecture slides available here: http://users.ecs.soton.ac.uk/mb8/stats/datamining.html Outline Why? The WWW is a major application of
The Mathematical Description of Networks
Modelling Complex Systems University of Manchester, 21 st 23 rd June 2010 Tim Evans Theoretical Physics The Mathematical Description of Networs Page 1 Notation I will focus on Simple Graphs with multiple
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/
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
Distribution-Free Models of Social and Information Networks
Distribution-Free Models of Social and Information Networks Tim Roughgarden (Stanford CS) joint work with Jacob Fox (Stanford Math), Rishi Gupta (Stanford CS), C. Seshadhri (UC Santa Cruz), Fan Wei (Stanford
arxiv: v3 [cs.ni] 3 May 2017
![arxiv: v3 [cs.ni] 3 May 2017](/thumbs/80/80871209.jpg "arxiv: v3 [cs.ni] 3 May 2017")
Modeling Request Patterns in VoD Services with Recommendation Systems Samarth Gupta and Sharayu Moharir arxiv:1609.02391v3 [cs.ni] 3 May 2017 Department of Electrical Engineering, Indian Institute of Technology
Modelling data networks research summary and modelling tools
Modelling data networks research summary and modelling tools a 1, 3 1, 2 2, 2 b 0, 3 2, 3 u 1, 3 α 1, 6 c 0, 3 v 2, 2 β 1, 1 Richard G. Clegg (richard@richardclegg.org) December 2011 Available online at
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
Transitivity and Triads
1 / 32 Tom A.B. Snijders University of Oxford May 14, 2012 2 / 32 Outline 1 Local Structure Transitivity 2 3 / 32 Local Structure in Social Networks From the standpoint of structural individualism, one
CS 124/LINGUIST 180 From Languages to Information. Social Networks: Small Worlds, Weak Ties, and Power Laws. Dan Jurafsky Stanford University
CS 124/LINGUIST 180 From Languages to Information Dan Jurafsky Stanford University Social Networks: Small Worlds, Weak Ties, and Power Laws Slides from Jure Leskovec, Lada Adamic, James Moody, Bing Liu,
Graph Mining and Social Network Analysis
Graph Mining and Social Network Analysis Data Mining and Text Mining (UIC 583 @ Politecnico di Milano) References q Jiawei Han and Micheline Kamber, "Data Mining: Concepts and Techniques", The Morgan Kaufmann
Lecture on Game Theoretical Network Analysis
Lecture on Game Theoretical Network Analysis Prof. Maria Papadopouli CS 590.21 Analysis and Modeling of Brain Networks Department of Computer Science University of Crete ACKNOWLEDGEMENTS Most of the slides
C N O S N T S RA R INT N - T BA B SE S D E L O L C O A C L S E S A E RC R H
LECTURE 11 & 12 CONSTRAINT-BASED LOCAL SEARCH Constraint-based Local Search Problem given in CSP form : a set of variables V={V1, V2,, Vn} a set of constraints C={C1, C2,, Ck} i.e. arithmetic or symbolic
Flat Routing on Curved Spaces
Flat Routing on Curved Spaces Dmitri Krioukov (CAIDA/UCSD) dima@caida.org Berkeley April 19 th, 2006 Clean slate: reassess fundamental assumptions Information transmission between nodes in networks that
MODELS FOR EVOLUTION AND JOINING OF SMALL WORLD NETWORKS
MODELS FOR EVOLUTION AND JOINING OF SMALL WORLD NETWORKS By SURESH BABU THIPIREDDY Bachelor of Technology in Computer Science Jawaharlal Nehru Technological University Hyderabad, Andhra Pradesh, India
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-
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:
Topology Enhancement in Wireless Multihop Networks: A Top-down Approach
Topology Enhancement in Wireless Multihop Networks: A Top-down Approach Symeon Papavassiliou (joint work with Eleni Stai and Vasileios Karyotis) National Technical University of Athens (NTUA) School of
Reconstruction of Images Distorted by Water Waves
Reconstruction of Images Distorted by Water Waves Arturo Donate and Eraldo Ribeiro Computer Vision Group Outline of the talk Introduction Analysis Background Method Experiments Conclusions Future Work
Trace Analysis, Clustering and Network Theory NOMADS
Trace Analysis, Clustering and Network Theory NOMADS Usage Trace in RAW Form 2007 11 17 00:00:03 EST b430bar-win-ap1200-1 [info] 189341: Nov 17 00:00:02 EST: %DOT11-6-ASSOC: Interface Dot11Radio0, Station
Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition
Bluman & Mayer, Elementary Statistics, A Step by Step Approach, Canadian Edition Online Learning Centre Technology Step-by-Step - Minitab Minitab is a statistical software application originally created
CSE 258 Lecture 12. Web Mining and Recommender Systems. Social networks
CSE 258 Lecture 12 Web Mining and Recommender Systems Social networks Social networks We ve already seen networks (a little bit) in week 3 i.e., we ve studied inference problems defined on graphs, and
Network Data Sampling and Estimation
Network Data Sampling and Estimation Hui Yang and Yanan Jia September 25, 2014 Yang, Jia September 25, 2014 1 / 33 Outline 1 Introduction 2 Network Sampling Designs Induced and Incident Subgraph Sampling
Universal Properties of Mythological Networks Midterm report: Math 485
Universal Properties of Mythological Networks Midterm report: Math 485 Roopa Krishnaswamy, Jamie Fitzgerald, Manuel Villegas, Riqu Huang, and Riley Neal Department of Mathematics, University of Arizona,
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
CSE 158 Lecture 11. Web Mining and Recommender Systems. Social networks
CSE 158 Lecture 11 Web Mining and Recommender Systems Social networks Assignment 1 Due 5pm next Monday! (Kaggle shows UTC time, but the due date is 5pm, Monday, PST) Assignment 1 Assignment 1 Social networks
E6885 Network Science Lecture 5: Network Estimation and Modeling
E 6885 Topics in Signal Processing -- Network Science E6885 Network Science Lecture 5: Network Estimation and Modeling Ching-Yung Lin, Dept. of Electrical Engineering, Columbia University October 7th,
ECS 253 / MAE 253, Lecture 10 May 3, Web search and decentralized search on small-world networks
ECS 253 / MAE 253, Lecture 10 May 3, 2018 Web search and decentralized search on small-world networks Announcements First example of the problems introduced by using software routines rather than working
Bayesian Spherical Wavelet Shrinkage: Applications to Shape Analysis
Bayesian Spherical Wavelet Shrinkage: Applications to Shape Analysis Xavier Le Faucheur a, Brani Vidakovic b and Allen Tannenbaum a a School of Electrical and Computer Engineering, b Department of Biomedical
modern database systems lecture 10 : large-scale graph processing
modern database systems lecture 1 : large-scale graph processing Aristides Gionis spring 18 timeline today : homework is due march 6 : homework out april 5, 9-1 : final exam april : homework due graphs
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
Using the DATAMINE Program
6 Using the DATAMINE Program 304 Using the DATAMINE Program This chapter serves as a user s manual for the DATAMINE program, which demonstrates the algorithms presented in this book. Each menu selection
Sample questions with solutions Ekaterina Kochmar
Sample questions with solutions Ekaterina Kochmar May 27, 2017 Question 1 Suppose there is a movie rating website where User 1, User 2 and User 3 post their reviews. User 1 has written 30 positive (5-star
Overview of Network Theory, I
Overview of Network Theory, I ECS 253 / MAE 253, Spring 2016, Lecture 1 Prof. Raissa D Souza University of California, Davis Raissa s background: 1999, PhD, Physics, Massachusetts Inst of Tech (MIT): Joint
Network Environments in AnyLogic. Nathaniel Osgood Agent-Based Modeling Bootcamp for Health Researchers
Network Environments in AnyLogic Nathaniel Osgood Agent-Based Modeling Bootcamp for Health Researchers August 23, 2011 Hands on Model Use Ahead Load model: Network Modification of SIR AB The Environment
Extracting Information from Complex Networks
Extracting Information from Complex Networks 1 Complex Networks Networks that arise from modeling complex systems: relationships Social networks Biological networks Distinguish from random networks uniform
Random Graph Model; parameterization 2
Agenda Random Graphs Recap giant component and small world statistics problems: degree distribution and triangles Recall that a graph G = (V, E) consists of a set of vertices V and a set of edges E V V.
