Abstract
We are flooded with large-scale, dynamic, directed, networked data. Analyses requiring exact comparisons between networks are computationally intractable, so new methodologies are sought. To analyse directed networks, we extend graphlets (small induced sub-graphs) and their degrees to directed data. Using these directed graphlets, we generalise state-of-the-art network distance measures (RGF, GDDA and GCD) to directed networks and show their superiority for comparing directed networks. Also, we extend the canonical correlation analysis framework that enables uncovering the relationships between the wiring patterns around nodes in a directed network and their expert annotations. On directed World Trade Networks (WTNs), our methodology allows uncovering the core-broker-periphery structure of the WTN, predicting the economic attributes of a country, such as its gross domestic product, from its wiring patterns in the WTN for up-to ten years in the future. It does so by enabling us to track the dynamics of a country’s positioning in the WTN over years. On directed metabolic networks, our framework yields insights into preservation of enzyme function from the network wiring patterns rather than from sequence data. Overall, our methodology enables advanced analyses of directed networked data from any area of science, allowing domain-specific interpretation of a directed network’s topology.
Highlights
We are flooded with large-scale, dynamic, directed, networked data
They showed that similar to scale free topology, World Trade Networks (WTNs) is characterized by a sharp power-law distribution of directed edges and that trade relationships are disassortative
We compare the performance of our novel directed graphlet-based network distances (DGCD-129, Directed Graphlet Correlation Distance (DGCD)-13, DRGF and Directed Graphlet Degree Distribution Agreement (DGDDA)) used for clustering networks coming from six directed network models (ER, SFBA-Sink, SFBA-Source, GEO, GEO-GD and SF-GD), which we define as follows
Summary
We are flooded with large-scale, dynamic, directed, networked data. Analyses requiring exact comparisons between networks are computationally intractable, so new methodologies are sought. Garlaschelli and Loffredo[7] were the first ones to hypothesise the modular organization of WTN, due to its similarities with scale-free networks[8] They showed that similar to scale free topology, WTN is characterized by a sharp power-law distribution of directed edges (e.g., many countries are involved in a few trades but only few countries are involved in large numbers of trades) and that trade relationships are disassortative (e.g., countries with many trade partners are connected to countries with few partners and vice-versa). A popular network statistic is network motifs[14], which are defined as small partial sub-graphs that are over-represented in a network with respect to a given null model (partial sub-graph means that when selecting a sub-set of nodes from the large network, we can select any edges between them)
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