Social network analysis

For years, it has been agreed that centrality is an important structural factor of social networks, and many measures of centrality have been proposed, including four widely used measure

Abstract

Social network analysis is one of the most active topics in the central of research nowadays It has been widely used in various domains such as sociology, biology, economics, as well as information science

From the very early start, researchers used the concept of centrality to analyze networks In 1948, Bavelas [14] proposed the idea of centrality as applied

to human communication He was specifically concerned with communication in small groups and hypothesized a relationship between structural centrality and influence in group processes

For years, it has been agreed that centrality is an important structural factor

of social networks, and many measures of centrality have been proposed, including four widely used measures: degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality [34]

The Web is an example of social network, references from page to page create a hyperlink structure of the internet The most interesting application of analyzing this network is information retrieval system (or search engine) After crawling web pages to a local store, we create a network based on the links between the pages, and then compute the quality of each page, which is called static rank The static rank helps information retrieval systems to return more relevant results to a query PageRank and HITS are the two most widely used algorithms in today search engines to calculate the static rank

Besides, social networking sites, known as blog in another word, have become more and more popular These sites have its own properties that challenge traditional search engines in some context, such as users searching for users, which we have to find all users that have the shortest path to the user

issuing the query [23] It is also possible to apply PageRank to blog search, but with some modification to fit the blog’s properties

Recently, several local search engines have appeared in Vietnam, including

xalo, 7sac, baamboo, socbay, headvances, etc, but only three o of them, xalo, bamboo and headvances, have blog search, and none uses any link-based ranking

algorithm to improve their ranking

We consider that there is a link between two bloggers if one of them left a comment on the other More precisely, we model these relations as a network with nodes are bloggers and ties are “commenting” relations If blogger A left n comments on blogger B, we construct two corresponding nodes A and B, and a directional tie from A to B with the weight n We have modified the PageRank algorithm to take the weight of tie into account, which calculate the static rank of each blogger more precisely

Acknowledgement

I would like to thank my supervisors, Assoc Prof Dr Ha Quang Thuy and

Ms Nguyen Thu Trang at College of Technology, VNUH, for all their understanding, supports and encouragements that help me finish this thesis

I also want to thank my colleagues at Tinh Van Media for all their helps, especially Mr Pham Thuc Truong Luong and Mr Nguyen Quan Son for allowing

me doing experiments with their search platform

My last words are to thank my dear friends, who always beside me, encourage me and spend time proofreading the manuscript

Contents

Abstract 1

Acknowledgement 3

List of Figures 5

Chapter 1 6

Introduction to Social Network 6

1 Social network 6

2 Network construction 8

3 Network representation 10

4 A brief introduction of graph theory 12

5 Social network’s characteristics 14

6 Social network analysis – SNA 17

Chapter 2 19

Ranking in social network – Social rank 19

1 Introduction 19

2 Ranking in social networks 20

Chapter 3 29

Ranking bloggers and Experiments 29

1 Background and Motivation 29

2 Ranking bloggers by PageRank 34

3 Experiment setup and Results 35

Conclusion and Future works 40

List of Figures

Figure 1: A symmetric relationship 6

Figure 2: A directional relationship 6

Figure 3: Internet Alliances 8

Figure 4: A socio-gram 10

Figure 5: Graph and adjacent matrix 11

Figure 6: six degrees of separation 15

Figure 7: Real world example of small world networks 16

Figure 8: The Kite Network 21

Figure 9: An example showing how pagerank works 26

Figure 10: Đầu gấu’s blog 33

Figure 11: The corresponding network of Đầu gấu’s blog 34

Figure 12: Blog Ranking Architecture 35

Figure 13: A part of the Yahoo 360 network 37

Figure 14: Top 10 bloggers based on number Of comments 38

Figure 15: Top 10 bloggers based on PageRank 38

In the simplest form, the network contains two nodes and one relationship that connects them [12] The context might be people studying at the same university As you can see Minh and Thu has a relationship because they study at the same class at university, so in this kind of network, there is a tie between the two nodes Minh and Thu

Figure 1: A symmetric relationship The previous network is un-directional or symmetric, that mean A knows B and B knows A as well, such relationships are friendships, neighbor, kinship, companionship, or just living in the same room But in reality, there are a lot of relationships which are directional such as financial exchange, like (dislike), information flow, or disease transmission For instance, Minh likes Thu, but Thu might not like Minh

Figure 2: A directional relationship

studying at the same university

likes

More complex networks have multi-relationships These networks model many kinds of relationship between objects, or there might be many different ties between some two nodes [12]

Relationships might be more than sharing some attributes or being at the same place at the same time; the flow between the objects can form a relationship Liking, for example, might lead to an exchange of gifts In an organization, there

is the flow of knowledge between people; they share information, experiences… and constitutes a network [12]

