Science: Graph theory and networks
Dr Andy Evans
Graph/Network maths
Graph theory deals with networks as mixes of nodes and
vertices (edges).
Was limited to relatively simple graphs until more data on
links and more processing power.
Now huge research and development area.
Network statistics
Distribution/average of node degree (edges connected).
Distances:
Eccentricity: distance from a node to the node furthest
from it.
Average path length: average eccentricity.
Radius: minimum eccentricity in the graph.
Diameter: maximum eccentricity in the graph.
Global clustering: how many nodes are connected in
complete connection triangles (triadic closures) as a
proportion of the connected triplets in the graph.
Other key statistics
Centrality: various measures, including degree, but two
are:
Betweenness centrality: number of shortest paths
passing through a node.
Closeness centrality: average of shortest paths to all
other nodes.
Node degree (or other) correlation: how similar are
nodes to their neighbours?
Masses of software
E.g. Inflow
Software
Network Centrality
Small-World Networks
Cluster Analysis
Network Density
Prestige / Influence
Structural Equivalence
Network Neighborhood
External / Internal Ratio
Weighted Average Path Length
Shortest Paths & Path Distribution
Pajek - for Large Network Analysis
http://pajek.imfm.si/doku.php?id=pajek
http://en.wikipedia.org/wiki/Social_network_analysis_software
Programming Graphs
GUESS (Open Source Java program)
http://graphexploration.cond.org/
Nicely uses GraphML, XML for representing graphs.
JUNG library
http://jung.sourceforge.net/
R: various packages,
including igraph.