most influential member(s) of a social network; key infrastructure nodes; in an urban network; superspreaders of disease;...


 Cecilia Wheeler
 1 years ago
 Views:
Transcription
1 Ranking in Networks Question: Given a communication network N, how to discover important nodes? How to define the importance of members of the network? The answer may help in discovery of most influential member(s) of a social network; key infrastructure nodes; in an urban network; superspreaders of disease;... Polling the members is not efficient and is not accurate. Examples of networks: The Web; The protein network; The network of scientific cooperation;... The answer is implemented via the notion of centrality which gives a realvalued function on the nodes of a graph. The values of the function provide a ranking which identifies the most important nodes. On the other hand, it is often meaningless for not most important nodes. 1
2 The word importance has a wide number of meanings, leading to many different definitions of centrality. What are the network features that characterize the importance of a node in a network? Degree centrality The degree can be interpreted as the chances of a node to catch whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), two separate measures of degree centrality, are defined: indegree indeg(v), and outdegree, outdeg(v). indegree is interpreted as a measure of popularity; outdegree is interpreted as a measure of social involvement. Graph Centralization. Let G be a connected graph; let X V(G), where G[X] is also conneted. Denote (X) the highest degree centrality in X. Define H = max { ( (X)) deg(x))}. X x X The degree centralization of the graph G as follows: C(G) = v V(G) [ (V) deg(v)] H ThevalueofHismaximizedwhenthegraphX containsonecentral node to which all other nodes are connected (a star graph), and in this case H = (n 1)(n 2). 2
3 Closeness centrality In connected graphs, dist(x, y) denotes the length of a shortest path from x to y. The farness of x is defined as farness(x) = y x dist(x,y). The closeness of x is defined as 1 cl(x) = farness(x). If G is disconnected and vertices x and y belong to different connectdd components, dist(x, y) =. When a graph is not strongly connected, and no path connects y with x, then we assume dist(y,x) =, and use the sum of reciprocal of distances, instead of the reciprocal of the sum of distances, with the convention 1/ = 0: H(x) = y x 1 dist(y,x). For undirected graphs, the notion is known as harmonic centrality. A variation of the notion is defined as D(x) = 1 2 dist(y,x). y x 3
4 Betweenness centrality. Betweenness is a centrality measure of a vertex within a graph. Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network. Vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness. The betweenness of a vertex v in a graph G = (V,E) is computed as follows: 1. For each pair of vertices (x,y), compute the shortest paths between them. 2. For each pair of vertices (x,y), determine the fraction of shortest paths that pass through the vertex v. 3. Sum this fraction over all pairs of vertices (x,y). CB(v) = x v y V σ xy (v) σ xy where σ xy is the total number of shortest paths from node x to node y and σ xy (v) is the number of those paths that pass through v. The betweenness may be normalised by dividing through the number of pairs of vertices not including v which for directed graphs is (n 1)(n 2) and for undirected graphs is (n 1)(n 2)/2. 4
5 Computational complexity Both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires Θ(V 3 ) time with the Floyd Warshall algorithm. However, on sparse graphs, Johnson s algorithm may be more efficient, taking O(V 2 logv +VE) time. In the case of unweighted graphs the calculations can be done with Brandes algorithm[19] which takes O(V E) time. 5
6 PageRank PageRank is a link analysis algorithm; It assigns a numerical weighting to each node of a hyperlinked set of documents, such as the World Wide Web, with the purpose of measuring its relative importance within the set. The numerical weight that it assigns to any given document E is referred to as the PageRank of E and denoted by PR(E). Other factors like Author Rank can contribute to the importance of a document. A hyperlink to a page counts as a vote of support. The PageRank of a page is defined recursively and depends on the number and PageRank metric of all pages that link to it ( incoming links ). The main idea of ranking: a page that is linked to by many pages with high PageRank receives a high rank itself. 6
7 A B C D Initialization: PR(A) = PR(B) = PR(C) = PR(D) = 1; A better idea is to assume a probability distribution within [0,1]. PR(A) = PR(B)+PR(C)+PR(D). A B C D PR(A) = PR(B) 2 +PR(C)+ PR(D). 3 u v 1 v 2 v d PR(u) = v E in (u) PR(v) L(v) 7
