Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets

SynGraphy: Succinct Summarisation of Large Networks via Small Synthetic Representative Graphs

We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is crucial to understand and make sense of networked data and the relationships it represents. Due to the large size of many networks, visualisation is extremely difficult; the simple method of drawing large networks like those of Facebook or Twitter leads to graphics that convey little or no information. While modern graph layout algorithms can scale computationally to large networks, their output tends to a common "hairball" look, which makes it difficult to even distinguish different graphs from each other. Graph sampling and graph coarsening techniques partially address these limitations but they are only able to preserve a subset of the properties of the original graphs. In this paper we take the problem of visualising large graphs from a novel perspective: we leave the original graph's nodes and edges behind, and instead summarise its properties such as the clustering coefficient and bipartivity by generating a completely new graph whose structural properties match that of the original graph. To verify the utility of this approach as compared to other graph visualisation algorithms, we perform an experimental evaluation in which we repeatedly asked experimental subjects (professionals in graph mining and related areas) to determine which of two given graphs has a given structural property and then assess which visualisation algorithm helped in identifying the correct answer. Our summarisation approach SynGraphy compares favourably to other techniques on a variety of networks.Comment: 24 page

A Graph Theory approach to assess nature’s contribution to people at a global scale

The use of Graph Theory on social media data is a promising approach to identify emergent properties of the complex physical and cognitive interactions that occur between humans and nature. To test the effectivity of this approach at global scales, Instagram posts from fourteen natural areas were selected to analyse the emergent discourse around these areas. The fourteen areas, known to provide key recreational, educational and heritage values, were investigated with different centrality metrics to test the ability of Graph Theory to identify variability in ecosystem social perceptions and use. Instagram data (i.e., hashtags associated to photos) was analysed with network centrality measures to characterise properties of the connections between words posted by social media users. With this approach, the emergent properties of networks of hashtags were explored to characterise visitors’ preferences (e.g., cultural heritage or nature appreciation), activities (e.g., diving or hiking), preferred habitats and species (e.g., forest, beach, penguins), and feelings (e.g., happiness or place identity). Network analysis on Instagram hashtags allowed delineating the users’ discourse around a natural area, which provides crucial information for effective management of popular natural spaces for peopleThis work is a product of ECOMAR research network (Evaluation and monitoring of marine ecosystem services in Iberoamerica; project number 417RT0528, funded by CYTED). Three co-authors were funded by H2020-Marie Skłodowska-Curie Action during the conduction of this work: SdJ, funded by MSCA-IF-2016 (ref. 743545); AOA, funded by MSCA-IF-2016 (ref. 746361); ARF, funded by MSCA-IF-2014 (ref. 655475)S

Geospatial Social Networks of East German Opposition (1975-1989/90)

During the last two decades single photographs and photograph corpora have gained in popularity as sources for historical research. In addition to their important function as carriers of the past, photographs also contain valuable information about past social relations. However, to utilise this information a researcher needs a more structured dataset, a photograph corpus containing rich metadata, which allows us to explore and analyse contextual information stored in alphanumeric form. My paper will exemplify how photography corpora could be used as a source for network analysis seeking to explore, reconstruct and visualise hidden historical social networks. The empirical case of my paper revolves around regional and interregional networks of East German dissident movement. The main empirical material explored for network analysis and visualisations consists of a large enriched photograph corpus on East German dissident movement maintained by Robert Havemann Foundation in Berlin. Based on this corpus my paper will explore the structure and dynamics of regional and interregional networks of East German opposition. The results introduce evidence that regional connectedness based on personal mobility among the East German dissidents both changes and increases over time, thus resulting in continuously evolving patterns of social interaction. Further, the analysis of Roland Jahn’s geospatial networks evidences the usefulness and power of historical network analysis when it comes to tackling changes in patterns of social interaction.</p

Balancing between the Local and Global Structures (LGS) in Graph Embedding

We present a method for balancing between the Local and Global Structures (LGS) in graph embedding, via a tunable parameter. Some embedding methods aim to capture global structures, while others attempt to preserve local neighborhoods. Few methods attempt to do both, and it is not always possible to capture well both local and global information in two dimensions, which is where most graph drawing live. The choice of using a local or a global embedding for visualization depends not only on the task but also on the structure of the underlying data, which may not be known in advance. For a given graph, LGS aims to find a good balance between the local and global structure to preserve. We evaluate the performance of LGS with synthetic and real-world datasets and our results indicate that it is competitive with the state-of-the-art methods, using established quality metrics such as stress and neighborhood preservation. We introduce a novel quality metric, cluster distance preservation, to assess intermediate structure capture. All source-code, datasets, experiments and analysis are available online.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023