Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience, cyber security, social network analysis, and ...bioinformatics, among others. Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph. Often, two graphs are compared via a pairwise distance measure, with a small distance indicating structural similarity and vice versa. Common choices include spectral distances and distances based on node affinities. However, there has of yet been no comparative study of the efficacy of these distance measures in discerning between common graph topologies at different structural scales. In this work, we compare commonly used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and real world networks. We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures. We make recommendations on the applicability of different distance measures to the analysis of empirical graph data based on this multi-scale view. Finally, we introduce the Python library NetComp that implements the graph distances used in this work.
Persistent homology theory provides approaches for analyzing topological features, which is now widely applied in graph comparison on social networks, biological networks, and co-location networks. ...These approaches utilize filtration techniques to extract the topological properties of a graph and construct vectorizations that represent these properties for further computation. However, most existing methods are designed for static scenarios and are unsuitable for the time-varying structure in realistic dynamic graphs. In this paper, we propose the Stable Distance of Persistent Homology (SDPH) to compare and quantify the differences in the topological properties of dynamic graphs. In detail, we design Dynamic Dowker Filtration (DDF) to map dynamic graph to a persistent complex based on the ɛ-interleaved theory, which enables us to trace the structure holes formed by the accumulation of temporal edge via computing the persistent homology. DDF exhibits stability and duality, inducing a time-structure triangle inequality. Based on this inequality, we finally construct Time-interlevel Kernel (TIK) for vectorizing the extracted topological features with an inner product. We conduct the graph clustering and classification experiments on synthetic and real-world datasets. Experimental results show that the proposed SDPH outperforms the baseline methods in these tasks and validate that the proposed SDPH can effectively measure the topological difference of dynamic graphs. Through SDPH, we would provide insight and inspiration on how to apply persistent homology theory to dynamic graph analysis.
Visualizing small‐world networks such as protein‐protein interaction networks or social networks often leads to visual clutter and limited interpretability. To overcome these problems, we present ...ProtEGOnist, a visualization approach designed to explore small‐world networks. ProtEGOnist visualizes networks using ego‐graphs that represent local neighborhoods. Ego‐graphs are visualized in an aggregated state as a glyph where the size encodes the size of the neighborhood and in a detailed version where the original network nodes can be explored. The ego‐graphs are arranged in an ego‐graph network, where edges encode similarity using the Jaccard index. Our design aims to reduce visual complexity and clutter while enabling detailed exploration and facilitating the discovery of meaningful patterns. To achieve this, our approach offers a network overview using ego‐graphs, a radar chart for a one‐to‐many ego‐graph comparison and meta‐data integration, and detailed ego‐graph subnetworks for interactive exploration. We demonstrate the applicability of our approach on a co‐author network and two different protein‐protein interaction networks. A web‐based prototype of ProtEGOnist can be accessed online at https://protegonist-tuevis.cs.uni-tuebingen.de/.
Abstract
Analogous to genomic sequence alignment that allows for across-species transfer of biological knowledge between conserved sequence regions, biological network alignment can be used to guide ...the knowledge transfer between conserved regions of molecular networks of different species. Hence, biological network alignment can be used to redefine the traditional notion of a sequence-based homology to a new notion of network-based homology. Analogous to genomic sequence alignment, there exist local and global biological network alignments. Here, we survey prominent and recent computational approaches of each network alignment type and discuss their (dis)advantages. Then, as it was recently shown that the two approach types are complementary, in the sense that they capture different slices of cellular functioning, we discuss the need to reconcile the two network alignment types and present a recent first step in this direction. We conclude with some open research problems on this topic and comment on the usefulness of network alignment in other domains besides computational biology.
•We compare three samples of Twitter data collected through the search and streaming APIs.•We assess differences in reconstructed networks of communication (RTs and mentions).•Both sample size and ...boundary specification introduce network bias.•The bias is stronger for mention networks than for networks of RTs.
We consider the sampling bias introduced in the study of online networks when collecting data through publicly available APIs (application programming interfaces). We assess differences between three samples of Twitter activity; the empirical context is given by political protests taking place in May 2012. We track online communication around these protests for the period of one month, and reconstruct the network of mentions and re-tweets according to the search and the streaming APIs, and to different filtering parameters. We find that smaller samples do not offer an accurate picture of peripheral activity; we also find that the bias is greater for the network of mentions, partly because of the higher influence of snowballing in identifying relevant nodes. We discuss the implications of this bias for the study of diffusion dynamics and political communication through social media, and advocate the need for more uniform sampling procedures to study online communication.
