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Network ecology is an emerging field that allows researchers to conceptualize and analyse ecological networks and their dynamics. Here, we focus on the dynamics of ecological networks in response to environmental changes. Specifically, we formalize how network topologies constrain the dynamics of ecological systems into a unifying framework in network ecology that we refer to as the ‘ecological network dynamics framework’. This framework stresses that the interplay between species interaction networks and the spatial layout of habitat patches is key to identifying which network properties (number and weights of nodes and links) and trade-offs among them are needed to maintain species interactions in dynamic landscapes. We conclude that to be functional, ecological networks should be scaled according to species dispersal abilities in response to landscape heterogeneity. Determining how such effective ecological networks change through space and time can help reveal their complex dynamics in a changing world.

Background Dysbiosis, an imbalance in the bacterial composition of the human gut microbiota, is linked to inflammatory bowel disease (IBD). Advances in biological techniques have generated vast microbiota datasets, presenting both opportunities and challenges for clinical research in that field. Network theory offers powerful tools to analyze these complex datasets. Methods Utilizing genetically unrelated individuals from the Kiel IBD-KC cohort, we compared network properties of the gut microbiota between patients with inflammatory bowel disease (IBD, n  = 522) and healthy controls ( n  = 365), and between Crohn's disease (CD, n  = 230) and Ulcerative Colitis (UC, n  = 280). Correlation-based microbial networks were constructed, with genera as nodes and significant pairwise correlations as edges. We used centrality measures to identify key microbial constituents, called hubs, and suggest a network-based definition for a core microbiota. Using Graphlet theoretical approaches, we analyzed network topology and individual node roles. Results Global network properties differed between cases and controls, with controls showing a potentially more robust network structure characterized by e.g., a greater number of components and a lower edge density. Local network properties varied across all groups. For cases and both UC and CD, Faecalibacterium and Veillonella , and for unaffected controls Bacteroides , Blautia , Clostridium XIVa , and Clostridium XVIII emerged as unique hubs in the respective networks. Graphlet analysis revealed significant differences in terminal node orbits among all groups. Four genera which act as hubs in one state, were found to be terminal nodes in the opposite disease state: Bacteroides , Clostridium XIVa , Faecalibacterium , and Subdoligranulum . Comparing our network-based core microbiota definition with a conventional one showed an overlap in approximately half of the core taxa, while core taxa identified through our new definition maintained high abundance. Conclusion The network-based approach complements previous investigations of alteration of the human gut microbiota in IBD by offering a different perspective that extends beyond a focus solely on highly abundant taxa. Future studies should further investigate functional roles of hubs and terminal nodes as potential targets for interventions and preventions. Additionally, the advantages of the newly proposed network-based core microbiota definition, should be investigated more systematically.

The B-factor or temperature factor is one of the most important parameters in addition to the atomic coordinates, and which is refined during the determination of the protein structure and stored in the Protein Data Bank. It reflects the uncertainty of the atomic positions and is closely linked to atomic flexibility. By using graphlet degree vectors as feature descriptors in a linear model—together with appropriate data transformation and consideration of various experimental factors—the model provides better prediction results. For example, the inclusion of crystal contacts in the linear model significantly improves the prediction accuracy. Since the distributions of the B-factors typically follow an inverse gamma distribution, applying a logarithmic transformation further improves the performance of the model. It has also been shown that large ligands, such as those found in protein–DNA complexes, have a significant impact on the quality of the prediction. A linear model based on graphlet degree vectors proves to be effective not only for the prediction of B-factors and the validation of deposited protein structures but also for the qualitative estimation of root-mean-square fluctuations derived from molecular dynamics.

Volumetric brain reconstructions provide an unprecedented opportunity to gain insights into the complex connectivity patterns of neurons in an increasing number of organisms. Here, we model and quantify the complexity of the resulting neural connectomes in the fruit fly, mouse, and human and unveil a simple set of shared organizing principles across these organisms. To put the connectomes in a physical context, we also construct contactomes, the network of neurons in physical contact in each organism. With these, we establish that physical constraints—either given by pairwise distances or the contactome—play a crucial role in shaping the network structure. For example, neuron positions are highly optimal in terms of distance from their neighbors. Yet, spatial constraints alone cannot capture the network topology, including the broad degree distribution. Conversely, the degree sequence alone is insufficient to recover the spatial structure. We resolve this apparent mismatch by formulating scalable maximum entropy models, incorporating both types of constraints. The resulting generative models have predictive power beyond the input data, as they capture several additional biological and network characteristics, like synaptic weights and graphlet statistics. We investigate the interplay of the spatial and topological structure of millimeter-scale neural connectomes in fly, mouse, and human. As a spatial observation, we demonstrate that the probability of synaptic connection decays exponentially with distance. Additionally, we show that the wiring length in neural connectomes is highly optimal. To quantify the physical constraints on synapse formation, we construct the physical contact network for each organism and demonstrate that contact edge probability follows the same exponential functional form as the connectome. At the same time, we show that spatial constraints are necessary but not sufficient to reconstruct the connectome topology. We present maximum-entropy models capturing key spatial and topological aspects of the connectomes and demonstrate their predictive power beyond the input data.

Clique counting is a crucial task in graph mining, as the count of cliques provides different insights across various domains, social and biological network analysis, community detection, recommendation systems, and fraud detection. Counting cliques is algorithmically challenging due to combinatorial explosion, especially for large datasets and larger clique sizes. There are comprehensive surveys and reviews on algorithms for counting subgraphs and triangles (three-clique), but there is a notable lack of reviews addressing k-clique counting algorithms for k > 3. This paper addresses this gap by reviewing clique counting algorithms designed to overcome this challenge. Also, a systematic analysis and comparison of exact and approximation techniques are provided by highlighting their advantages, disadvantages, and suitability for different contexts. It also presents a taxonomy of clique counting methodologies, covering approximate and exact methods and parallelization strategies. The paper aims to enhance understanding of this specific domain and guide future research of k-clique counting in large-scale graphs.

