Social Network Analysis

The assignment content describes a social network represented by pairs of friends or a dictionary where keys are person's names and values are sets of their friends. It asks to implement several functions on this network: counting the number of people with a certain number of friends, finding suggestions for new friendships, detecting cliques, finding the most common mutual friends, identifying absolute strangers, checking if a group covers the entire network, counting triangles (triplets of people who know each other), and finding the minimal cover of the network.

pairs = {("Ana", "Berta"), ("Ana", "Greta"), ("Ana", "Helga"),
("Berta", "Cilka"), ("Berta", "Helga"),
("Cilka", "Dani"),
("Dani", "Ema"), ("Dani", "Greta"), ("Dani", "Helga"),
("Ema", "Fanči"), ("Ema", "Greta"), ("Ema", "Helga"),
("Fanči", "Iva"), ("Fanči", "Jana"), ("Fanči", "Klavdija"),
("Greta", "Helga")}
For simplicity and efficiency, every pair is listed just once, in alphabetic order (e.g. ("Ana",
"Berta") and not also ("Berta", "Ana").
The other representation is a dictionary, where keys contain names and the corresponding
values are sets of friends.
network = {"Ana": {"Berta", "Greta", "Helga"},
"Berta": {"Ana", "Helga", "Cilka"},
"Cilka": {"Berta", "Dani"},
"Dani": {"Cilka", "Ema", "Greta", "Helga"},
"Ema": {"Dani", "Fanči", "Greta", "Helga"},
"Fanči": {"Ema", "Iva", "Jana", "Klavdija"},
"Greta": {"Ana", "Dani", "Ema", "Helga"},
"Helga": {"Ana", "Berta", "Dani", "Ema", "Greta"},
"Iva": {"Fanči"},
"Jana": {"Fanči"},
"Klavdija": {"Fanči"}
}

Write following functions.
 by_n_friends(network) returns a dictionary with keys from 1 to len(mreza) - 1 and
the corresponding sets of people with that number of friends. For instance, for the
small network, the function must return {1: {"D"}, 2: {"A", "B"}, 3: {"C"}}. See the
example for the large network in the tests.
 suggestions(network) returns a list of pairs that are not friends but have at least one
common friend. The pair must be sorted alphabetically (e.g. ("Ana", "Berta") and not
("Berta", "Ana")).
 clique(network, names) returns True if all persons from the group names know each
other, and False otherwise.
 most_commons(network) returns the pair with the most mutual friends.
 strangers(network, names) returns True if the group names contains absolute
strangers - not even one pair knows each other -, and False otherwise.
 is_cover(network, names) returns True if the group "covers" the entire network in
the sense that every person in the network is either in the group or is a friend with
someone in the group.
 triangles(network) computes the number of "triangles" - triplets of people who know
each other.
 minimal_cover(mreza) returns the smallest set of names that cover the network (in
the sense described at function is_cover, above).