8 The values of P R(v) approximate a probability distribution of the likelihood that a person randomly clicking on links will arrive at any particular page. The PageRank computations require several iterations through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value. Damping factor The PageRank theory holds that an imaginary surfer who is randomly clicking on links will eventually stop clicking. The probability, at any step, that the person will continue is a damping factor d. Various studies have tested different damping factors, but it is generally assumed that the damping factor will be set around PR(p i ) = 1 d N +d p j M(p i ) PR(p j ) L(p j ) 8
9 Computation For t = 0, PR(p i ;0) = 1 N. PR(p i ;t+1) = 1 d N +d p j M(p i ) PR(p j ;t) L(p j ) The computataion ends when j p(j,t+1) p(j,t) < ǫ. 9
Social Media Mining. Network Measures
Klout Measures and Metrics 22 Why Do We Need Measures? Who are the central figures (influential individuals) in the network? What interaction patterns are common in friends? Who are the likeminded users
More informationV. Adamchik 1. Graph Theory. Victor Adamchik. Fall of 2005
V. Adamchik 1 Graph Theory Victor Adamchik Fall of 2005 Plan 1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs Introduction A.Aho and J.Ulman acknowledge that Fundamentally, computer
More informationCourse on Social Network Analysis Graphs and Networks
Course on Social Network Analysis Graphs and Networks Vladimir Batagelj University of Ljubljana Slovenia V. Batagelj: Social Network Analysis / Graphs and Networks 1 Outline 1 Graph...............................
More informationPractical Graph Mining with R. 5. Link Analysis
Practical Graph Mining with R 5. Link Analysis Outline Link Analysis Concepts Metrics for Analyzing Networks PageRank HITS Link Prediction 2 Link Analysis Concepts Link A relationship between two entities
More informationSocial Network Mining
Social Network Mining Data Mining November 11, 2013 Frank Takes (ftakes@liacs.nl) LIACS, Universiteit Leiden Overview Social Network Analysis Graph Mining Online Social Networks Friendship Graph Semantics
More informationTrust and Reputation Management
Trust and Reputation Management Omer Rana School of Computer Science and Welsh escience Centre, Cardiff University, UK Omer Rana (CS, Cardiff, UK) CM0356/CMT606 1 / 28 Outline 1 Context Defining Trust
More informationGraphs and Network Flows IE411 Lecture 1
Graphs and Network Flows IE411 Lecture 1 Dr. Ted Ralphs IE411 Lecture 1 1 References for Today s Lecture Required reading Sections 17.1, 19.1 References AMO Chapter 1 and Section 2.1 and 2.2 IE411 Lecture
More informationEnhancing the Ranking of a Web Page in the Ocean of Data
Database Systems Journal vol. IV, no. 3/2013 3 Enhancing the Ranking of a Web Page in the Ocean of Data Hitesh KUMAR SHARMA University of Petroleum and Energy Studies, India hkshitesh@gmail.com In today
More informationSocial Media Mining. Graph Essentials
Graph Essentials Graph Basics Measures Graph and Essentials Metrics 2 2 Nodes and Edges A network is a graph nodes, actors, or vertices (plural of vertex) Connections, edges or ties Edge Node Measures
More informationChapter 2 Paths and Searching
Chapter 2 Paths and Searching Section 2.1 Distance Almost every day you face a problem: You must leave your home and go to school. If you are like me, you are usually a little late, so you want to take
More informationSolutions to Final Exam Sample Questions
Solutions to Final Exam Sample Questions CSE 31 1. Show that the proposition p ((q (r s)) t) is a contingency WITHOUT constructing its full truth table. If p is false, then the proposition is true, because
More informationBig Data Analytics. Lucas Rego Drumond
Big Data Analytics Lucas Rego Drumond Information Systems and Machine Learning Lab (ISMLL) Institute of Computer Science University of Hildesheim, Germany MapReduce II MapReduce II 1 / 33 Outline 1. Introduction
More informationGraph theory and network analysis. Devika Subramanian Comp 140 Fall 2008
Graph theory and network analysis Devika Subramanian Comp 140 Fall 2008 1 The bridges of Konigsburg Source: Wikipedia The city of Königsberg in Prussia was set on both sides of the Pregel River, and included
More informationAnalysis of Algorithms, I
Analysis of Algorithms, I CSOR W4231.002 Eleni Drinea Computer Science Department Columbia University Thursday, February 26, 2015 Outline 1 Recap 2 Representing graphs 3 Breadthfirst search (BFS) 4 Applications
More informationWarshall s Algorithm: Transitive Closure
CS 0 Theory of Algorithms / CS 68 Algorithms in Bioinformaticsi Dynamic Programming Part II. Warshall s Algorithm: Transitive Closure Computes the transitive closure of a relation (Alternatively: all paths
More information6.042/18.062J Mathematics for Computer Science October 3, 2006 Tom Leighton and Ronitt Rubinfeld. Graph Theory III
6.04/8.06J Mathematics for Computer Science October 3, 006 Tom Leighton and Ronitt Rubinfeld Lecture Notes Graph Theory III Draft: please check back in a couple of days for a modified version of these
More informationGraph Algorithms using MapReduce
Graph Algorithms using MapReduce Graphs are ubiquitous in modern society. Some examples: The hyperlink structure of the web 1/7 Graph Algorithms using MapReduce Graphs are ubiquitous in modern society.
