1. Introduction
Network Science
It is an interdisciplinary, that uses input and addresses research questions from sociology,
economics, physics, biology, psychology, computer science, etc.
● Empirical (data-driven): differs from graph theory because tools and analysis are judged
by the substantive insights they offer
● Quantitative (mathematical & statistical): measuring how strong influence is and whether
it is statistically significant instead of whether there is a connection
Graph Theory
Study of how entities (nodes) are connected through edges or links.
Social Network
Any relationship between people that is interesting to study.
Complexity Science
The study of different effects on a variable. If relations between effects and variables become
too complex to explain it is called emergent.
2. Network Measures
Walk
Moving across a network adhering to the direction of the edges.
Path
A walk that never goes through the same edge (every path is a walk → but not every walk is a
path).
Length
The number of edges a path goes through.
Geodesic
The shortest path from 𝑖 to 𝑗.
Geodesic Length (Distance)
The minimum number of edges needed to move from 𝑖 to 𝑗.
Diameter
The longest distance across all pairs of nodes.
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, Shortest Path
In a weighted graph the shortest path from 𝑖 to 𝑗 is the path that has the smallest possible sum
of weights among all possible paths from 𝑖 to 𝑗.
Cycle
A closed loop of edges with all arrows pointing the same way around the loop.
Weighted Network
A network where the edges are not binary but have a numeric value (i.e. the average number of
times two people talk to each other).
Multiplex (Multilayer) Network
A network where multiple kinds of edges are possible between nodes (i.e. two people being
connected by friendship, trust, coworkership, advice-sharing, etc.).
Bipartite Network
A network that contains two kinds of vertices and edges only go between the different types of
vertices (i.e. students and courses).
Multipartite Network
A network that can be collapsed/projected to a lower structure (i.e. co-authorship).
Small World
The concept where many people have low numbers of connections and few people have a high
number of connections (hubs). By traveling through these hubs it’s possible to jump through the
network.
Transitivity
Look at each set of 3 vertices that have a path of length 2 (open triad) and count the proportion
of them that form a full cycle (closed triad).
● 1: implies perfect transitivity
● 0: implies no closed triads
𝑛𝑜. 𝑐𝑙𝑜𝑠𝑒𝑑 𝑡𝑟𝑖𝑎𝑑𝑠
𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑛𝑜. 𝑝𝑎𝑡ℎ𝑠 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 2
Transitivity: 0.6 (3 out of 5)
● y-x-z: closed
● y-z-x: closed
● x-yz-: closed
● w-z-y: open
● w-z-x: open
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Network Science
It is an interdisciplinary, that uses input and addresses research questions from sociology,
economics, physics, biology, psychology, computer science, etc.
● Empirical (data-driven): differs from graph theory because tools and analysis are judged
by the substantive insights they offer
● Quantitative (mathematical & statistical): measuring how strong influence is and whether
it is statistically significant instead of whether there is a connection
Graph Theory
Study of how entities (nodes) are connected through edges or links.
Social Network
Any relationship between people that is interesting to study.
Complexity Science
The study of different effects on a variable. If relations between effects and variables become
too complex to explain it is called emergent.
2. Network Measures
Walk
Moving across a network adhering to the direction of the edges.
Path
A walk that never goes through the same edge (every path is a walk → but not every walk is a
path).
Length
The number of edges a path goes through.
Geodesic
The shortest path from 𝑖 to 𝑗.
Geodesic Length (Distance)
The minimum number of edges needed to move from 𝑖 to 𝑗.
Diameter
The longest distance across all pairs of nodes.
1
, Shortest Path
In a weighted graph the shortest path from 𝑖 to 𝑗 is the path that has the smallest possible sum
of weights among all possible paths from 𝑖 to 𝑗.
Cycle
A closed loop of edges with all arrows pointing the same way around the loop.
Weighted Network
A network where the edges are not binary but have a numeric value (i.e. the average number of
times two people talk to each other).
Multiplex (Multilayer) Network
A network where multiple kinds of edges are possible between nodes (i.e. two people being
connected by friendship, trust, coworkership, advice-sharing, etc.).
Bipartite Network
A network that contains two kinds of vertices and edges only go between the different types of
vertices (i.e. students and courses).
Multipartite Network
A network that can be collapsed/projected to a lower structure (i.e. co-authorship).
Small World
The concept where many people have low numbers of connections and few people have a high
number of connections (hubs). By traveling through these hubs it’s possible to jump through the
network.
Transitivity
Look at each set of 3 vertices that have a path of length 2 (open triad) and count the proportion
of them that form a full cycle (closed triad).
● 1: implies perfect transitivity
● 0: implies no closed triads
𝑛𝑜. 𝑐𝑙𝑜𝑠𝑒𝑑 𝑡𝑟𝑖𝑎𝑑𝑠
𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑛𝑜. 𝑝𝑎𝑡ℎ𝑠 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 2
Transitivity: 0.6 (3 out of 5)
● y-x-z: closed
● y-z-x: closed
● x-yz-: closed
● w-z-y: open
● w-z-x: open
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