Evaluation of Graph Sampling: A Visualization Perspective Yanhong Wu; Nan Cao; Archambault, Daniel ...
IEEE transactions on visualization and computer graphics,
2017-Jan., 2017-01-00, 2017-1-00, 20170101, Letnik:
23, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Graph sampling is frequently used to address scalability issues when analyzing large graphs. Many algorithms have been proposed to sample graphs, and the performance of these algorithms has been ...quantified through metrics based on graph structural properties preserved by the sampling: degree distribution, clustering coefficient, and others. However, a perspective that is missing is the impact of these sampling strategies on the resultant visualizations. In this paper, we present the results of three user studies that investigate how sampling strategies influence node-link visualizations of graphs. In particular, five sampling strategies widely used in the graph mining literature are tested to determine how well they preserve visual features in node-link diagrams. Our results show that depending on the sampling strategy used different visual features are preserved. These results provide a complimentary view to metric evaluations conducted in the graph mining literature and provide an impetus to conduct future visualization studies.
Distance measures for embedded graphs Akitaya, Hugo A.; Buchin, Maike; Kilgus, Bernhard ...
Computational geometry : theory and applications,
April 2021, 2021-04-00, Letnik:
95
Journal Article
Recenzirano
Odprti dostop
We introduce new distance measures for comparing straight-line embedded graphs based on the Fréchet distance and the weak Fréchet distance. These graph distances are defined using continuous mappings ...and thus take the combinatorial structure as well as the geometric embeddings of the graphs into account. We present a general algorithmic approach for computing these graph distances. Although we show that deciding the distances is NP-hard for general embedded graphs, we prove that our approach yields polynomial time algorithms if the graphs are trees, and for the distance based on the weak Fréchet distance if the graphs are planar embedded and if the embedding meets a certain geometric restriction. Moreover, we prove that deciding the distances based on the Fréchet distance remains NP-hard for planar embedded graphs and show how our general algorithmic approach yields an exponential time algorithm and a polynomial time approximation algorithm for this case.
There is a hindrance in modeling Gibbs energies of high melting alloys via the CALPHAD approach because of the scarcity of experimental results. All the conventional methods suffer to overcome the ...practical difficulties at high temperatures. Despite these setbacks, this paper provides a reliable way of using an arc-melting device in conjunction with a pyrometer to measure high-temperature phase transitions and developing a hybrid approach to construct a Ni-Si-Zr phase diagram. First, the preparation of Ni-Si-Zr alloy is via arc-melting technique. Forty-two as-cast sample analyses provide the primary solidifying phase encompassing the Ni-Si-Zr composition domain. Heat-treatment of fifteen samples at 1073 K refines the isothermal section, emphasizing the Zr-rich corner. Ni-Si-Zr alloy’s temperature recording using pyrometer in the arc-melting device while cooling after melting reveals novel Ni-Si-Zr’s invariant reactions. The time versus temperature graph comparison with its as-cast electron micrograph reveals several phase transitions. The notable research output of this research work is the hybrid approach, including the experiments circumventing hurdles at high temperatures and the first-principles method to calculate the intermetallic phase’s formation energy. The hybrid approach in the present work has established a phase diagram and the thermodynamic description over the extensive temperature and composition ranges for a highly complicated ternary system. The presently developed hybrid methodology is also applicable to construct a phase diagram for other complex ternary systems up to ≈ 3700 K.
Measurements of high phase transition temperatures and construction of 3D Ni-Si-Zr phase diagram. Display omitted
•This work presents exhaustive experimental information about Ni-Si-Zr: invariant reaction, phase boundaries, solid-state phase equilibria at 1073 K, and primary solidifying phase details.•Ab initio method calculates the energy of formation of Ni-Si-Zr intermetallic phases.•Clarify the number of Ni-Si-Zr intermetallic phases and their compositionscompositions.•CALPHAD-type modeling of Ni-Si-Zr system.
This paper is aimed at optimizing the synchronizability of a complex network when the total of its edge weights is given and fixed. We try to allocate edge weights on a complex network to optimize ...the network's synchronizability from the perspective of spectral graph theory. Most of the existing analysis on multilayer networks assumes the weights of intralayer or interlayer edges to be identical. Such a restrictive assumption is not made in this work. Using the graph comparison based method, different edge weights are allocated according to topological features of networks, which is more reasonable and consistent with most physical complex networks. Furthermore, in order to find out the best edge-weight allocation scheme, we carried out numerical simulations on typical duplex networks and real-world networks. The simulation results show that our proposed edge-weight allocation schemes outperform the average, degree-based, and edge betweenness centrality allocations.
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