More informationThe origins of graph theory are humble, even frivolous. Biggs, E. K. Lloyd, and R. J. Wilson)
Chapter 11 Graph Theory The origins of graph theory are humble, even frivolous. Biggs, E. K. Lloyd, and R. J. Wilson) (N. Let us start with a formal definition of what is a graph. Definition 72. A graph
More informationSociology and CS. Small World. Sociology Problems. Degree of Separation. Milgram s Experiment. How close are people connected? (Problem Understanding)
Sociology Problems Sociology and CS Problem 1 How close are people connected? Small World Philip Chan Problem 2 Connector How close are people connected? (Problem Understanding) Small World Are people
More informationGraph Theory and Complex Networks: An Introduction. Chapter 08: Computer networks
Graph Theory and Complex Networks: An Introduction Maarten van Steen VU Amsterdam, Dept. Computer Science Room R4.20, steen@cs.vu.nl Chapter 08: Computer networks Version: March 3, 2011 2 / 53 Contents
More informationGRAPH THEORY and APPLICATIONS. Trees
GRAPH THEORY and APPLICATIONS Trees Properties Tree: a connected graph with no cycle (acyclic) Forest: a graph with no cycle Paths are trees. Star: A tree consisting of one vertex adjacent to all the others.
More information1 Digraphs. Definition 1
1 Digraphs Definition 1 Adigraphordirected graphgisatriplecomprisedofavertex set V(G), edge set E(G), and a function assigning each edge an ordered pair of vertices (tail, head); these vertices together
More informationCOT5405 Analysis of Algorithms Homework 3 Solutions
COT0 Analysis of Algorithms Homework 3 Solutions. Prove or give a counter example: (a) In the textbook, we have two routines for graph traversal  DFS(G) and BFS(G,s)  where G is a graph and s is any
More informationGraph. Consider a graph, G in Fig Then the vertex V and edge E can be represented as:
Graph A graph G consist of 1. Set of vertices V (called nodes), (V = {v1, v2, v3, v4...}) and 2. Set of edges E (i.e., E {e1, e2, e3...cm} A graph can be represents as G = (V, E), where V is a finite and
More informationLesson 3. Algebraic graph theory. Sergio Barbarossa. Rome  February 2010
Lesson 3 Algebraic graph theory Sergio Barbarossa Basic notions Definition: A directed graph (or digraph) composed by a set of vertices and a set of edges We adopt the convention that the information flows
More informationNetwork Analysis and Visualization of Staphylococcus aureus. by Russ Gibson
Network Analysis and Visualization of Staphylococcus aureus by Russ Gibson Network analysis Based on graph theory Probabilistic models (random graphs) developed by Erdős and Rényi in 1959 Theory and tools
More informationSolutions to Exercises 8
Discrete Mathematics Lent 2009 MA210 Solutions to Exercises 8 (1) Suppose that G is a graph in which every vertex has degree at least k, where k 1, and in which every cycle contains at least 4 vertices.
