Leo Torres

Feature: Added compressed file I/O. #709 (@kaiser-dan) Docs: automated the generation of the "Using XGI" page. #710 (@nwlandry) Optimized line graph construction. #706 (@Ved235) Added examples to the gallery. #711 (@maximelucas) Feature: add type stubs for stats on view classes. #700 (@leotrs) Docs: introduce stats earlier, add cheat sheet, link quickstart. #701 (@leotrs) Feature: forward stat function docstrings to stat objects. #708 (@leotrs) Docs: added references to using-xgi.rst. #698 (@jbd7qp) Feature: make built-in stats discoverable in dir() and IDE autocomplete. #699 (@leotrs) Fix: update ReadTheDocs OS to ubuntu-24.04. (Closes Issue #702) #703 (@leotrs) Feature: add __repr__, __copy__, __deepcopy__ to core classes. #693 (@leotrs) Docs: cross-reference algorithms and stats from core classes. #695 (@leotrs) Performance: reduce import time by deferring heavy dependencies. #692 (@leotrs) Migrate all seeded functions from global random state to local RNG instances. #689 (@leotrs) Docs: document exception hierarchy in module docstring. #691 (@leotrs) Migrate all seeded functions from global random state to local RNG instances. #689 (@leotrs) Docs: document exception hierarchy in module docstring. #691 (@leotrs) Migrate all seeded functions from global random state to local RNG instances. #689 (@leotrs) Fix: remove deprecated edge methods from SimplicialComplex. #696 (@leotrs) Docs: document exception hierarchy in module docstring. #691 (@leotrs) Migrate all seeded functions from global random state to local RNG instances. #689 (@leotrs) Define __all__ across all subpackage __init__.py files. #688 (@leotrs) Clean up exception hierarchy for v1.0. #687 (@leotrs) Fix scipy FutureWarning in laplacian_matrix. #685 (@leotrs)

Complex systems, composed at the most basic level of units and their interactions, describe phenomena in a wide variety of domains, from neuroscience to computer science and economics. The wide variety of applications has resulted in two key challenges: the generation of many domain-specific strategies for complex systems analyses that are seldom revisited, and the compartmentalization of representation and analysis ideas within a domain due to inconsistency in complex systems language. In this work we propose basic, domain-agnostic language in order to advance toward a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system under study and data collected, then moving through different mathematical frameworks for encoding the observed data (i.e., graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each framework. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of an interaction among a set of units in a system may affect the possibility of the existence of another relation. We discuss how dependencies may arise and how they may alter the interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and the choice of mathematical representation influence the results. We hope this work can serve as an opportunity for reflection for experienced complex systems scientists, as well as an introductory resource for new researchers.

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 July 2020Accepted: 12 January 2021Published online: 13 May 2021Keywordsnonbacktracking, node immunization, centrality measure, complex networksAMS Subject Headings05C50, 05C82, 05C85, 68R10Publication DataISSN (online): 2577-0187Publisher: Society for Industrial and Applied MathematicsCODEN: sjmdaq

Graph distance and graph embedding are two fundamental tasks in graph mining. For graph distance, determining the structural dissimilarity between networks is an ill-defined problem, as there is no canonical way to compare two networks. Indeed, many of the existing approaches for network comparison differ in their heuristics, efficiency, interpretability, and theoretical soundness. Thus, having a notion of distance that is built on theoretically robust first principles and that is interpretable with respect to features ubiquitous in complex networks would allow for a meaningful comparison between different networks. For graph embedding, many of the popular methods are stochastic and depend on black-box models such as deep networks. Regardless of their high performance, this makes their results difficult to analyze which hinders their usefulness in the development of a coherent theory of complex networks. Here we rely on the theory of the length spectrum function from algebraic topology, and its relationship to the non-backtracking cycles of a graph, in order to introduce two new techniques: Non-Backtracking Spectral Distance (NBD) for measuring the distance between undirected, unweighted graphs, and Non-Backtracking Embedding Dimensions (NBED) for finding a graph embedding in low-dimensional space. Both techniques are interpretable in terms of features of complex networks such as presence of hubs, triangles, and communities. We showcase the ability of NBD to discriminate between networks in both real and synthetic data sets, as well as the potential of NBED to perform anomaly detection. By taking a topological interpretation of non-backtracking cycles, this work presents a novel application of topological data analysis to the study of complex networks.

. This field is built around the idea that an increased understanding of the complex structural properties of a variety systems will allow us to better observe, predict, and even control the behavior of these systems.