Network Analytics – Study Notes &
Extended Summary (GL1)
1. What is Network Analytics?
Network analytics studies data that can be represented as a network (graph):
- Nodes (vertices) represent entities (people, cities, web pages, products)
- Edges (links) represent relationships (friendship, roads, hyperlinks, similarity)
Many complex systems are naturally networks:
● Social networks (people ↔ people)
● Transportation networks (cities ↔ routes)
● Information networks (web pages ↔ links)
● Biological networks (proteins ↔ interactions)
The key question is often:
Who or what is important, central, influential, or structurally critical in the
network?
2. Birth of Graph Theory: Königsberg Bridges
The classical example is the Königsberg bridge problem:
● Can you walk through the city and cross each bridge exactly once?
Leonhard Euler (1736):
● Represented the city as a graph
● Proved mathematically that it was impossible
● This marked the birth of graph theory
Key insight: Real‑world problems can be abstracted into nodes and edges, revealing hidden
structure.
,3. Types of Networks
Networks differ depending on constraints and information stored.
3.1 Directed vs. Undirected
● Undirected: relationship is mutual
○ Example: friendship
● Directed: relationship has direction
○ Example: web link A → B
If you have ONE directed edge, you have a DIRECTED network
3.2 Weighted vs. Unweighted
● Unweighted: edge exists or not: binary indication (0/1)
→ all connections are treated as equally important
● Weighted: edge has a value
thick stripe: more weight
○ Distance
○ Strength
○ Similarity
Examples:
● Road network: travel time as weight
● Social network: frequency of contact
3.3 Homogeneous vs. Heterogeneous
● Homogeneous network: all nodes/edges are of the same type
● Heterogeneous network: different types of nodes and/or edges
Example: heterogenous network
one node type and multiple edge types ⇔ one edge type and multiple node type
,3.4 Bipartite Networks (Special Case)
A bipartite network has:
● Two distinct node sets
● Edges only between the sets, not within (= inter-type edges)
All edges connect blue → purple, and never blue → blue or purple → purple.
There is only one kind of relation (edge-homogeneous)
but different kinds of entities (node-heterogeneous)
Examples:
● Students ↔ courses
● Authors ↔ papers
Often projected into a one‑mode network:
● Students linked if they take the same course
⚠️ Projection increases density and can cause visual clutter.
3.5 Node and Edge Features
Extra attributes can be attached onto the netwerk:
Node features:
● Age, role, capacity, facilities
Edge features:
● Distance, travel time, cost, electrification
➡ This moves from pure topology to rich network data.
, 4. Why Network Representation Matters
The way we represent a network affects:
● Representation determines how the data is actually implemented (memory usage)
● The chosen representation determines whether this complexity is preserved,
simplified, or lost
→ edge weight vs no weight, one edge type vs multiple edge types
● Different representations make different operations fast or slow
Two main categories:
1. Visual representations
2. Mathematical representations
5. Visualising Networks
5.1 Purpose of Visualisation
Visualisation is the graphical drawing of nodes and edges
● Storytelling
● Exploratory insight for small networks
● Communication tool, not an analytical method by itself.
1) Force‑Directed / Spring‑Based Layouts
● Nodes repel each other
● Edges act like springs pulling nodes together (connected nodes want to stay close)
● System evolves to a minimum‑energy state
PROS
Very intuitive (due to physics)
Reveals clusters and symmetries
CONS
Computationally expensive
Suffers from hairball effect for large networks
Extended Summary (GL1)
1. What is Network Analytics?
Network analytics studies data that can be represented as a network (graph):
- Nodes (vertices) represent entities (people, cities, web pages, products)
- Edges (links) represent relationships (friendship, roads, hyperlinks, similarity)
Many complex systems are naturally networks:
● Social networks (people ↔ people)
● Transportation networks (cities ↔ routes)
● Information networks (web pages ↔ links)
● Biological networks (proteins ↔ interactions)
The key question is often:
Who or what is important, central, influential, or structurally critical in the
network?
2. Birth of Graph Theory: Königsberg Bridges
The classical example is the Königsberg bridge problem:
● Can you walk through the city and cross each bridge exactly once?
Leonhard Euler (1736):
● Represented the city as a graph
● Proved mathematically that it was impossible
● This marked the birth of graph theory
Key insight: Real‑world problems can be abstracted into nodes and edges, revealing hidden
structure.
,3. Types of Networks
Networks differ depending on constraints and information stored.
3.1 Directed vs. Undirected
● Undirected: relationship is mutual
○ Example: friendship
● Directed: relationship has direction
○ Example: web link A → B
If you have ONE directed edge, you have a DIRECTED network
3.2 Weighted vs. Unweighted
● Unweighted: edge exists or not: binary indication (0/1)
→ all connections are treated as equally important
● Weighted: edge has a value
thick stripe: more weight
○ Distance
○ Strength
○ Similarity
Examples:
● Road network: travel time as weight
● Social network: frequency of contact
3.3 Homogeneous vs. Heterogeneous
● Homogeneous network: all nodes/edges are of the same type
● Heterogeneous network: different types of nodes and/or edges
Example: heterogenous network
one node type and multiple edge types ⇔ one edge type and multiple node type
,3.4 Bipartite Networks (Special Case)
A bipartite network has:
● Two distinct node sets
● Edges only between the sets, not within (= inter-type edges)
All edges connect blue → purple, and never blue → blue or purple → purple.
There is only one kind of relation (edge-homogeneous)
but different kinds of entities (node-heterogeneous)
Examples:
● Students ↔ courses
● Authors ↔ papers
Often projected into a one‑mode network:
● Students linked if they take the same course
⚠️ Projection increases density and can cause visual clutter.
3.5 Node and Edge Features
Extra attributes can be attached onto the netwerk:
Node features:
● Age, role, capacity, facilities
Edge features:
● Distance, travel time, cost, electrification
➡ This moves from pure topology to rich network data.
, 4. Why Network Representation Matters
The way we represent a network affects:
● Representation determines how the data is actually implemented (memory usage)
● The chosen representation determines whether this complexity is preserved,
simplified, or lost
→ edge weight vs no weight, one edge type vs multiple edge types
● Different representations make different operations fast or slow
Two main categories:
1. Visual representations
2. Mathematical representations
5. Visualising Networks
5.1 Purpose of Visualisation
Visualisation is the graphical drawing of nodes and edges
● Storytelling
● Exploratory insight for small networks
● Communication tool, not an analytical method by itself.
1) Force‑Directed / Spring‑Based Layouts
● Nodes repel each other
● Edges act like springs pulling nodes together (connected nodes want to stay close)
● System evolves to a minimum‑energy state
PROS
Very intuitive (due to physics)
Reveals clusters and symmetries
CONS
Computationally expensive
Suffers from hairball effect for large networks
