Node / Vertice / Player

Node or player (in network
Network science will most often use the term Vertice (abbreviation: V) and computer science in Node.
In the social sciences they will most often use the term actor.

And

Edge / Connection

Arc or connection (abbreviated: E) between two nodes, to produce a network or graph.

Network
Graph
Network
graph

A network (or G: for short) is connections between nodes as the essence of each similar node (e.g. "people") and the essence of each similar arc (e.g., "encounters"). A graph is most often the visual representation of a network of connections.

Attributed Network
Attributed Graph

Tagged network

Tagged graph
A graph in which nodes / arcs have a label. Example

And

bipartite graph

A graph with 2 types of nodes, with type X nodes being related to type Y nodes, for example, a network of connections between people and workplaces.

And

Heterogeneous Network / Semantic Network
Heterogeneous Graph / Semantic Graph
Heterogeneous network / semantic network

Heterogeneous graph / Semantic graph

A network in which the nodes are fundamentally different from each other or the arcs are fundamentally different from each other (or both),

For example: a network with "people" and "places" nodes. A network with arches of the "meeting" and "family ties" type.
In computer networks, the term heterogeneous network (abbreviated: HetNet) is used for a network with different devices that use different protocols.

And

Multilayer Network
Multilayer Graph

A network consisting of several networks.

The connections between the networks can be between
Example

And

Temporal Networks, Location-aware Networks, Knowledge Networks, Probabilistic Networks

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