More informationGephi Network Statistics
Gephi Network Statistics Google Summer of Code 2009 Project Proposal Patrick J. McSweeney pjmcswee@syr.edu 1 Introduction My name is Patrick J. McSweeney and I am a fourth year PhD candidate in computer
More informationSocial and Technological Network Analysis. Lecture 3: Centrality Measures. Dr. Cecilia Mascolo (some material from Lada Adamic s lectures)
Social and Technological Network Analysis Lecture 3: Centrality Measures Dr. Cecilia Mascolo (some material from Lada Adamic s lectures) In This Lecture We will introduce the concept of centrality and
More informationGraph Processing and Social Networks
Graph Processing and Social Networks Presented by Shu Jiayu, Yang Ji Department of Computer Science and Engineering The Hong Kong University of Science and Technology 2015/4/20 1 Outline Background Graph
More informationGraph Theory and Complex Networks: An Introduction. Chapter 06: Network analysis
Graph Theory and Complex Networks: An Introduction Maarten van Steen VU Amsterdam, Dept. Computer Science Room R4.0, steen@cs.vu.nl Chapter 06: Network analysis Version: April 8, 04 / 3 Contents Chapter
More informationAsking Hard Graph Questions. Paul Burkhardt. February 3, 2014
Beyond Watson: Predictive Analytics and Big Data U.S. National Security Agency Research Directorate  R6 Technical Report February 3, 2014 300 years before Watson there was Euler! The first (Jeopardy!)
More informationTheorem A graph T is a tree if, and only if, every two distinct vertices of T are joined by a unique path.
Chapter 3 Trees Section 3. Fundamental Properties of Trees Suppose your city is planning to construct a rapid rail system. They want to construct the most economical system possible that will meet the
More informationMining Social Network Graphs
Mining Social Network Graphs Debapriyo Majumdar Data Mining Fall 2014 Indian Statistical Institute Kolkata November 13, 17, 2014 Social Network No introduc+on required Really? We s7ll need to understand
More informationGraph Theory and Complex Networks: An Introduction. Chapter 06: Network analysis. Contents. Introduction. Maarten van Steen. Version: April 28, 2014
Graph Theory and Complex Networks: An Introduction Maarten van Steen VU Amsterdam, Dept. Computer Science Room R.0, steen@cs.vu.nl Chapter 0: Version: April 8, 0 / Contents Chapter Description 0: Introduction
More informationPredicting Influentials in Online Social Networks
Predicting Influentials in Online Social Networks Rumi Ghosh Kristina Lerman USC Information Sciences Institute WHO is IMPORTANT? Characteristics Topology Dynamic Processes /Nature of flow What are the
More informationFast Algorithms for Connectivity Problems in Networks
Fast Algorithms for Connectivity Problems in Networks Steiner Cuts, GomoryHu Trees, and Edge Splitting Strand Life Sciences 29 May 2008/ MCDES The Setting A network G of n nodes and m edges. Many nodes,
More informationDATA ANALYSIS II. Matrix Algorithms
DATA ANALYSIS II Matrix Algorithms Similarity Matrix Given a dataset D = {x i }, i=1,..,n consisting of n points in R d, let A denote the n n symmetric similarity matrix between the points, given as where
More informationNodeXL for Network analysis Demo/handson at NICAR 2012, St Louis, Feb 24. Peter Aldhous, San Francisco Bureau Chief. peter@peteraldhous.
NodeXL for Network analysis Demo/handson at NICAR 2012, St Louis, Feb 24 Peter Aldhous, San Francisco Bureau Chief peter@peteraldhous.com NodeXL is a template for Microsoft Excel 2007 and 2010, which
More informationThe PageRank Citation Ranking: Bring Order to the Web
The PageRank Citation Ranking: Bring Order to the Web presented by: Xiaoxi Pang 25.Nov 2010 1 / 20 Outline Introduction A ranking for every page on the Web Implementation Convergence Properties Personalized
More informationScientific Collaboration Networks in China s System Engineering Subject
, pp.3140 http://dx.doi.org/10.14257/ijunesst.2013.6.6.04 Scientific Collaboration Networks in China s System Engineering Subject Sen Wu 1, Jiaye Wang 1,*, Xiaodong Feng 1 and Dan Lu 1 1 Dongling School
More informationStrong and Weak Ties
Strong and Weak Ties Web Science (VU) (707.000) Elisabeth Lex KTI, TU Graz April 11, 2016 Elisabeth Lex (KTI, TU Graz) Networks April 11, 2016 1 / 66 Outline 1 Repetition 2 Strong and Weak Ties 3 General
More informationLARGESCALE GRAPH PROCESSING IN THE BIG DATA WORLD. Dr. Buğra Gedik, Ph.D.
