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For example, for the above mentioned world map the ids are ISO country codes. The values can be either colors or numbers in case the geographic entities should be associated with numeric data: DE=lightblue marks Germany in light blue color, and DE=80.6 assigns Germany the value 80.6 (population in millions).
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The clique problem arises in the following real-world setting. Consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance. Then a clique represents a subset of people who all know each other, and algorithms for finding cliques can be used to discover these groups of mutual friends.
For example, for the above mentioned world map the ids are ISO country codes. The values can be either colors or numbers in case the geographic entities should be associated with numeric data: DE=lightblue marks Germany in light blue color, and DE=80.6 assigns Germany the value 80.6 (population in millions).
Image:BlankMap-World-v6-Borders.png – Version of v6 with borders around each country. Image:BlankMap-World-v7.png – Version of v4 with thin lines to join areas owned by the same country for one-click colouring and with dots for dependencies as well as sovereign territories (merged content from v5 and v6).
Though 50% is a tight bound, in practice, this greedy peeling procedure yields about 80% of the optimal density on real-world graphs. [3] In 2020, Boob et al. gave an iterative peeling algorithm that aims to get closer to the optimal subgraph by repeated the peeling procedure multiple times. [3]
It is known that a wide variety of abstract graphs exhibit the small-world property, e.g., random graphs and scale-free networks. Further, real world networks such as the World Wide Web and the metabolic network also exhibit this property. In the scientific literature on networks, there is some ambiguity associated with the term "small world".
Watts–Strogatz small-world model generated by igraph and visualized by Cytoscape 2.5. 100 nodes. The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering.