Synthetic disjoint and overlapping dynamic attributed networks with ground-truth information

1. Synthetic network 1: We use the synthetic benchmark DANCer to create 12 datasets with ten timestamps for attributed graphs with undirected edges that can change over time, where nodes are grouped into densely connected sets, relatively homogeneous according to the attributes. The number of nodes starts at 256 nodes, the number of communities at 5, and the number of edges at 1000 increases over time, ending with a maximum value of 1868 nodes, ten communities, and 11905 edges among the built networks.

2. Synthetic network 2: Graphs were built with 200 nodes and 20 snapshots. In the initialization, the nodes are divided into two groups, each with 100 nodes. Then, at a randomly selected time step, 40 % of the nodes are chosen to migrate to a new community in Dataset 1, and 80 % in Dataset 2. The membership of each node is chosen according to a stochastic block model, where nodes within the same community are connected with a probability of 0.3 and the edges between communities are drawn with a probability of 0.1.

3. Synthetic network 3: We generated ten timestamps with growing and shrinking communities. We designed three datasets with three groups of 80, 90, and 100 nodes. A degree-corrected stochastic block model generates the network structure. Three types of attributed networks were proposed, with different original link probabilities, to assess strongly assortative structures (Dataset 1), weakly assortative structures (Dataset 2), and disassortative structures (Dataset 3).

4. Overlapping synthetic networks: Using Greene's benchmark, we create eleven overlapping datasets with ten snapshots. Each network has 250 nodes, overlapping nodes from 0 to 50, and overlapping memberships from 2 to 25. Specific kinds of changes in communities of a dynamic network were simulated:

- Birth and death: There are two birth events per time step and two death events per time step. Dataset 1 has no overlapping nodes; Dataset 2 has five overlapping nodes and two overlapping memberships; Dataset 3 has ten overlapping nodes and two overlapping memberships; Dataset 4 has 25 overlapping nodes and two overlapping memberships; Dataset 5 has 50 overlapping nodes and two overlapping memberships; Dataset 6 has five overlapping nodes and five overlapping memberships; Dataset 7 has five overlapping nodes and ten overlapping memberships; Dataset 8 has five overlapping nodes and 25 overlapping memberships.

- Merge and split: With two merge events per time step and two split events per time step. Dataset 9 has five overlapping nodes and two overlapping memberships.

- Expansion and contraction: With two expansion events per time step and two contraction events per time step, with a rate of 0.1. Dataset 10 has five overlapping nodes and two overlapping memberships.

- Node switching between communities: With a probability of 0.2 for a node to switch its community membership. Dataset 11 has five overlapping nodes and two overlapping memberships.