The GraphTempo Framework for Exploring the Evolution of a Graph through Pattern Aggregation

TL;DR

GraphTempo tackles the challenge of analyzing evolving graphs by introducing temporal, attribute, and pattern aggregation, enabling compact representations and multi-resolution views of network evolution. It defines time projection operators and an evolution graph to model stability, growth, and shrinkage, and proposes exploration strategies (Union/Intersection) to efficiently locate interval pairs where at least $k$ events occur. The framework supports distinct and non-distinct aggregations, pattern-based grouping (e.g., triangles) via a pattern graph $G_P$, and offers optimization techniques such as partial materialization and distributive properties to scale to large datasets. Empirical results on DBLP, MovieLens, and Primary School demonstrate performance gains and reveal actionable insights into disease-spread-like dynamics and social interactions, highlighting GraphTempo’s practical impact for graph analytics and visualization. The work advances graph OLAP by closing gaps in temporal, attribute, and pattern-aware evolution analysis while providing concrete algorithms and implementation strategies.

Abstract

When the focus is on the relationships or interactions between entities, graphs offer an intuitive model for many real-world data. Such graphs are usually large and change over time, thus, requiring models and strategies that explore their evolution. We study the evolution of aggregated graphs and introduce the GraphTempo model that allows temporal and attribute aggregation not only on node level by grouping individual nodes, but on a pattern level as well, where subgraphs are grouped together. Furthermore, We propose an efficient strategy for exploring the evolution of the graph based on identifying time intervals of significant growth, shrinkage or stability. Finally, we evaluate the efficiency and effectiveness of the proposed approach using three real graphs.

Figures (14)

• Figure 1: A temporal attributed graph.
• Figure 2: Union graph of the graph of Fig. \ref{['fig:1']} in $[t_0, t_1]$.
• Figure 3: (a) Evolution graph on (Gender, #Publications), (b) its aggregation, and (c) triangle-based evolution graph aggregation on Gender for $t_0$, $t_1$ of the graph of Fig. \ref{['fig:1']}.
• Figure 4: Time point aggregate (a-c) graphs on (gender, #publications) and (d-e) tri-graphs on gender for the graph of Fig.\ref{['fig:1']}.
• Figure 5: Aggregate (a-b) graphs on (gender, #publications) and (c-d) triangle-based graphs on gender for the graph of Fig. \ref{['fig:335']}.

Theorems & Definitions (12)

• Definition 2.1: Temporal Attributed Graph
• Definition 2.2: Time Project Operator
• Definition 2.3: Graph Aggregation
• Definition 2.4: Pattern Aggregation
• Definition 3.1: Monotonically Increasing/Decreasing
• Lemma 1
• Definition 3.2: Minimal/Maximal Interval Pair
• Definition 3.3: Problem Definition
• Theorem 1
• Theorem 2