LARGESCALE GRAPH PROCESSING IN THE BIG DATA WORLD Dr. Buğra Gedik, Ph.D. MOTIVATION Graph data is everywhere Relationships between people, systems, and the nature Interactions between people, systems,
More informationMinimum Spanning Trees
Minimum Spanning Trees Algorithms and 18.304 Presentation Outline 1 Graph Terminology Minimum Spanning Trees 2 3 Outline Graph Terminology Minimum Spanning Trees 1 Graph Terminology Minimum Spanning Trees
More information1 o Semestre 2007/2008
Departamento de Engenharia Informática Instituto Superior Técnico 1 o Semestre 2007/2008 Outline 1 2 3 4 5 Outline 1 2 3 4 5 Exploiting Text How is text exploited? Two main directions Extraction Extraction
More informationWalkBased Centrality and Communicability Measures for Network Analysis
WalkBased Centrality and Communicability Measures for Network Analysis Michele Benzi Department of Mathematics and Computer Science Emory University Atlanta, Georgia, USA Workshop on Innovative Clustering
More informationSocial Network Analysis
Social Network Analysis Challenges in Computer Science April 1, 2014 Frank Takes (ftakes@liacs.nl) LIACS, Leiden University Overview Context Social Network Analysis Online Social Networks Friendship Graph
More informationN.CN.7, A.CED.1, 2, 3, N.Q.2, A.SSE.1,
Learning Targets: I can solve interpret key features of quadratic functions from different form. I can choose a method to solve, and then, solve a quadratic equation and explain my reasoning. #1 4 For
More informationClass One: Degree Sequences
Class One: Degree Sequences For our purposes a graph is a just a bunch of points, called vertices, together with lines or curves, called edges, joining certain pairs of vertices. Three small examples of
More informationIE 680 Special Topics in Production Systems: Networks, Routing and Logistics*
IE 680 Special Topics in Production Systems: Networks, Routing and Logistics* Rakesh Nagi Department of Industrial Engineering University at Buffalo (SUNY) *Lecture notes from Network Flows by Ahuja, Magnanti
More informationAbout the Tutorial. Audience. Prerequisites. Disclaimer & Copyright
About the Tutorial This tutorial offers a brief introduction to the fundamentals of graph theory. Written in a readerfriendly style, it covers the types of graphs, their properties, trees, graph traversability,
More informationNetwork (Tree) Topology Inference Based on Prüfer Sequence
Network (Tree) Topology Inference Based on Prüfer Sequence C. Vanniarajan and Kamala Krithivasan Department of Computer Science and Engineering Indian Institute of Technology Madras Chennai 600036 vanniarajanc@hcl.in,
More informationSimplified External memory Algorithms for Planar DAGs. July 2004
Simplified External Memory Algorithms for Planar DAGs Lars Arge Duke University Laura Toma Bowdoin College July 2004 Graph Problems Graph G = (V, E) with V vertices and E edges DAG: directed acyclic graph
More information8.1 Min Degree Spanning Tree
CS880: Approximations Algorithms Scribe: Siddharth Barman Lecturer: Shuchi Chawla Topic: Min Degree Spanning Tree Date: 02/15/07 In this lecture we give a local search based algorithm for the Min Degree
More informationCMPSCI611: Approximating MAXCUT Lecture 20
CMPSCI611: Approximating MAXCUT Lecture 20 For the next two lectures we ll be seeing examples of approximation algorithms for interesting NPhard problems. Today we consider MAXCUT, which we proved to
More informationExtracting Information from Social Networks
Extracting Information from Social Networks Aggregating site information to get trends 1 Not limited to social networks Examples Google search logs: flu outbreaks We Feel Fine Bullying 2 Bullying Xu, Jun,
More informationProtein Protein Interaction Networks
Functional Pattern Mining from Genome Scale Protein Protein Interaction Networks YoungRae Cho, Ph.D. Assistant Professor Department of Computer Science Baylor University it My Definition of Bioinformatics
