Multilayer Networks 101

This chapter explains what multilayer networks are, when to use them, and how to choose the right type for your data.

You will learn:

What distinguishes multilayer from single-layer networks
Types: multiplex, heterogeneous, temporal, interdependent
When to use multilayer modeling
Common pitfalls to avoid

What are Multilayer Networks?

A multilayer network models systems with multiple types of relationships, node types, or interaction contexts.

Example: A researcher’s social world includes coauthors, colleagues, students, and Twitter followers. These are different relationship types with different meanings. A multilayer network keeps them as separate layers rather than flattening into one graph.

Traditional vs. Multilayer:

Aspect	Single-Layer	Multilayer
Node types	One (e.g., only people)	Multiple (people, orgs, docs)
Edge types	One (e.g., only friendship)	Multiple per layer
Structure	Homogeneous	Heterogeneous
Analysis	Standard graph algorithms	Layer-aware algorithms

Types of Multilayer Networks

Multiplex Networks

Same nodes, different relationship types.

from py3plex.core import multinet

network = multinet.multi_layer_network(network_type="multiplex")
network.add_edges([
    ['Alice', 'friends', 'Bob', 'friends', 1],
    ['Bob', 'friends', 'Carol', 'friends', 1],
    ['Alice', 'colleagues', 'Bob', 'colleagues', 1],
    ['Bob', 'colleagues', 'Dave', 'colleagues', 1],
], input_type="list")

Examples: Social networks across platforms, transportation via air/rail/road, communication via email/phone/chat.

Heterogeneous Information Networks

Different node types with type-specific relationships.

network = multinet.multi_layer_network()
network.add_edges([
    ['Alice', 'authors', 'P1', 'papers', 1],
    ['P1', 'papers', 'ICML', 'venues', 1],
], input_type="list")

Examples: Academic networks (authors, papers, venues), e-commerce (users, products, sellers), biomedical (drugs, diseases, targets).

Temporal Networks

Networks that evolve over time, with time-sliced layers.

network = multinet.multi_layer_network()
network.add_edges([
    ['A', '2020', 'B', '2020', 1],
    ['A', '2021', 'B', '2021', 1],
    ['B', '2021', 'C', '2021', 1],
], input_type="list")

Examples: Communication over time, social dynamics, disease spread.

Interdependent Networks

Multiple networks where nodes depend on each other.

Examples: Power grid depends on communication network, supply chains, cyber-physical systems.

When to Use Multilayer Networks

Use multilayer modeling when:

Multiple relationship types matter — Friendship and professional connections behave differently
Node roles vary by context — A hub in work network may be peripheral in hobby network
Layer interactions are important — Transportation failures in one mode affect others
Temporal evolution matters — Relationships change over time
System-level properties emerge — Cross-layer dependencies affect resilience

Choosing a Modeling Approach

Ask these questions:

Layers vs. attributes? If relationships have different types → use layers. If they vary only in weight → use edge attributes.
Same or different nodes? Same entities in all layers → multiplex. Different entity types → heterogeneous.
Coupling strength? Identity coupling only → omega=1.0. Nodes can differ → lower omega.
Temporal structure? Yes → time-sliced layers. No → aggregate into static network.

What Goes Wrong When You Flatten

Community structure destroyed: Flattening can create spurious bridges between groups that are distinct in the layer structure.

Centrality becomes misleading: A researcher with 2 coauthors and 500 Twitter followers has degree 502 when flattened, but academic influence is only 2.

Path analysis fails: Email → meeting transitions matter for information flow but are invisible in a flattened network.

Common Pitfalls

Over-aggregating — Combining layers that should stay separate
Under-aggregating — Too many sparse layers (use edge weights instead)
Ignoring coupling — Treating layers as independent when nodes correspond
Wrong coupling strength — Too high forces artificial consistency; too low loses information
Mismatched identifiers — Same entity must have same ID across layers

Key Terminology

Intra-layer edges — Within a single layer
Inter-layer edges — Between layers (often identity edges connecting same node)
Node-layer pairs — (node_id, layer_id) tuples, the fundamental unit
Supra-adjacency matrix — Block matrix encoding both intra- and inter-layer connections

Next Steps

The py3plex Core Model — Internal data structures
Design Principles — Why py3plex works this way
Algorithm Landscape — Available algorithms

References:

Kivelä et al. (2014). “Multilayer networks.” J. Complex Networks 2(3): 203-271.
Boccaletti et al. (2014). “The structure and dynamics of multilayer networks.” Physics Reports 544(1): 1-122.