I analyse political talks among actors across time. I have a dataset that contains information on who talked to whom and when. I want to model this information into a graph so to apply community detection algorithms. But clearly the representation of the data as a static network will (partially) lose the information concerning the time of the talk.
Then, let consider a directed graph $D=(V,E)$, where $V$ is the set of $N$ vertices (actors) and $E$ is set of edges (direct referrals). The vertices $\{v_1,v_2,v_3,...,v_n\}$ are connected by edges $(v_i,v_j)$ and each edge is oriented from $v_i$ to $v_j$, $i,j \in \mathbb{N} = \{1,2,3,...,N\}$. To each edge $(v_i,v_j)$ we assign an attribute $t_{ij}$, $t \in \mathbb{N} = \{1,2,3,...,N\}$, corresponding to the time of direct referrals of actor $v_i$ to actor $v_j$.
I have two options in representing the graph. (1) The simplest option will suggest to drop the attribute $t_{ij}$ in favour of a weight $e_{ij}$, corresponding to the sum of all multi-edges from $v_i$ to actor $v_j$. (2) Yet probably the most interesting option will be to create a series of subgraphs $D_t$ where edges $(v_i,v_j)$ and $(v_k,v_l)\in D$, for $i,j,k,l \in \mathbb{N} = \{1,2,3,...,N\}$, while $t_{ij}=t_{kl}$.
Option (1) does not present problems of sorts: I can simply apply one of the many community detection algorithms on the market and analyse the results. But in case I am interest in option (2), thus to observe the evolution of the communities - how many communities at time $t$? how many actors switch communities from $D_t$ and $D_{t+1}$?, the problem is much more complicated, especially since I am not familiar with the complexities of modelling of dynamic networks.
I am then looking for an algorithm that is easy to interpret and captures information of the evolution of the graph in terms of its community structure. What might I consider?