Nomenclature¶

Standard terminology used throughout the craeft codebase and documentation.

Guiding principles¶

Consistency over legacy — use one term throughout, even if papers used another
Accessibility over jargon — prefer terms that newcomers can understand
Precision where it matters — mathematical concepts get precise names

Primary terms¶

Network structure¶

Standard term	Definition	Avoid
network	A collection of nodes connected by edges	graph (except in mathematical definitions)
node	A vertex in the network	vertex (except in mathematical contexts)
edge	A connection between two nodes	link, connection, arc
adjacency matrix	Square matrix where entry (i,j) = 1 if nodes i and j are connected
degree	Number of edges incident to a node	connectivity
degree sequence	Ordered list of all node degrees in the network

Motifs¶

Standard term	Definition	Avoid
motif	A small, recurring substructure pattern in a network	subgraph (except for the mathematical concept)
motif instance	A specific occurrence of a motif pattern using particular nodes	subgraph instance
corner	A node's participation slot in a motif instance	position, vertex
corner type	Classification of corners by their degree within the motif
cardinality	The degree of a corner within its motif (edges contributed)

Algorithm components¶

Standard term	Definition	Context
stub	A "half-edge" representing one unit of degree capacity	Configuration model
hyperstub	A stub allocated to participate in motif formation	CCM algorithm
single	A remaining stub after motif allocation	CCM algorithm
connector	Strategy for forming motif instances from hyperstubs	CCM Step 3
pairer	Strategy for pairing single stubs into edges	CCM Step 4

Parameter naming¶

Network generation¶

Parameter	Symbol	Description	Range
`n`	n	Number of nodes	positive integer
`phi`	\(\phi\)	Target clustering coefficient	[0, 1]
`p`	p	Edge probability (Erdos-Renyi)	[0, 1]

Epidemic simulation (SIR)¶

Parameter	Symbol	Description	Range
`tau`	\(\tau\)	Transmission rate	\([0, \infty)\)
`gamma`	\(\gamma\)	Recovery rate	\([0, \infty)\)
`initial_infected`	—	Number of initially infected nodes	positive integer

Motif naming¶

Motifs use Pržulj graphlet notation (G0-G29). For motifs beyond 5 nodes, standard graph-theoretic notation is used (C_n for cycles, K_n for complete graphs).

Legacy terminology¶

Legacy term	Standard term	Notes
network-simulation	craeft	Original repository name
netsubgraph	craeft	First package name
motifnet	craeft	Second package name
graph	network	Use "network" in code
subgraph	motif	Use "motif" for the recurring pattern concept
TRIANGLE	G2	Use Pržulj notation
TOAST / BOWTIE	G14	Use Pržulj notation
K3	G2	Use Pržulj notation
K4	G8	Use Pržulj notation
SQUARE	G5	Use Pržulj notation
PENTAGON	G12	Use Pržulj notation
DIAMOND	G7	Use Pržulj notation
HEXAGON	C6	Extended motif (6 nodes)