Scale-free networks are rare
Scale-free networks are rare Anna Broido 1 and Aaron Clauset 2, 3 1. Applied Math Dept., CU Boulder 2. Computer Science Dept. & BioFrontiers Institute, CU Boulder 3. External Faculty, Santa Fe Institute
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
Supplementary Information for: Global similarity and local divergence in human and mouse gene co-expression networks
Supplementary Information for: Global similarity and local divergence in human and mouse gene co-expression networks Panayiotis Tsaparas 1, Leonardo Mariño-Ramírez 2, Olivier Bodenreider 3, Eugene V. Koonin
Chapter 7: Competitive learning, clustering, and self-organizing maps
Chapter 7: Competitive learning, clustering, and self-organizing maps António R. C. Paiva EEL 6814 Spring 2008 Outline Competitive learning Clustering Self-Organizing Maps What is competition in neural
Impact of Clustering on Epidemics in Random Networks
Impact of Clustering on Epidemics in Random Networks Joint work with Marc Lelarge INRIA-ENS 8 March 2012 Coupechoux - Lelarge (INRIA-ENS) Epidemics in Random Networks 8 March 2012 1 / 19 Outline 1 Introduction
Chapter 1 Introduction Motivation Approach Significance of Research Overview of Material... 5
ACKNOWLEDGEMENT First and foremost, I would like to thank my thesis advisor, Dr. A. Lynn Abbott, for his invaluable guidance and patience throughout my entire study at Virginia Tech. Beyond gaining academic
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
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
CS224W: Social and Information Network Analysis Jure Leskovec, Stanford University
CS224W: Social and Information Network Analysis Jure Leskovec, Stanford University http://cs224w.stanford.edu 10/4/2011 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu
Distributed Detection in Sensor Networks: Connectivity Graph and Small World Networks
Distributed Detection in Sensor Networks: Connectivity Graph and Small World Networks SaeedA.AldosariandJoséM.F.Moura Electrical and Computer Engineering Department Carnegie Mellon University 5000 Forbes
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
Statistics 202: Data Mining. c Jonathan Taylor. Outliers Based in part on slides from textbook, slides of Susan Holmes.
Outliers Based in part on slides from textbook, slides of Susan Holmes December 2, 2012 1 / 1 Concepts What is an outlier? The set of data points that are considerably different than the remainder of the
MAE 298, Lecture 9 April 30, Web search and decentralized search on small-worlds
MAE 298, Lecture 9 April 30, 2007 Web search and decentralized search on small-worlds Search for information Assume some resource of interest is stored at the vertices of a network: Web pages Files in
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
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
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
Topology of the Erasmus student mobility network
Topology of the Erasmus student mobility network Aranka Derzsi, Noemi Derzsy, Erna Káptalan and Zoltán Néda The Erasmus student mobility network Aim: study the network s topology (structure) and its characteristics
TELCOM2125: Network Science and Analysis
School of Information Sciences University of Pittsburgh TELCOM2125: Network Science and Analysis Konstantinos Pelechrinis Spring 2015 Figures are taken from: M.E.J. Newman, Networks: An Introduction 2
TELCOM2125: Network Science and Analysis
School of Information Sciences University of Pittsburgh TELCOM2125: Network Science and Analysis Konstantinos Pelechrinis Spring 2015 Figures are taken from: M.E.J. Newman, Networks: An Introduction 2
Link Analysis from Bing Liu. Web Data Mining: Exploring Hyperlinks, Contents, and Usage Data, Springer and other material.
Link Analysis from Bing Liu. Web Data Mining: Exploring Hyperlinks, Contents, and Usage Data, Springer and other material. 1 Contents Introduction Network properties Social network analysis Co-citation
Introduction To Graphs and Networks. Fall 2013 Carola Wenk
Introduction To Graphs and Networks Fall 203 Carola Wenk On the Internet, links are essentially weighted by factors such as transit time, or cost. The goal is to find the shortest path from one node to
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
Distributed Data Management
Distributed Data Management Christoph Lofi José Pinto Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tu-bs.de 7.0 Network Models 7.0 Introduction 7.1 Graph Model
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
Volume Profile Indicator Pro Version
Volume Profile Indicator Pro Version Introduction... 2 Getting Started... 3 Choose your chart history... 3 Selecting Volume Profile and Volume Profile Filter in Chart Indicator window... 3 Overview of
Degree Distribution, and Scale-free networks. Ralucca Gera, Applied Mathematics Dept. Naval Postgraduate School Monterey, California
Degree Distribution, and Scale-free networks Ralucca Gera, Applied Mathematics Dept. Naval Postgraduate School Monterey, California rgera@nps.edu Overview Degree distribution of observed networks Scale