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huiyuxie committed Nov 15, 2023
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14 changes: 12 additions & 2 deletions notebooks/algorithms/centrality/Centrality.ipynb
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"__Degree Centrality__ <br>\n",
"Degree centrality is based on the notion that whoever has the most connections must be important. \n",
"\n",
"$C_{degree}(v) = \\frac{{\\text{degree of vertex} v}}{{\\text{total number of vertices} - 1}}$\n",
"$C_{degree}(v) = \\frac{{\\text{degree of vertex} \\ v}}{{\\text{total number of vertices} - 1}}$\n",
"\n",
"See:\n",
"* [Degree (graph theory) on Wikipedia](https://en.wikipedia.org/wiki/Degree_(graph_theory)) for more details on the algorithm.\n",
"* [Learn more about Degree Centrality](https://www.sci.unich.it/~francesc/teaching/network/degree.html)\n",
"\n",
"__Closeness Centrality__ <br>\n",
"Closeness is a measure of the shortest path to every other node in the graph. A node that is close to every other node, can reach over other node in the fewest number of hops, means that it has greater influence on the network versus a node that is not close.\n",
"\n",
"$C_{closeness}(v)=\\frac{n-1}{\\sum_{t} d(v,t)}$\n",
"\n",
"See:\n",
"* [Closeness Centrality on Wikipedia](https://en.wikipedia.org/wiki/Closeness_centrality) for more details on the algorithm.\n",
"* [Learn more about Closeness Centrality](https://www.sci.unich.it/~francesc/teaching/network/closeness.html)\n",
"\n",
"__Betweenness Centrality__ <br>\n",
"Betweenness is a measure of the number of shortest paths that cross through a node, or over an edge. A node with high betweenness means that it had a greater influence on the flow of information. \n",
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"\n",
"To speedup runtime of betweenness centrailty, the metric can be computed on a limited number of nodes (randomly selected) and then used to estimate the other scores. For this example, the graphs are relatively small (under 5,000 nodes) so betweenness on every node will be computed.\n",
"\n",
"See:\n",
"* [Betweenness Centrality on Wikipedia](https://en.wikipedia.org/wiki/Betweenness_centrality) for more details on the algorithm.\n",
"* [Learn more about Betweenness Centrality](https://www.sci.unich.it/~francesc/teaching/network/betweeness.html)\n",
"\n",
"__Katz Centrality__ <br>\n",
"Katz is a variant of degree centrality and of eigenvector centrality. \n",
"Katz centrality is a measure of the relative importance of a node within the graph based on measuring the influence across the total number of walks between vertex pairs.\n",
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"\n",
"\n",
"See:\n",
"* [Katz on Wikipedia](https://en.wikipedia.org/wiki/Katz_centrality) for more details on the algorithm.\n",
"* [Katz Centrality on Wikipedia](https://en.wikipedia.org/wiki/Katz_centrality) for more details on the algorithm.\n",
"* [Learn more about Katz Centrality](https://www.sci.unich.it/~francesc/teaching/network/katz.html)\n",
"\n",
"__Eigenvector Centrality__ <br>\n",
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