Network theory is the study of graphs as representations of either symmetric or asymmetric relations between discrete objects. In computer science, a network is a graph in which nodes and/or edges carry attributes — weights, labels, directions.
Network theory has played an important role across many disciplines, and it comes with a rich set of interesting problems: graph coloring, minimum spanning tree, min/max flow, shortest path, and more.
Applications
- Social networks
- Network optimization
- Link analysis
- Centrality measure
Social Networks
A social network is a network of actors, dyadic ties, and social interactions. Analysis typically operates at three levels:
- Micro level — begins with an individual or small group and traces outward through connections.
- Meso level — analyses the bridge between micro and macro groups.
- Macro level — reveals abstract, structural information about the entire network rather than tracing individual paths.
Network Optimization
Network optimization involves problems such as: finding the shortest path between two nodes, maximizing network flow, solving transport and routing problems. The common thread is optimizing some objective over the structure of the network.
Link Analysis
Link analysis focuses on relationships between nodes rather than on the nodes themselves. How strongly or weakly connected are two nodes? How does the value of a link change over time? One important application is finding suspects in criminal networks by analyzing connection strength.
Centrality Measure
Unlike link analysis, centrality focuses on the actors. It determines the relative importance of each node in the network. Centrality is widely used in sociology, epidemiology, and any field where identifying influential nodes matters.
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