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# Social network analysis study ch3 4.2-120108

## on Jan 08, 2013

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## Social network analysis study ch3 4.2-120108Presentation Transcript

• Social Network Analysis Study Chapter 3 - 4.2 Jan 8 2013, 박성규
• (1) Chapter 3: Notation for social Network Data 3가지 Notations  Graph theoretic: centrality and prestige methods, cohesive subgroup ideas, dyadic and triadic methods  Actor 와 Relation 으로 표현되는 scheme  Sociometric: study of structural equivalence and blockmodels  Social network 분야에서 가장 일반적인 notation  Algebraic: role and positional analyses and relational algebras  Multiple relation 에서 많이 사용됨
• (1) Chapter 3: Notation for social Network Data  Graph theoretic notation Set of actors: N={n1, n2, ng} Set of relations (lines, ordered pairs of actors, arcs, ties): L={l1,l2,lL} Graph는 수학적으로 두 개의 Set 으로 정리 가능: G={N, L} Self choices 는 일반적으로 고려하지 않음 Directional<·,·>: L=g(g-1) pairs Nondirectional(·,·): L=g(g-1)/2 pairs Strength or frequency of the interaction for a pair of actors (valued relation) 기록에는 적절치 않음  Single relation: 그래프 안에 단일 relation  Multiple relation: 그래프 안에 relation 여러 개, e.g. Friendship at Beginning<·,·>, Friendship and End<·,·>, Lives near(·,·)
• (1) Chapter 3: Notation for social Network Data  Sociometric notation The study of positive and negative affective(정서적인) relations. To measure affective relations, two-way matrices → 결국 sociomatrix 로 표현됨 (page 82 표 참조, relation 당 matrix 한 개) Dichotomous: 2분법으로 표현 → relation set {0, 1} for C=2 좋은 특징: valued relation 처리 가능, directional, nondirectional 관계 모두 표현 가능 단점: can not easily quantify or denote actor attributes(속성) e.g. ethnicity of the actors  Single relation: xij = the value of the tie from ni to nj  Multiple relation: xijr = the value of the tie from ni to nj on relation Xr e.g. x121 = the value of the tie from n1 to n2 on relation X121=the value of the tie from n1 to n2 on relation X1 = 1
• (1) Chapter 3: Notation for social Network Data  Algebraic notation e.g. iFj 로 표현됨 (c.f. Sociometric: xijF=1) 장점: multi-relational 관계 다루는 데에 가장 적합 -> 관계들 간의 combinations 을 다루기 때문 단점: 값이 항상 0 아니면 1이기 때문에(dichotomous) 감정이나 가 치를 측정하지는 못함
• (2) Chapter 4: Graphs and Matrices
• (2) Chapter 4: Graphs and Matrices  Density Δ = 2L / g(g-1) → no lines: Δ=0, all possible lines: Δ=1  Walks, Trails, Paths Walks > Trails > Paths (page 106 참조) Walks: a sequence of nodes and lines, starting and ending with nodes, in which each node is incident with the lines following and preceding it in the sequence. Trails: walks with lines are distinct, though some nodes included more than once. Paths: walks with all nodes, all lines distinct
• (2) Chapter 4: Graphs and Matrices  Closed walks, Tours, Cycles Closed walks: A walk that begins and ends ant the same node. Tours: A closed walk, 라인이 적어도 한 번 이상은 쓰여야 함 Cycles: 적어도 3개 이상 노드로 이루어진 closed walks, all lines and nodes(except the beginning and ending node) are distinct. → 중요: balance and clusterability in signed graphs 에 쓰임  Connected Graphs and Components Components: The connected Subgraphs in a graph, maximal connected subgraph
• (2) Chapter 4: Graphs and Matrices  Geodesics, Distance, Diameter Geodesics: A shortest path between two nodes (Geodesic) Distance: length of a geodesic between two nodes Diameter: diameter of a connected graph is the length of the largest geodesic between any pair of nodes. Important since it quantifies how far apart the farthest two nodes in the graph are.  Cutpoints and Bridges Cutpoints: A node ni is a cutpoint if the number of components in the graphs that contains ni is fewer than the number of components in the subgraph that results from deleting ni from the graph. Bridges: The same to cutpoint in terms of a line
• (2) Chapter 4: Graphs and Matrices  Node- and Line- connectivity Cohesive graphs have many short geodesic, and small diameters relative their sizes. point-connectivity or node-connectivity of a graph, k(g) is the minimum number of k for which the graph has a k-node cut. Page 116, in Figure 4.12, k(g)=2 line-connectivity or edge-connectivy, λ(g) is the minimum number λ fir which the grapg has a λ-line cut. Page 116, Figure 4.10 예제 관련 설명 이상함?  Isomorphic(동형의) Graphs Isomorphism between graphs are important because if two graphs are isomorphic, then they are identical on all graph theoretic properties. Page 118 Figure 4.13 그래프 참조
• (2) Chapter 4: Graphs and Matrices  Special Graphs Trees: A graph that is connected and is acyclic. Trees are minimally connected graphs since every line in the graph is a bridge. The number of lines in a tree equals the number of nodes minus one, L=g- 1. There is only one path between any two nodes. Forest: A graph is connected and contains no cycles, the number of lines = nodes – the number of components  Bipartite Graphs and s-partite Graphs Bipartite Graphs: All lines are between nodes in different 2 subsets and no nodes in the same subset are adjacent. (Page 120 Figure 4.15 및 Page 121 예제 참조), Complete bipartite: Bipartite with every nodes in one subsets is adjacent to every node in another subsets S-partite graphs: All lines are between nodes in different subsets and no nodes in the same subset are adjacent.
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