Science: Graph theory and networks Dr Andy Evans.

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Presentation transcript:

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?

Software Masses of software E.g. Inflow 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

Programming Graphs GUESS (Open Source Java program) Nicely uses GraphML, XML for representing graphs. JUNG library R: various packages, including igraph.