Algorithm 1 The weighted co-association matrix based community fusion algorithm, WCMFA, which detects community structure in attributed networks based on the two-layer representation

Input:  $\mathcal{G}=\langle \left(G\right(V,E),\mathcal{A})\rangle$: an attributed network; ${\left\{f\right\}}_{i=1}^N$: a set of base community detector; N: the number of candidate community partitions; M: the total number of node in the attributed network $\mathcal{G}$; $si{m}^t(·,·)$: the node pair similarity measure for topological structure; $si{m}^a(·,·)$: the node pair similarity measure for attribute set; $\mathcal{M}(·)$: a similarity matrix based clustering algorithm. Output:  $P^{\ast }$: the consensus community partition. 1:${\mathcal{R}}^{low}\leftarrow \mathcal{G}\langle G(V,E),\mathcal{A}\rangle$; 2://calculate the candidate community partitions $\mathcal{P}$; 3: for $i=1,2,\dots ,N$ do 4:    if $f_i$ is an instance of $f^t$ for $G(V,E)$ then 5:        $\mathcal{P}\left[i\right]\leftarrow f_i^t\left(G\right)$; 6:    else 7:        $\mathcal{P}\left[i\right]\leftarrow f_i^a\left(G\right)$; 8:        calculate the matrix ${\mathsf{\Psi }}^i$ associated with $\mathcal{P}\left[i\right]$; 9:    end if 10: end for 11:${\mathcal{R}}^{high}\leftarrow \langle {\left\{f_i\right\}}_{i=1}^N,\mathcal{P},{\left\{{\mathsf{\Psi }}^i\right\}}_{i=1}^N\rangle$; 12://community fusion; 13: for $i=1,2,\dots ,N$ do 14:    if $P^i$ is generated by $f^t\left(\mathcal{G}\right)$ then 15:        $w_i(·,·)\leftarrow si{m}^t(·,·)$; 16:    else 17:        $w_i(·,·)\leftarrow si{m}^a(·,·)$; 18:    end if 19: end for 20: for $u=1,2,\dots ,n$ do 21:    for $v=1,2,\dots ,n$ do 22:        if $u\ge v$ then 23:           continue; 24:        end if 25:        $C_{uv}\leftarrow 0$; 26:        for $k=1,2,\dots ,N$ do 27:           $C_{uv}\leftarrow C_{uv}+w_k(u,v)·\delta (P^k\left(u\right),P^k\left(v\right))$; 28:        end for 29:        $C_{uv}\leftarrow \frac{1}{N}·C_{uv}$; 30:    end for 31: end for 32:$\mathbf{C}\leftarrow \mathbf{C}+{\mathbf{C}}^T$; 33:$P^{\ast }\leftarrow \mathcal{M}\left(\mathbf{C}\right)$; 34:return the consensus community partition $P^{\ast }$.