A tie might have a weight associated with it, explaining the strength of the relationship between the two objects A long time friendship should be stronger than the friendship with someone you have just said “hi” in the street

Social network is unnecessary to be social in context There are many world instances of technological, business, economic, and biologic social networks; such as electrical power grids, telephone call graphs, the World Wide Web, co-authorship and citation networks of scientists, the spread of computer viruses or water flow network in a city The exchange of emails within organizations, newsgroups, chat rooms, friendships are examples from sociology [16]

real-Figure 3: Internet Alliances

Source: http://www.orgnet.com/netindustry.html

2 Network construction

Given a set of nodes, there are several strategies to collect information (objects and relations) and creating a network The first approaches are full network methods, which yields the maximum of information, but can also be costly and difficult to execute, and may be difficult to generalize On the other hand, there are approaches that yield considerably less information about the network structure, but are often less costly, and often more easily generalize from the observations in the sample to some large population And there is no one right way for all research questions and problems; each method has their own advantages and disadvantages

In this section, I will introduce an overview of 4 major methods in practice, refer to [29] for more details

2.1.1 Full network methods

This approach begins with a set of actors and tries to collect information (relations or ties) with all other actors For example, we could collect friendship data from all pairs of students in a college; we could count the number of vehicles moving between all pairs of cities or look at the flow of email between all pairs of employees in an organization

Because we collect information between all pairs of actors, full network methods draw a complete picture of relations in the population Full network data is needed to properly define and measure many structural concepts of network analysis The disadvantages of this approach is the cost of collecting information; the process is very expensive

2.1.2 Snowball methods

In these methods, we choose a set of actors as a starting point We then include some other actors who have connections with each actor in the set The process continue until no new actors are indentified, or until we decide to stop Isolated actors are not located by this method, and the structure of the network depends greatly on how we choose the initial actors

2.1.3 Ego-centric networks (with alter connections)

It will not feasible and necessary to track down the full networks beginning with some initial nodes as in the snowball method for many cases We can also begin with a set of some initial nodes and identify nodes that have connections with the initial nodes Then, we determine which of the nodes identified in the first stage are connected to one another

2.1.4 Ego-centric networks (ego only)

Ego-centric methods really focus on the individual, rather than on the network as a whole These methods collect information on the connections among the actors connected to each focal ego, which still present a pretty good picture of the “local” networks, or “neighborhoods” of individuals Such information is useful for understanding how networks affect individuals

3 Network representation

In order to analyze the social network, we need a way to represent it in a computational structure and to see how it looks like Network analysis use graphs and adjacent matrices to model social networks, and use graph theories to

do analyzing

Graphs are a very useful ways to present information about social networks

In simple networks, it is easy for us to look at the graph and predict patterns of information Network analysis uses one kind of graphic display that consists of points to represent objects or nodes, and lines to represent ties or relations The graphic is called socio-gram They use various colors, shapes, names, etc, to represent different actors and relations [29]

Figure 4: A socio-gram Source: http://blogs.bnet.com/bnet1/images/sociogram_los_alamos.jpg

In more complex networks, when there are thousands of actors and many different kinds of relations, graphs (social-grams) can become very visually complicated that it is difficult to see patterns In this situation, we can represent information about social networks in the form of matrices This approach allows the application of mathematical and computer tools to summarize and find patterns [29]

The most common form of matrix in social network analysis is adjacent matrix, a square matrix with as many rows and columns as there are actors in the network The weights or scores in the cells of the matrix show information about the ties between each pair of actors This kind of matrix represents who is next to,

or adjacent to whom in the “social space” mapped by relations that we have measured [29]

Figure 5: Graph (right) and adjacent matrix (left)

Source: [25]

Formally, we represent a network as a graph G = <V,E> consisting of a set of vertices V = {vi} that represent social entities and a set of edges E = {eij} where eij represent information of the connection between the nodes i and j [25]

4 A brief introduction of graph theory

A necessary course in social network analysis is graph theory As social networks can be represented as graphs, understanding fundamental concepts in graph theories is essential In this section we will give some concepts that are

often used when analyzing networks More details can be found at [29]

The degree of a node is defined as the number of ties incident upon that node

In directed graph, each node has both indegree and outdegree The indegree is the

number of ties pointing to the node, whereas the outdegree is the number of ties

pointing out from that nodes

A path is an alternating sequence of nodes and ties, beginning at a node and

ending at a node, and which does not visit any node more than once

A walk is like a path except that there is no restriction on the number of times

a point can be visited A path is a kind of walk

A cycle is just like a path except that it starts and ends at the same point

The length of a path or walk (or cycle) is defined as the number of ties in it

A path between two nodes with the shortest length is called a shortest path

(also a geodesic) between the two nodes It is not always unique (that is, there may be several paths between the same two points that are equally short) The

graph-theoretic distance between two nodes is defined as the length of the shortest

path between them

A graph is connected if there exists a path (of any length) from every node to

every other node The longest possible path between any two nodes in a connected graph is n-1, where n is the number of nodes in the graph