The ability to find and count subgraphs of a given network is an important non trivial task with multidisciplinary applicability. Discovering network motifs or computing graphlet signatures are two examples of methodologies that at their core rely precisely on the subgraph counting problem. Here we present the g-trie, a data-structure specifically designed for discovering subgraph frequencies. We produce a tree that encapsulates the structure of the entire graph set, taking advantage of common topologies in the same way a prefix tree takes advantage of common prefixes. This avoids redundancy in the representation of the graphs, thus allowing for both memory and computation time savings. We introduce a specialized canonical labeling designed to highlight common substructures and annotate the g-trie with a set of conditional rules that break symmetries, avoiding repetitions in the computation. We introduce a novel algorithm that takes as input a set of small graphs and is able to efficiently find and count them as induced subgraphs of a larger network. We perform an extensive empirical evaluation of our algorithms, focusing on efficiency and scalability on a set of diversified complex networks. Results show that g-tries are able to clearly outperform previously existing algorithms by at least one order of magnitude.

Background Graphlets are useful for bioinformatics network analysis. Based on the structure of Hočevar and Demšar’s ORCA algorithm, we have created an orbit counting algorithm, named Jesse. This algorithm, like ORCA, uses equations to count the orbits, but unlike ORCA it can count graphlets of any order. To do so, it generates the required internal structures and equations automatically. Many more redundant equations are generated, however, and Jesse’s running time is highly dependent on which of these equations are used. Therefore, this paper aims to investigate which equations are most efficient, and which factors have an effect on this efficiency. Results With appropriate equation selection, Jesse’s running time may be reduced by a factor of up to 2 in the best case, compared to using randomly selected equations. Which equations are most efficient depends on the density of the graph, but barely on the graph type. At low graph density, equations with terms in their right-hand side with few arguments are more efficient, whereas at high density, equations with terms with many arguments in the right-hand side are most efficient. At a density between 0.6 and 0.7, both types of equations are about equally efficient. Conclusions Our Jesse algorithm became up to a factor 2 more efficient, by automatically selecting the best equations based on graph density. It was adapted into a Cytoscape App that is freely available from the Cytoscape App Store to ease application by bioinformaticians.

Despite being very successful within the pattern recognition and machine learning community, graph-based methods are often unusable because of the lack of mathematical operations defined in graph domain. Graph embedding, which maps graphs to a vectorial space, has been proposed as a way to tackle these difficulties enabling the use of standard machine learning techniques. However, it is well known that graph embedding functions usually suffer from the loss of structural information. In this paper, we consider the hierarchical structure of a graph as a way to mitigate this loss of information. The hierarchical structure is constructed by topologically clustering the graph nodes and considering each cluster as a node in the upper hierarchical level. Once this hierarchical structure is constructed, we consider several configurations to define the mapping into a vector space given a classical graph embedding, in particular, we propose to make use of the stochastic graphlet embedding (SGE). Broadly speaking, SGE produces a distribution of uniformly sampled low-to-high-order graphlets as a way to embed graphs into the vector space. In what follows, the coarse-to-fine structure of a graph hierarchy and the statistics fetched by the SGE complements each other and includes important structural information with varied contexts. Altogether, these two techniques substantially cope with the usual information loss involved in graph embedding techniques, obtaining a more robust graph representation. This fact has been corroborated through a detailed experimental evaluation on various benchmark graph datasets, where we outperform the state-of-the-art methods.

MicroRNAs (miRNAs) have been confirmed to be closely related to various human complex diseases by many experimental studies. It is necessary and valuable to develop powerful and effective computational models to predict potential associations between miRNAs and diseases. In this work, we presented a prediction model of Graphlet Interaction for MiRNA‐Disease Association prediction (GIMDA) by integrating the disease semantic similarity, miRNA functional similarity, Gaussian interaction profile kernel similarity and the experimentally confirmed miRNA‐disease associations. The related score of a miRNA to a disease was calculated by measuring the graphlet interactions between two miRNAs or two diseases. The novelty of GIMDA lies in that we used graphlet interaction to analyse the complex relationships between two nodes in a graph. The AUCs of GIMDA in global and local leave‐one‐out cross‐validation (LOOCV) turned out to be 0.9006 and 0.8455, respectively. The average result of five‐fold cross‐validation reached to 0.8927 ± 0.0012. In case study for colon neoplasms, kidney neoplasms and prostate neoplasms based on the database of HMDD V2.0, 45, 45, 41 of the top 50 potential miRNAs predicted by GIMDA were validated by dbDEMC and miR2Disease. Additionally, in the case study of new diseases without any known associated miRNAs and the case study of predicting potential miRNA‐disease associations using HMDD V1.0, there were also high percentages of top 50 miRNAs verified by the experimental literatures.

Predicting the evolution of viral processes on networks is an important problem with applications arising in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used for the prediction of viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks and recent attempts have been made to use assortativity to address this shortcoming. In this paper, we show that adding assortativity does not fully explain the variance in the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution in combination with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data-driven approach by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95% of the variance in virality on networks with the same degree distribution but different network topologies. Our results not only highlight the importance of graphlets but also identify a small collection of graphlets which may have the highest influence over the viral processes on a network.