An unlabeled graph is a graph in which individual nodes have no distinct identifications except through their interconnectivity. Graphs in which labels (which are most commonly numbers) are assigned to nodes are called labeled graphs. Unless indicated otherwise by context, the unmodified term "graph" generally refers to an unlabeled graph.
For a nonempty finite simple graph 
, its sibling number 
is the largest number of vertices
sharing a closed neighborhood, minus one.
Its tuft number 
is the largest number of pendant vertices adjacent
to any one graph vertex. Among the unlabeled connected
graphs of a fixed positive order 
, these statistics have a symmetric
joint distribution (Fürnsinn et al. 2026). In particular,
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where each sum includes one representative of each graph isomorphism class.
