Table 1 Summary of the main notation

\(\mathscr {P}(\alpha , \mu , f)\)

Model class \(\mathscr {P}\) (non-linear preferential attachment model with homophily)

\({\mathcal {A}}\)

Attribute space

\(\mu\)

Attribute distribution of an arriving node

\(\alpha\)

Preferential attachment parameter

\(f(a,a')\)

Propensity of a pair of nodes with attributes a and \(a'\) to interact

m

Number of edges a new node entering the system connects to pre-existing nodes

\(\deg _i(v,{n})\)

Degree of v at time n when i of the edges of \(v_{{n}+1}\) have connected to the network

\(\mathscr {U}(\alpha , \nu , f)\)

Model class \(\mathscr {U}\)

\(\nu\)

Resolvable measure

\({\mathcal {E}}\)

Set of edges of the network

N

Number of nodes in the network

\({\mathcal {V}}_a\)

Set of nodes of type a

\({\mathcal {E}}_{aa'}\)

Set of edges between nodes of attributes a and \(a'\)

\(D_{a}\)

Dyadicity of nodes with attribute a

\(H_{aa'}\)

Heterophilicity between nodes with attributes a and \(a'\)

p(a)

Proportion of nodes with attribute a

|.|

Number of elements of a set

p(k|a)

proportion of nodes of degree k having attribute a

\(\widehat{.}\)

Estimator of a quantity

\(d_i\)

Degree of node i

\(\pi _i\)

Probability of sampling node i

\(\pi _{(i,j)}\)

Probability of sampling edge (i, j)

\(w_{ij}\)

Eeight of edge (i, j)

\(\theta\)

propensity of N2V to backtrack

\(\gamma\) (\(\beta\))

Propensity of a N2V to reach a (non-)common neighbor of the currently visited node

and the previously visited node

\(\delta\)

Spectral gap