Schalal

Data input format

• list of dyads
• adjacency matrix
• adjacency list

  principles of network visualization

• structure
• element
• layout：optimization for speed and aesthetic，如最小化节点和边的重叠，确保所有边长度的相似性

推荐软件：Gephi

Local and global measures

local

(1) popularity, importance and power（基于节点）

1. 度中心度 度的大小，degree centrality，centrality(G, 'degree', 'Importance', G.Edges.Weight)
2. 特征向量中心度 同时顾及邻接节点的度的大小，eigenvector centrality，centrality(G, 'eigenvector', 'Importance', G.Edges.Weight)
3. 接近中心性 到其他节点的最短距离之和越短，则接近中心度越高，closeness centrality，centrality(G, 'closeness', 'Importance', G.Edges.Weight)
4. 中介中心性 所有节点间最短路径通过某节点的次数y，betweenness centrality，centrality(G, 'betweenness', 'Importance', G.Edges.Weight)

centralities will be positively correlated. When they are not, it tells you something interesting. ||high d|high e|high b|high c| |:—-:|:—-:|:—-:|:—-:|:—-:| |||||| |||||| |||||| |||||| ||||||

other measures:

random walk centrality improved centrality measures of weighted networks

(2) dyads, homophily and mutuality（基于边）

relationship/connection

social theories defining relational ties: homophily: introduced into social theory by Lazrsfeld and Merton(1978).

• status homophily
• value homophily

two causes of homophily: (1) norm attribute; (2)structural location

summary of homophily(Kadushin, 2012)：相同属性的人的聚集->相互影响，在此过程中变得相似->end up in the same social position or placd->the very place influence them to become alike once they are in the same place.

four possible dyadic relationship: (0,0),(0,1),(1,0),(1,1)

measures:

1. edge betweenness
2. bridge: a bridge is a line whose removal will increases the number of components in the network.

Girvan-Newman algorithm for community detection

global

different network structure:

• regular: all nodes have the same link
• random: random connected
• scale-free: hierarchical structure. few nodes with many connections and many nodes with few connections, e.g. air and maritime network.

• small-world: dense connections among close neighbors and few among distant neighbors, e.g. multi-city highway network

• network size，网络规模–>network density
• component
• isolate
• centralization

measures of segregation

• tradic closure
• clustering coefficient

edge embeddedness

mesoscale( or intermediate) structure

2 basic type:

• community structrure
• clusters with similar social positions

typology of mesoscale structure：可以用邻接矩阵表示社群之间的联系

• assortative：边仅在每个社群内部存在
• disassortative：边在不同的社群之间存在
• core-periphery：核心社群与边缘社群存在联系，边缘社群之间互不联系
• ordered：按照某一顺序两两社群之间存在联系
• hybrid：

based on the typology, we have different mesoscale analysis:

• cohesive subgroups
• community detection
• social positions/core-periphery/blockmodeling
• stochastic mesoscale network analysis

Cohesive Subgroups

why finding cohesive subgroups?

凝聚子群，找到最密集的组团即可，不关心其他节点，与community在概念上并不一致

properties leading to cohesive subgroups

• cliques + + +

一些衡量的指标：

• component：同一组团内的节点相互连接，不同组团内的节点不连接
• k-cores：a k-core is a maximum subnetwork in which each vertex has at least degree k within the subnetwork. 一些属性：
• k-clique：a set of vertices in which each vertex is directly connected to all other vertices. A clique is a maximal complete subnetwork containing three vertices or more. k is the size of a clique.
• m-slice: a maximal subnetwork containing the lines with a weight equal to or greater than m and the vertices incident with these lines.
• island:
• community: no comnsistent definition definition of communities!
• community detection is important
• the aim of cd is to identify …

null model

modularity，模块度

\[Q=\frac{1}{2m}\sum_{ij}{(A_{ij}-P_{ij})\delta(C_i, C_j)}\]

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