Common Permutation Methods in Animal Social Network Analysis Do Not Control for Non-independence

The non-independence of social network data is a cause for concern among behavioural ecologists conducting social network analysis. This has led to the adoption of several permutation-based methods for testing common hypotheses. One of the most common types of analysis is nodal regression, where the relationships between node-level network metrics and nodal covariates are analysed using a permutation technique known as node-label permutation. We show that, contrary to accepted wisdom, node-label permutations do not account for the types of non-independence assumed to exist in network data, because regression-based permutation tests still assume exchangeability of residuals. The same theoretical condition also applies to the quadratic assignment procedure (QAP), a permutation-based method often used for conducting dyadic regression. We highlight that node-label permutations produce the same p-values as equivalent parametric regression models, but that in the presence of confounds, parametric regression models produce more accurate effect size estimates. We also note that QAP only controls for a specific type of non-independence between edges that are connected to the same nodes, and that appropriate parametric regression models are also able to account for this type of non-independence. Based on this, we advocate the retirement of permutation tests for regression analyses, in favour of well-specified parametric models. Moving away from permutation-based methods will reduce over-reliance on p-values, generate more reliable estimates of effect sizes, and facilitate the adoption of more powerful types of statistical analysis.

Enhanced Unsupervised Graph Embedding via Hierarchical Graph Convolution Network

Graph embedding aims to learn the low-dimensional representation of nodes in the network, which has been paid more and more attention in many graph-based tasks recently. Graph Convolution Network (GCN) is a typical deep semisupervised graph embedding model, which can acquire node representation from the complex network. However, GCN usually needs to use a lot of labeled data and additional expressive features in the graph embedding learning process, so the model cannot be effectively applied to undirected graphs with only network structure information. In this paper, we propose a novel unsupervised graph embedding method via hierarchical graph convolution network (HGCN). Firstly, HGCN builds the initial node embedding and pseudo-labels for the undirected graphs, and then further uses GCNs to learn the node embedding and update labels, finally combines HGCN output representation with the initial embedding to get the graph embedding. Furthermore, we improve the model to match the different undirected networks according to the number of network node label types. Comprehensive experiments demonstrate that our proposed HGCN and HGCN∗ can significantly enhance the performance of the node classification task.

Label propagation algorithm based on local cycles for community detection

Label propagation algorithm (LPA) has been proven to be an extremely fast method for community detection in large complex networks. But an important issue of the algorithm has not yet been properly addressed that random update orders in label propagation process hamper the algorithm robustness of algorithm. We note that when there are multiple maximal labels among a node neighbors' labels, choosing a node' label from which there is a local cycle to the node instead of a random node' label can avoid the labels propagating among communities at random. In this paper, an improved LPA based on local cycles is given. We have evaluated the proposed algorithm on computer-generated networks with planted partition and some real-world networks whose community structure are already known. The result shows that the performance of the proposed approach is even significantly improved.