###### Abstract  
Temporal knowledge graph completion (TKGC) refers to the prediction and filling in of missing facts on time series, which is essential for many downstream applications. However, many existing TKGC methods suffer from two limitations: (1) they only consider direct relations between entities and fail to express high-order structural dependencies between entities; and (2) they only leverage relation quadruples of temporal knowledge graphs, ignoring attribute information that contains rich semantic information. This makes them vulnerable to sparsity and incompleteness problems. In response, we propose HCAE, a temporal knowledge graph completion model that includes high-order connectivity and attribute information. This consists mainly of a recursive embedding propagation layer and a multi-head attention aggregation layer. The former leverages a recursive mechanism to update entity embeddings and can learn high-order connectivity information between entities in linear complexity time. The latter leverages an attention mechanism to understand the importance of different attributes for entity representation automatically. Combining high-order connectivity and attribute information can lead to more diverse entity representations and help enhance the model's ability to infer unknown entities. Comparative experiments on three real-world datasets show that the model's inference accuracy significantly outperforms other benchmark methods, especially regarding knowledge graphs with many unknown entities or relations. t +
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into two subtasks: predicting missing entities for queries like \((?,r,o,t)\) or \((s,r,?,t)\) and predicting missing relationships for queries like \((s,?,o,t)\). The symbol? represents the missing entity or relation. The main challenge lies in effectively integrating timestamps into the model to accurately capture and leverage the temporal dynamics of entities, relationships, and the underlying graph, thereby enhancing the ability to predict missing facts [8]. In this regard, researchers have explored various timestamp integration strategies, such as tensor decomposition based on timestamps [9], timestamp transformation-based methods [10], dynamic embeddings [11], and predictions based on historical contexts [12]. The goal is to incorporate timestamps into the fact-scoring function. However, these methods mainly model the structural features and temporal dependencies of TKGs at a single timescale, and they do not consider the potential temporal variability of TKGs, which leads to the limited performance of TKGC solutions. Building upon this, the MtGCN [13] model utilizes a gated recurrent unit (GRU) to learn the temporal dependencies of TKGs across multiple timescales. Additionally, it combines organically with graph convolutional networks (GCNs) to achieve end-to-end temporal link prediction and synergistic enhancement of temporal modeling and graph structure learning. However, existing research still has some limitations: firstly, it only considers direct relationships between entities while overlooking the high-order connectivity among entities. Secondly, it models only the relationship quadruples, neglecting the abundant attribute information in the KG. These limitations make these methods susceptible to the sparsity and incompleteness of the KG. Additionally, the structural information cannot express the specific meanings between entities and relations, severely inhibiting model prediction ability enhancement. To overcome these limitations, this paper proposes HCAE, a temporal knowledge graph completion model that fuses high-order connectivity and attribute information, which continues the idea of MtGCN multi-timescale modeling. There are two novelties: (1) Explicitly capturing the high-order connectivity between entities. High-order structured relationships contain rich semantic information that can reflect the complex connections between entities, which is conducive to multi-step prediction and to improving the matching ability of KG representation learning.