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Author: Admin | 2025-04-28
Edges that start at 𝑣𝑖 the following equationholds 43. 43Social Media Mining Measures and Metrics 43Social Media Mining Graph Essentialshttp://socialmediamining.info/Random Walk: ExampleMark a spot on the ground– Stand on the spot and flip the coin (or more than onecoin depending on the number of choices such as left,right, forward, and backward)– If the coin comes up heads, turn to the right and take astep– If the coin comes up tails, turn to the left and take a step– Keep doing this many times and see where you end up 44. 44Social Media Mining Measures and Metrics 44Social Media Mining Graph Essentialshttp://socialmediamining.info/Connectivity• A node 𝒗𝒊 is connected to node 𝒗𝒋 (or reachablefrom 𝑣𝑗) if it is adjacent to it or there exists a pathfrom 𝑣𝑖 to 𝑣𝑗.• A graph is connected, if there exists a pathbetween any pair of nodes in it– In a directed graph, a graph is strongly connected ifthere exists a directed path between any pair of nodes– In a directed graph, a graph is weakly connected ifthere exists a path between any pair of nodes, withoutfollowing the edge directions• A graph is disconnected, if it not connected. 45. 45Social Media Mining Measures and Metrics 45Social Media Mining Graph Essentialshttp://socialmediamining.info/Connectivity: Example 46. 46Social Media Mining Measures and Metrics 46Social Media Mining Graph Essentialshttp://socialmediamining.info/Component• A component in an undirected graph is aconnected subgraph, i.e., there is a path betweenevery pair of nodes inside the component• In directed graphs, we have a stronglyconnected components when there is a pathfrom 𝑢 to 𝑣 and one from 𝑣 to 𝑢 for every pair ofnodes 𝑢 and 𝑣.• The component is weakly connected if replacingdirected edges with undirected edges results in aconnected component 47. 47Social Media Mining Measures and Metrics 47Social Media Mining Graph Essentialshttp://socialmediamining.info/Component Examples:3 components 3 Strongly-connectedcomponents 48. 48Social Media Mining
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