Luận văn Social network analysis - Nguyễn Hữu Bình Minh

~ 1 ~  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 ~ 2 ~  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. ~ 3 ~  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. ~ 4 ~  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 Biblography ..................................................................................................................... 41 ~ 5 ~  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 ~ 6 ~  Chapter 1 Introduction to Social Network 1. Social network Social network is a social structure made of nodes and ties, where nodes might be people, groups, organizations… and ties might be relations, flow or exchange between the nodes [33]. 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 Minh Thu likes Minh Thu ~ 7 ~  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 real- 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]. ~ 8 ~  Figure 3: Internet Alliances Source: 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. ~ 9 ~  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. ~ 10 ~  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: ~ 11 ~  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 = 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]. ~ 12 ~  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. ~ 13 ~  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 sub- graph: you could not find another node anywhere in the graph such that it could be added to the sub-graph and all the nodes in the sub-graph would still 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. ~ 14 ~  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