Statistical Analysis of Networks

Statistics and Analysis of Networks

Descriptive statistics for networks: 2/3 of all work done in this area

Different from standard statistical descriptions

Network Characterization

Social dynamics: patterns of edges among vertex triples

Routes of movement of information: shortest path between vertices

Importance of vertices: centrality

Groups/communities via graph partitioning

Structural Analysis

Social network analysis

Math and computer science

Statistical physics

Many tools:

• characterize vertices and edges
• characterhize network cohesion

Examples:

• degree distribution
• vertex/edge centrality
• role/positional analysis

Vertex Centrality

centrality measures can capture vertex importance

Coarser Scales

Beyond the individual vertices and edges, increasing scales can tell you abou tcohesion of a network

Cohesion notions:

• clustering
• density
• connectivity
• flow
• partitioning

Network sampling

List of examples characteristics:

• degree exponent
• average path length
• betweenness
• assortativity
• clustering coefficient

sampling designs and biases

Network inference

predict edge wstatus for all potential edges with missing information

Further topics

Uncertainty in graphs, summary statistics, under noisy conditions

asymptotics for paramter estimation in network models

Estimation of degree distribution from sampled data

bayesian latent factor network perturbation

multi-attribute networks