6.12. Matching

Q-1:
• Barabási-Albert Model
• Algorithm for generating random scale-free networks using a preferential attachment mechanism.
• WS Model
• Has characteristics of a small world network, like the data, but it has low variability in the number of neighbors from node to node, unlike the data.
• Probability Mass Function (PmF)
• A function that maps from each value to it's probabilities.
• Growth
• Instead of starting with a fixed number of vertices, the BA model starts with a small graph and adds vertices one at a time.
• Heavy-tailed Distributions
• A probability theory with probability distributions whose tails are not exponentially bounded.
• Standard Deviation
• Used to indicate the extent of deviation for a group as a whole.
• Power Law
• A distribution follows this law if :math:${\displaystyle PMF\left(k\right)\sim k-\alpha }$ where ${\displaystyle }$PMF(k)${\displaystyle }$ is the fraction of nodes with degree ${\displaystyle }$k${\displaystyle }$, ${\displaystyle }$α${\displaystyle }$ is a parameter, and the symbol ∼ indicates that the ${\displaystyle }$PMF${\displaystyle }$ is asymptotic to ${\displaystyle }$k−α${\displaystyle }$ as ${\displaystyle }$k${\displaystyle }$ increases.
• Preferential Attachment
• A quantity of something is distributed according to how much already exsisting recipients have.
• Scale-Free Network
• A network whose degree distribution follows a power law, at least asymptotically.
• Cumulative Distribution Function
• Maps a value to the fraction of values less thank or equal to x.
• Complementary CDF
• :math:${\displaystyle ℂDF\left(x\right)\equiv 1-CDF\left(x\right)}$
• Explanatory Models
• A model that gives a useful description of why and how a phenomenon is the way it is.

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