More informationCluster detection algorithm in neural networks
Cluster detection algorithm in neural networks David Meunier and Hélène PaugamMoisy Institute for Cognitive Science, UMR CNRS 5015 67, boulevard Pinel F69675 BRON  France Email: {dmeunier,hpaugam}@isc.cnrs.fr
More informationCS5314 Randomized Algorithms. Lecture 16: Balls, Bins, Random Graphs (Random Graphs, Hamiltonian Cycles)
CS5314 Randomized Algorithms Lecture 16: Balls, Bins, Random Graphs (Random Graphs, Hamiltonian Cycles) 1 Objectives Introduce Random Graph Model used to define a probability space for all graphs with
More informationLecture Notes on Spanning Trees
Lecture Notes on Spanning Trees 15122: Principles of Imperative Computation Frank Pfenning Lecture 26 April 26, 2011 1 Introduction In this lecture we introduce graphs. Graphs provide a uniform model
More information2.3 Convex Constrained Optimization Problems
42 CHAPTER 2. FUNDAMENTAL CONCEPTS IN CONVEX OPTIMIZATION Theorem 15 Let f : R n R and h : R R. Consider g(x) = h(f(x)) for all x R n. The function g is convex if either of the following two conditions
More informationSEMITOTAL AND TOTAL BLOCKCUTVERTEX GRAPH
CHAPTER 3 SEMITOTAL AND TOTAL BLOCKCUTVERTEX GRAPH ABSTRACT This chapter begins with the notion of block distances in graphs. Using block distance we defined the central tendencies of a block, like Bradius
More informationHandout #Ch7 San Skulrattanakulchai Gustavus Adolphus College Dec 6, 2010. Chapter 7: Digraphs
MCS236: Graph Theory Handout #Ch7 San Skulrattanakulchai Gustavus Adolphus College Dec 6, 2010 Chapter 7: Digraphs Strong Digraphs Definitions. A digraph is an ordered pair (V, E), where V is the set
More informationSocial network analysis with R sna package
Social network analysis with R sna package George Zhang iresearch Consulting Group (China) bird@iresearch.com.cn birdzhangxiang@gmail.com Social network (graph) definition G = (V,E) Max edges = N All possible
More informationGeneral Network Analysis: Graphtheoretic. COMP572 Fall 2009
General Network Analysis: Graphtheoretic Techniques COMP572 Fall 2009 Networks (aka Graphs) A network is a set of vertices, or nodes, and edges that connect pairs of vertices Example: a network with 5
More informationGraph definition Degree, in, out degree, oriented graph. Complete, regular, bipartite graph. Graph representation, connectivity, adjacency.
Mária Markošová Graph definition Degree, in, out degree, oriented graph. Complete, regular, bipartite graph. Graph representation, connectivity, adjacency. Isomorphism of graphs. Paths, cycles, trials.
More informationAlgorithms for representing network centrality, groups and density and clustered graph representation
COSIN IST 2001 33555 COevolution and Selforganization In dynamical Networks Algorithms for representing network centrality, groups and density and clustered graph representation Deliverable Number: D06
More informationprinceton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora
princeton univ. F 13 cos 521: Advanced Algorithm Design Lecture 6: Provable Approximation via Linear Programming Lecturer: Sanjeev Arora Scribe: One of the running themes in this course is the notion of
More informationarxiv: v2 [math.co] 30 Nov 2015
PLANAR GRAPH IS ON FIRE PRZEMYSŁAW GORDINOWICZ arxiv:1311.1158v [math.co] 30 Nov 015 Abstract. Let G be any connected graph on n vertices, n. Let k be any positive integer. Suppose that a fire breaks out
More informationWAN Wide Area Networks. Packet Switch Operation. Packet Switches. COMP476 Networked Computer Systems. WANs are made of store and forward switches.
Routing WAN Wide Area Networks WANs are made of store and forward switches. To there and back again COMP476 Networked Computer Systems A packet switch with two types of I/O connectors: one type is used
More informationLong questions answer Advanced Mathematics for Computer Application If P= , find BT. 19. If B = 1 0, find 2B and 3B.
