Studying real-world dynamic networks and their evolution is crucial for understanding the complex systems that govern various domains, from social interactions to financial transactions. The evolution of these networks provides insights into the underlying mechanisms driving their changes, which can be pivotal for applications such as node segmentation, prediction of future states, and role discovery. Among the various approaches to studying network evolution, graph evolution rules (GERs) stand out since they produce human-readable outcomes without requiring any pre-assumptions about the underlying evolutionary mechanisms. In this work, we leverage GER to derive evolutionary node profiles (NEPs), capturing the distinct patterns of how nodes change over time within the network. These profiles allow us to identify groups of accounts characterized by similar evolution rules, revealing common interaction patterns. As a case study, we apply our approach to Sarafu, a complementary currency platform with rich temporal data, representing a contemporary human complex system that integrates humanitarian aid, collaboration, and financial aspects. Our findings suggest the efectiveness of using graph evolution rules in real-world dynamic networks, showcasing their potential to enhance our understanding of the node-level dynamics of complex systems.
Studying real-world dynamic networks and their evolution is crucial for understanding the complex
systems that govern various domains, from social interactions to financial transactions. The evolution of
these networks provides insights into the underlying mechanisms driving their changes, which can be
pivotal for applications such as node segmentation, prediction of future states, and role discovery.
Traditionally, models, mechanisms, and metrics have been introduced to interpret how dynamic networks
grow and evolve, often assuming that their growth is governed by a unique parameterized mechanism.
To address this limitation, graph evolution rules (GERs) have emerged as a promising frequency-based
method [
Figure 1 shows a graphical representation of a graph evolution rule (GER). Inspired by the concept of association rule, a GER has a body (precondition) and a head (postcondition), indicating that a subgraph matching the body often evolves into the head.
In this work, we leverage GER to derive evolutionary node profiles (NEPs), capturing the distinct patterns of how nodes change over time within the network. These profiles allow us to identify groups of accounts characterized by similar evolution rules, revealing common interaction patterns. As a case study, we apply our approach to Sarafu, a complementary currency platform with rich temporal data, representing a contemporary human complex system that integrates humanitarian aid, collaboration,
CEUR
ceur-ws.org t0 t1 and financial aspects. By analyzing Sarafu’s network using our GER-based method, we identify two distinct evolutionary traits, uncovering significant behaviors that contribute to the platform’s operation. Our findings suggest the efectiveness of using graph evolution rules in real-world dynamic networks, showcasing their potential to enhance our understanding of the node-level dynamics of complex systems.
From a node-centric perspective, our main aim is to represent nodes based on the mechanisms that
characterize the evolution of the interactions surrounding them. The methodology to get this kind of
representation is based on two main tasks: a) the extraction of the ego-networks from the overall
temporal network describing the system, i.e. interactions surrounding every single node; and b)
the identification of the mechanisms/rules driving the evolution of each ego-network through the
computation of the graph evolution rules. We first model the set of intera(cati)ons or transactions among
the members of a networked system as a temporal network = ( , ) . While is the set of users in the
system, is the set of timestamped directed links (, , ) , with (, ) ∈ × . Each link corresponds
to an interaction/transaction from node to user that occurs at time . To accomplish the first task ,
we extract the temporal ego-network from the temporal graph . For each node , its ego-network
() = ( , ) corresponds to the temporal subgraph induced by ’s neighborhood, including itself.
To deal with the second task, i.e. identifying the graph evolution rules characterizing a temporal
ego-network of a node, we rely on the EvoMine algorithm [
Our work on node temporal behavioral representation using graph evolution rules considers as a
case study a transaction network in the Web3 landscape: the Sarafu network[
We applied our methodology to the Sarafu transaction network, analyzing 40343 ego-networks. This number was reduced to 16030 after filtering for consecutive interactions (only ego-networks that show interactions with and among their neighbors in consecutive timestamps). To ensure suficient data for meaningful behavioral analysis, we focused on ego-networks with at least 116 interactions (80ℎ percentile of the size distribution), resulting in 3207 ego-networks for detailed study. Using the EvoMine algorithm, we set a minimum support of 1 and a maximum of three edges per pattern, using eventbased support. This process identified 40 distinct graph evolution patterns, which correspond to the dimensions of the node evolutionary profiles (NEPs). We collected all NEPs into a matrix, visualized as a heatmap (Figure 2) where rows represent ego-networks and columns indicate graph evolution rule IDs. From a column-wise inspection, we observe that in general, only a limited set of graph evolution rules characterizes the dynamics of the transactions in ego-networks. Indeed, there is concentration of frequency in rules 0, 1, 2, 3, 4, 10 and 15, with the first rule ( 0) being the most frequent for many ego-networks. The analysis of NEPs has pointed out two principal observations that are fundamental for showcasing how NEPs can be exploited for data discovery tasks: i) only a few GERs are frequent in NEPs; and ii) NEPs are varied but with a limited level of variability. Based on these observations, we 1https://www.grassrootseconomics.org/pages/about-us.html developed a clustering pipeline to identify distinct classes representing dynamic traits of ego-network evolution in Sarafu. We first applied Principal Component Analysis (PCA) for dimensionality reduction, preserving most of the information in the NEP matrix. Then, we used hierarchical clustering on the transformed NEPs to identify groups with similar evolutionary traits. This process revealed two main groups of accounts: one dominated by single-link expansion over other star- and chain-like expansions, and another with a more homogeneous distribution among the same expansion rules.
We introduced a method using subgraph-based evolution rules to represent ego-network dynamics, enabling detailed analysis of temporal node behaviors. Applied to the Sarafu transaction network, our Node Evolutionary Profiles (NEPs) revealed two main interaction traits: one dominated by singlelink expansion and another with more balanced expansion types. This approach efectively uncovers behavioral patterns in complex networks, supporting applications like distinguishing user behaviors in ifnancial networks and enhancing understanding of interaction dynamics.
The author(s) have not employed any Generative AI tools.