questions and correct answers| 2025-
2026
Allow us to test hypothesis. How it is special? or are they just random?
Digital footprint-- Collect Data-- analyze-- Hypothesis= check on this network
or
To deduce our hypothesis. - correct answers Random Networks
Random Graph - correct answers Erdos-Renyi Graph
Erdos-Renyi Graph/Random Graph - correct answers -Start with n nodes
-Form independent links (with a certain p (probability) OR from M(number) of links
-Properties of the graph
(what is the average degree of the network [ numerical solution]
or
analytical solution))
-We get 'almost sure' properties with specific G(n,...) setups
( 1)what is the degree distribution of the network?
2)What is the likelihood of getting a hub with almost all links concentrated on it alone?
3) What are most nodes connected in one giant component?)
, Likelihood of getting a property depends on P (probability), but !Non-linear phase transitions emerges!
at... - correct answers Tipping points
is a connected component of a given random graph that contains a finite fraction of the entire graph's.
Groups can merge and create this component.
Tipping point= Threshold Function
1 connection p/node = we can all be connected= emergence of groups - correct answers Giant
Component
Scale-free networks - correct answers -Add nodes with uniform likelihood
Start with # nods fully connected
Add new nodes with # links to existing nodes with equal likelihood
-Add nodes with non-uniform likelihood
Some nodes have many more links than others
Preferential attachment
growing through preferential attachment= add nodes - correct answers How Scale-free networks
evolve?
likelihood is proportional to number of existing degrees ( if you are more popular you are more likely to
get more connections)
(hub) exponentially Few have a lot of connections/ and a lot nodes who have 1 degree) - correct
answers Preferential attachment
random+ preferential attachment