Unified Framework for Complex Graph-Data: Introducing the Hybrid Layered Network Model

TL;DR

Hybrid Layered Network (HLN) addresses the need for a unified graph-data model that captures both heterogeneity and layering in complex networks. HLN is formally defined as $G=(V,E,L,T,\boldsymbol{\mathcal{R}})$ with $E\subseteq ((V\times L)\ times (V\times L))$ and layer/type-mapping functions, enabling a single framework that subsumes homogeneous, heterogeneous, and multilayer networks. The authors contribute a synthetic HLN generator with complexity analysis, a suite of HLN-specific structural measures, and extensive experiments on real and synthetic networks showing improved performance in layer-informed tasks and faithful replication of real-world network properties. The work demonstrates HLN’s potential to simplify data representations, enable scalable generation, and support more accurate modeling with graph neural networks in multi-typed, multi-layer contexts.

Abstract

The present paper provides a generalized model of network, namely, Hybrid Layered Network (HLN). We proved that the sets of all homogeneous, heterogeneous and multi-layered networks are subsets of the set of all HLNs depicting the model's generalizability. The proposed HLN is more efficient in encoding different types of nodes and edges {when compared to representing the same information through heterogeneous or multilayered networks}. It is found experimentally that the HLN model when used with GNNs improve tasks such as link prediction. In addition, we present a novel parameterized algorithm (with complexity analysis) for generating synthetic HLNs. The networks generated from our proposed algorithm are more consistent in modelling the layer-wise degree distribution of a real-world Twitter network (represented as HLN) than those generated by existing models. Moreover, we also show that our algorithm is capable of generating various multilayer and homogeneous network. Further, we define different structural measures for HLN {namely multilayer neighborhood, degree centrality, closeness centrality and betweeness centrality}. Accordingly, we established the equivalency of the proposed structural measures of HLNs with that of homogeneous, heterogeneous, and multi-layered networks.

Figures (5)

• Figure 1: a) An example to demonstrate a hybrid-layered network with node and edge types. In the figure the black colored edges are undirected and the green colored edges are directed. b) The figure shows the author paper relation for the authors and papers marked in bold in Figure \ref{['figure1label']}(\ref{['fig:fig2']}). The circle represents paper and the triangle represents author. The dotted links and circles are the possibilities of two authors collaborating on a paper in the future.
• Figure 2: An example twitter network with each rectangle representing a layer. The first layer (represented by circles) contains tweets and the second layer (represented by triangles) contains users.
• Figure 3: An example showing twitter represented as a heterogeneous network.
• Figure 4: Figures a and b show the t-SNE plot of the feature vector for the movie and user nodes without layer information. Figures c and d show the feature vectors after adding layer information. We can clearly see that the feature vectors have condensed after adding layer information bringing structurally similar nodes closer to one another thus increasing the result of link prediction. Features are obtained from GraphSAGE model.
• Figure 5: Comparing the smoothed (using regression) degree distribution of the different layers of the TWITT network with our synthetic network and other standard networks on a logarithmic scale.

Theorems & Definitions (34)

• Definition 2.1: Homogeneous Networks
• Definition 2.2: Heterogeneous Network 7536145
• Definition 2.3: Multi-layered Network BOCCALETTI20141
• Definition 3.1: Hybrid Layered Network
• Remark 3.1: Hybrid Layered Network is not another variant of a heterogeneous network
• Lemma 3.1
• proof
• Corollary 3.1.1
• proof
• Lemma 3.2