What are the entities?
Person, firm, neuron, router, city?
Node definition establishes the unit of analysis.
Side 34
Network
Science
A study of systems defined by relationships. Network science asks how connection patterns create reach, bottlenecks, influence, diffusion, resilience and cascades.
nodes→edges→structure→flow→cascade
06network lenses
05centrality ideas
05dynamic processes
34Side
Change the relation and you change the network.
The same set of entities can form radically different systems depending on which connections exist and what those connections mean.
What counts as a connection?
Trade, friendship, citation, road?
Edges encode a specific relation and should not be treated as generic connection.
Does the relation flow one way?
Directed or undirected?
Following, lending and citation differ from mutual friendship or physical adjacency.
Are all edges equal?
Frequency, capacity, strength?
Weighted networks preserve intensity that binary edges discard.
Is the network changing?
Static snapshot or dynamic graph?
Formation and dissolution of edges can matter as much as the observed structure.
Local connections create global topology.
Network structure can produce short paths, dense communities, hubs and bottlenecks even without central design.
Number of direct connections.
Degree distributions reveal whether connectivity is evenly spread or concentrated in hubs.
How many steps connect nodes?
Short average paths enable rapid reach across large networks.
Do neighbors connect to each other?
High clustering creates locally dense groups.
Are there dense subgroups?
Community detection searches for regions with more internal than external connection.
Connectivity is highly concentrated.
Hubs can increase efficiency while creating vulnerability to targeted failure.
One connection links clusters.
Bridges can carry novel information and become critical points of failure.
“Important” depends on what kind of importance matters.
Different centrality measures answer different structural questions.
| Measure | Idea | Useful question | Caution |
|---|---|---|---|
| Degree | Many direct ties | Who is locally connected? | Ignores wider topology |
| Betweenness | Falls on many shortest paths | Who brokers or bottlenecks flow? | Assumes shortest-path-like movement |
| Closeness | Short distance to others | Who can reach the network quickly? | Depends on connectivity and distance definition |
| Eigenvector | Connected to important nodes | Who sits near influential structure? | Can concentrate on dense cores |
| PageRank | Importance transmitted through directed links | Which nodes receive valuable incoming connection? | Depends on link interpretation and damping |
Networks shape how things spread.
Information, disease, behaviors, failures and innovations propagate differently depending on topology and transmission rules.
One exposure can transmit.
Many infectious processes and information exposures can spread through individual contacts.
Multiple exposures may be required.
Behavior adoption can depend on reinforcement from several neighbors.
Adopt after enough neighbors do.
Local thresholds can produce sudden global cascades.
Starting location matters.
Well-placed initial adopters can outperform larger but poorly located seed sets.
Similar nodes connect.
Observed diffusion can be confused with preexisting similarity among connected actors.
Spread changes the network.
Adoption or infection can create, destroy or reweight connections.
Connectivity creates both resilience and fragility.
Networks can route around random losses while remaining highly vulnerable to targeted attacks or cascading overload.
Random failure
Remove nodes indiscriminately.
Distributed networks can remain connected despite many random losses.
Targeted attack
Remove structurally critical nodes.
Hub-heavy networks may fragment quickly when high-degree nodes fail.
Cascade
Failure redistributes load.
Surviving nodes may overload, causing secondary failures.
Redundancy
Alternative paths preserve flow.
Path diversity limits dependence on one route or intermediary.
Modularity
Compartments contain damage.
Strong community boundaries can slow propagation while also reducing cross-network reach.
Network structure is produced by rules of attachment.
Understanding how edges form can explain why certain topologies recur.
Random attachment
Edges form with roughly equal probability, producing relatively homogeneous degree distributions.
Preferential attachment
Already well-connected nodes attract new links more readily, generating heavy-tailed degree patterns.
Homophily
Similarity increases connection probability, producing clustered social structure.
Triadic closure
Two nodes sharing a neighbor become more likely to connect.
Spatial cost
Physical distance constrains many transportation, infrastructure and biological networks.
Network ScienceAlbert-László Barabási · broad foundation
NetworksMark Newman · mathematical treatment
ConnectedChristakis & Fowler · social networks
LinkedBarabási · network intuition