Unit1: Matrix Algebra Short questions answer 1. What is Matrix? 2. Define the following terms : a) Elements matrix b) Row matrix c) Column matrix d) Diagonal matrix e) Scalar matrix f) Unit matrix OR
More informationWhy graph clustering is useful?
Graph Clustering Why graph clustering is useful? Distance matrices are graphs as useful as any other clustering Identification of communities in social networks Webpage clustering for better data management
More informationNetwork Analysis Basics and applications to online data
Network Analysis Basics and applications to online data Katherine Ognyanova University of Southern California Prepared for the Annenberg Program for Online Communities, 2010. Relational data Node (actor,
More informationLecture 1: Course overview, circuits, and formulas
Lecture 1: Course overview, circuits, and formulas Topics in Complexity Theory and Pseudorandomness (Spring 2013) Rutgers University Swastik Kopparty Scribes: John Kim, Ben Lund 1 Course Information Swastik
More informationThe Mathematics of Internet Search Engines
The Mathematics of Internet Search Engines David Marshall Department of Mathematics Monmouth University April 4, 2007 Introduction Search Engines, Then and Now Then... Now... Pagerank Outline Introduction
More informationDegree Hypergroupoids Associated with Hypergraphs
Filomat 8:1 (014), 119 19 DOI 10.98/FIL1401119F Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Degree Hypergroupoids Associated
More informationMidterm Practice Problems
6.042/8.062J Mathematics for Computer Science October 2, 200 Tom Leighton, Marten van Dijk, and Brooke Cowan Midterm Practice Problems Problem. [0 points] In problem set you showed that the nand operator
More informationThe world s largest matrix computation. (This chapter is out of date and needs a major overhaul.)
Chapter 7 Google PageRank The world s largest matrix computation. (This chapter is out of date and needs a major overhaul.) One of the reasons why Google TM is such an effective search engine is the PageRank
More informationNetwork Algorithms for Homeland Security
Network Algorithms for Homeland Security Mark Goldberg and Malik MagdonIsmail Rensselaer Polytechnic Institute September 27, 2004. Collaborators J. Baumes, M. Krishmamoorthy, N. Preston, W. Wallace. Partially
More informationDiscrete Mathematics & Mathematical Reasoning Chapter 10: Graphs
Discrete Mathematics & Mathematical Reasoning Chapter 10: Graphs Kousha Etessami U. of Edinburgh, UK Kousha Etessami (U. of Edinburgh, UK) Discrete Mathematics (Chapter 6) 1 / 13 Overview Graphs and Graph
More informationCSE 20: Discrete Mathematics for Computer Science. Prof. Miles Jones. Today s Topics: Graphs. The Internet graph
Today s Topics: CSE 0: Discrete Mathematics for Computer Science Prof. Miles Jones. Graphs. Some theorems on graphs. Eulerian graphs Graphs! Model relations between pairs of objects The Internet graph!
More informationChapter 8: The Mathematics of Scheduling
Discrete Math A, Chapter 8: Scheduling 2 Chapter 8: The Mathematics of Scheduling House Building See pages 280 & 281 8.1 Basic Elements of Scheduling: PROCESSOR: Whomever or whatever is working on a task
More informationTU e. Advanced Algorithms: experimentation project. The problem: load balancing with bounded lookahead. Input: integer m 2: number of machines
The problem: load balancing with bounded lookahead Input: integer m 2: number of machines integer k 0: the lookahead numbers t 1,..., t n : the job sizes Problem: assign jobs to machines machine to which
More informationMinimum Caterpillar Trees and RingStars: a branchandcut algorithm
Minimum Caterpillar Trees and RingStars: a branchandcut algorithm Luidi G. Simonetti Yuri A. M. Frota Cid C. de Souza Institute of Computing University of Campinas Brazil Aussois, January 2010 Cid de
More informationAn Empirical Study of Two MIS Algorithms
An Empirical Study of Two MIS Algorithms Email: Tushar Bisht and Kishore Kothapalli International Institute of Information Technology, Hyderabad Hyderabad, Andhra Pradesh, India 32. tushar.bisht@research.iiit.ac.in,
More informationLecture 11: AllPairs Shortest Paths