A node is reachable from another node if there exists a path of any length

from one to the other

A connected component is a maximal sub-graph in which all nodes are

reachable from every other Maximal means that it is the largest possible graph: you could not find another node anywhere in the graph such that it could

sub-be added to the sub-graph and all the nodes in the sub-graph would still sub-be connected

For directed graphs, there are strong components and weak components A

strong component is a maximal sub-graph in which there is a path from every node to every node following all the arcs in the direction they are pointing A weak component is a maximal sub-graph which would be connected if we ignored the direction of the arcs

A cutpoint is a vertex whose removal from the graph increases the number of

components That is, it makes some points unreachable from some others It disconnects the graph

A cutset is a collection of points whose removal increases the number of components in a graph A minimum weight cutset consists of the smallest set of

points that must be removed to disconnect a graph The number of points in a

minimum weight cutset is called the point connectivity of a graph If a graph has a

cutpoint, the connectivity of the graph is 1 The minimum number of points separating two nonadjacent points s and t is also the maximum number of point-disjoint paths between s and t

A bridge is an edge whose removal from a graph increases the number of components (disconnects the graph) An edge cutset is a collection of edges whose removal disconnects a graph A local bridge of degree k is an edge whose

removal causes the distance between the endpoints of the edge to be at least k

The edge-connectivity of a graph is the minimum number of lines whose removal would disconnect the graph The minimum number of edges separating two nonadjacent points s and t is also the maximum number of edge-disjoint paths between s and t

5 Social network’s characteristics

In the late of 1950s, two mathematicians Erdös and Rényi created a great important theory in graph by modeling many real world networks by a special type of graph – random graph To create a random graph with n nodes and m ties, they put n nodes next to each other, take pair of node at random and tie them together, the process continues until the graph has m ties Erdös and Rényi realize that “when m is small, the graph is likely to be fragmented into many small clusters” (components), “as m increases the components grow” For m > n/2, all nodes are connected to each other [31]

Beside regular and random graph, the two extreme types of graph, network analysts also study some other types of networks, two most important of them are small world and scale free networks

5.1 Small world networks

The experiments conducted by Stanley Milgram and his colleagues for social networks of people in the United States raising the concept of “small world” The phrase captures the initial surprise between two strangers (“What a small world”) when they realize that they are indirectly connected to one another through mutual friends People in Kansas and Nebraska were asked to direct letters to strangers in Boston by forwarding them to friends who thought might know the strangers in Boston And half of the letters were successfully delivered through no more than five intermediaries Another experiments show that there might be “six degrees of separation” between any two individuals in the world

The research was groundbreaking in that it showed that human society is a small world network characterized by shorter than expected path lengths [16]

In small world network, most nodes can be reached from every other by a small number of hops or steps

Figure 6: six degrees of separation Source: http://en.wikipedia.org

Figure 7: Real world example of small world networks

(a) science coauthor network, (b) connected pages on a part of the internet, (c) biochemical pathway network, and (d) New York state electric power grid

Figure 7 (a), (b), (c) are from www.nd.edu/~networks/publications.html#talks0001 by Barabasi, Oltvai, Jeong

et al Figure 6 (d) is from http://tam.cornell.edu/Strogatz.html#pub

5.2 Scale free networks

Many real world networks are scale free, which means the network will not

change its properties no matter how many nodes it has The degree distribution

of scale free networks follows the Yule-Simon distribution – a power law relationship defined by P(k) ~ k-α, where P(k) denotes the probability that a node

in the network connects with k other nodes, the coefficient α may very approximately from 2 to 3 for most cases, but some times it can takes a value between 1 and 2 [36]

Scale free networks have some highly connected hubs and the rest of nodes are of low degree The hubs are thought to serve some specific purposes in their networks, although this depends greatly on the domain The structure of this kind of network allows the ability of fault tolerant Because the random occurrence of failures and the number of small degree nodes are enormous, the likelihood that a hub would be affected is negligible Even if such even occurs, the networks will not lose its connectedness, because of the remaining hubs This property make scale free network highly stable and robust [36]

6 Social network analysis – SNA

SNA [15] deals with mapping and measuring the nodes and relations between the nodes in a social network As stated previously, the nodes might be people, organizations, etc, and relations might be friendship, kinship, or water flow

Social network analysis has become a key technique in modern sociology, anthropology, geography, social psychology, sociolinguistics, information science, communication studies, organizational studies, economics, and biology

as well For over a century, people have used social network metaphor to model complex sets of relationships between actors of social systems at all scale

Analysts reason from whole to part, from structure to relation to individual, from behavior to attitude [33]

So why do we have to study social networks and what we can learn about their structure? The reason is that the structure of a network affects its functionalities For example, the topology of social networks affects the way diseases spread through a population Consider a city water distribution network, delivering water to households via pipes and junctions Accidental or malicious instructions can cause contaminants to spread over the network Jure Leskovec and colleagues at Carnegie Melon University has proposed an algorithm to select a few locations to install sensors in order to detect these contaminants as soon as possible so that it minimizes the population consuming contaminants [18] The topology of power grid affects the stability and robustness

of its power transmission; the power failure in Cleveland, Ohio on August 14,

2003 is an example When occurred, the shutting down of nuclear power plants in New York State and Ohio led to widespread power blackouts in many parts of the Northeastern United States and Southeastern Canada through an interconnecting grid system, which affected about 50 million people [16]

of searching for information in documents The system is often very complex, and consists of four main parts: crawlers, document processors, indexers and search Crawlers (or spiders) collect documents and store them on disks Documents are usually web pages on the internet Then, these documents will be sent to document processors to process and extract necessary information, for example, remove un-wanted part of documents (advertises, header, footer, etc), extract title, body, descriptions, etc Information extracted from the process will be stored back to disks in a special structure that helps rapid access and search for a query Web front-end is a interface that standing in front of users, receives queries from users, contacts the search component and present the results back to users Refer

to [28] for more details about information retrieval

As you can imagine, because of the huge size of the internet (Google has about 60 billion documents in its index [17] in 2005), the number of results for each query might be millions, or even billions, for example, the query “search engine” returns over 200 million results from Google Users do not have time and patient to through every page to find an interested answer for their question The process of rearrange the results so that the most relevant documents appear first

in the list is called ranking Ranking helps users find their need-answer without much effort, that mean in a rapid and efficient way

Many ranking algorithms have been proposed to rank documents based on context, that mean whether the query terms match in the title, or in the body of a document; how early and how often they appear in a document It seems that a document is more relevant to a query if the query terms appear in the title rather than in the body of the document We often use freshness when searching for news Freshness is a measure of how fresh a document is Freshness help search engines rank documents based on the time it is created

We also measure the quality of a document to improve ranking So what is quality? Let me explain it by some examples Because of your search policy, you might want to favor web sites from government more than those from education, and focus on pages from education more than pages from the left In other words, you assume pages from government have higher quality than pages from education, and pages from education have higher quality than the left And another assumption is that home pages’ quality are higher than quality of pages that from a deeper position It is very useful in the context that users search for a product or a company, the homepage of the company or the product should be

on top For instance, the query “Microsoft” should return the homepage of Microsoft Corporation rather than the page of some users that complains about the Microsoft products

To calculate the quality of a document, we can borrow some algorithms from social network analysis, which use the link structure to determine the importance of individuals in the network

2 Ranking in social networks

In social network analysis, one fundamental problem is ranking individuals

in society according to their implicit importance, for example the power or influence, determined by the topology of the networks Precisely, given a social

network, the purpose is producing a rank point, which is a non negative value, assigned to each individual [7]

We measure the importance of individuals in concepts of centrality, including Degree centrality, Betweenness centrality, closeness centrality and Eigenvector centrality And we focus on Eigenvector centrality with the two most popular variants, PageRank and HITS

2.1 Centrality

Figure 8: The Kite Network Developed by David Krackhardt, source: http://www.orgnet.com/sna.html

2.1.1 Degree Centrality

Degree Centrality is measured by the number of direct connections a node has As illustrated in the kite network above, Diane has the most direct connections in the network, making her the most active node in the network For several contexts, it is better to have many connections, but not always right What really matters is where those connections lead to and how they connect the otherwise unconnected Diane has connections only to others in her clique, who are already connected to each other [26]

If the network is directed, we classify the degree centrality into two types: in-degree and out-degree In-degree of a node is the number of connections coming from other nodes to the node, whereas out-degree of a node is the count

of connections starting from the node [34]

2.1.2 Betweenness Centrality

A node is said to be in high betweenness position if it connects many pairs

of actors in the network, or stands in many shortest paths between any pairs of actors If two non adjacent actors j and k want to interact and actor i is on the path between j and k, then i may have some control over the interactions between j and k Betweenness measures this control of i over other pairs of actor Thus, if i

is on the paths of many such interactions, then i is an important actor [9]

In the network above, Heather has few direct connections but she has one of the best locations in the network, she is between the two most important clusters

As a cut-point in the shortest path connecting two other nodes, Heather could control the flow of information or exchange of resources Besides the powerful role Heather has, she is a single point of failure [26]