Lecture 11: AllPairs Shortest Paths Introduction Different types of algorithms can be used to solve the allpairs shortest paths problem: Dynamic programming Matrix multiplication FloydWarshall algorithm
More informationIntroduction to Graph Mining
Introduction to Graph Mining What is a graph? A graph G = (V,E) is a set of vertices V and a set (possibly empty) E of pairs of vertices e 1 = (v 1, v 2 ), where e 1 E and v 1, v 2 V. Edges may contain
More informationA SOCIAL NETWORK ANALYSIS APPROACH TO ANALYZE ROAD NETWORKS INTRODUCTION
A SOCIAL NETWORK ANALYSIS APPROACH TO ANALYZE ROAD NETWORKS Kyoungjin Park Alper Yilmaz Photogrammetric and Computer Vision Lab Ohio State University park.764@osu.edu yilmaz.15@osu.edu ABSTRACT Depending
More informationGraph Theory. Introduction. Distance in Graphs. Trees. Isabela Drămnesc UVT. Computer Science Department, West University of Timişoara, Romania
Graph Theory Introduction. Distance in Graphs. Trees Isabela Drămnesc UVT Computer Science Department, West University of Timişoara, Romania November 2016 Isabela Drămnesc UVT Graph Theory and Combinatorics
More informationAvailable online at ScienceDirect. Procedia Computer Science 74 (2015 ) 47 52
Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 74 (05 ) 47 5 International Conference on Graph Theory and Information Security Fractional Metric Dimension of Tree and
More informationData Structures and Algorithms Written Examination
Data Structures and Algorithms Written Examination 22 February 2013 FIRST NAME STUDENT NUMBER LAST NAME SIGNATURE Instructions for students: Write First Name, Last Name, Student Number and Signature where
More information1. Write the number of the lefthand item next to the item on the right that corresponds to it.
1. Write the number of the lefthand item next to the item on the right that corresponds to it. 1. Stanford prison experiment 2. Friendster 3. neuron 4. router 5. tipping 6. small worlds 7. jobhunting
More informationTriangle deletion. Ernie Croot. February 3, 2010
Triangle deletion Ernie Croot February 3, 2010 1 Introduction The purpose of this note is to give an intuitive outline of the triangle deletion theorem of Ruzsa and Szemerédi, which says that if G = (V,
More informationNetwork/Graph Theory. What is a Network? What is network theory? Graphbased representations. Friendship Network. What makes a problem graphlike?
What is a Network? Network/Graph Theory Network = graph Informally a graph is a set of nodes joined by a set of lines or arrows. 1 1 2 3 2 3 4 5 6 4 5 6 Graphbased representations Representing a problem
More informationThe TSP is a special case of VRP, which means VRP is NPhard.
49 6. ROUTING PROBLEMS 6.1. VEHICLE ROUTING PROBLEMS Vehicle Routing Problem, VRP: Customers i=1,...,n with demands of a product must be served using a fleet of vehicles for the deliveries. The vehicles,
More informationSGL: Stata graph library for network analysis
SGL: Stata graph library for network analysis Hirotaka Miura Federal Reserve Bank of San Francisco Stata Conference Chicago 2011 The views presented here are my own and do not necessarily represent the
More informationApproximation Algorithms
Approximation Algorithms or: How I Learned to Stop Worrying and Deal with NPCompleteness Ong Jit Sheng, Jonathan (A0073924B) March, 2012 Overview Key Results (I) General techniques: Greedy algorithms
More informationSystems and Algorithms for Big Data Analytics
Systems and Algorithms for Big Data Analytics YAN, Da Email: yanda@cse.cuhk.edu.hk My Research Graph Data Distributed Graph Processing Spatial Data Spatial Query Processing Uncertain Data Querying & Mining
More informationData Structures in Java. Session 16 Instructor: Bert Huang
Data Structures in Java Session 16 Instructor: Bert Huang http://www.cs.columbia.edu/~bert/courses/3134 Announcements Homework 4 due next class Remaining grades: hw4, hw5, hw6 25% Final exam 30% Midterm
More informationWhy? A central concept in Computer Science. Algorithms are ubiquitous.
Analysis of Algorithms: A Brief Introduction Why? A central concept in Computer Science. Algorithms are ubiquitous. Using the Internet (sending email, transferring files, use of search engines, online
More information