Building Blocks Of Complex Networks Research Articles

Local Fractional Strong Metric Dimension of Certain Complex Networks

Fractional variants of distance-based parameters have application in the fields of sensor networking, robot navigation, and integer programming problems. Complex networks are exceptional networks which exhibit significant topological features and have become quintessential research area in the field of computer science, biology, and mathematics. Owing to the possibility that many real-world systems can be intelligently modeled and represented as complex networks to examine, administer and comprehend the useful information from these real-world networks. In this paper, local fractional strong metric dimension of certain complex networks is computed. Building blocks of complex networks are considered as the symmetric networks such as cyclic networks C n , circulant networks C n 1,2 , mobious ladder networks M 2 n , and generalized prism networks G m n . In this regard, it is shown that LSFMD of C n n ≥ 3 and G m n n ≥ 6 is 1 when n is even and n / n − 1 when n is odd, whereas LSFMD of M 2 n is 1 when n is odd and n / n − 1 when n is even. Also, LSFMD of C n 1,2 is n / 2 ⌈ m + 1 / 2 ⌉ where n ≥ 6 and m = ⌈ n − 5 / 4 ⌉ .

MuMod: A Micro-Unit Connection Approach for Hybrid-Order Community Detection

In the past few years, higher-order community detection has drawn an increasing amount of attention. Compared with the lower-order approaches that rely on the connectivity pattern of individual nodes and edges, the higher-order approaches discover communities by leveraging the higher-order connectivity pattern via constructing a motif-based hypergraph. Despite success in capturing the building blocks of complex networks, recent study has shown that the higher-order approaches unavoidably suffer from the hypergraph fragmentation issue. Although an edge enhancement strategy has been designed previously to address this issue, adding additional edges may corrupt the original lower-order connectivity pattern. To this end, this paper defines a new problem of community detection, namely hybrid-order community detection, which aims to discover communities by simultaneously leveraging the lower-order connectivity pattern and the higherorder connectivity pattern. For addressing this new problem, a new Micro-unit Modularity (MuMod) approach is designed. The basic idea lies in constructing a micro-unit connection network, where both of the lower-order connectivity pattern and the higher-order connectivity pattern are utilized. And then a new micro-unit modularity model is proposed for generating the micro-unit groups, from which the overlapping community structure of the original network can be derived. Extensive experiments are conducted on five real-world networks. Comparison results with twelve existing approaches confirm the effectiveness of the proposed method.

Plant diversity alters the representation of motifs in food webs

Changes in the diversity of plant communities may undermine the economically and environmentally important consumer species they support. The structure of trophic interactions determines the sensitivity of food webs to perturbations, but rigorous assessments of plant diversity effects on network topology are lacking. Here, we use highly resolved networks from a grassland biodiversity experiment to test how plant diversity affects the prevalence of different food web motifs, the smaller recurrent sub-networks that form the building blocks of complex networks. We find that the representation of tri-trophic chain, apparent competition and exploitative competition motifs increases with plant species richness, while the representation of omnivory motifs decreases. Moreover, plant species richness is associated with altered patterns of local interactions among arthropod consumers in which plants are not directly involved. These findings reveal novel structuring forces that plant diversity exerts on food webs with potential implications for the persistence and functioning of multitrophic communities.

Motif discovery in biological network using expansion tree.

Networks are powerful representation of topological features in biological systems like protein interaction and gene regulation. In order to understand the design principles of such complex networks, the concept of network motifs emerged. Network motifs are recurrent patterns with statistical significance that can be seen as basic building blocks of complex networks. Identification of network motifs leads to many important applications, such as understanding the modularity and the large-scale structure of biological networks, classification of networks into super-families, protein function annotation, etc. However, identification of network motifs is challenging as it involves graph isomorphism which is computationally hard. Though this problem has been studied extensively in the literature using different computational approaches, we are far from satisfactory results. Motivated by the challenges involved in this field, an efficient and scalable network Motif Discovery algorithm based on Expansion Tree (MODET) is proposed. Pattern growth approach is used in this proposed motif-centric algorithm. Each node of the expansion tree represents a non-isomorphic pattern. The embeddings corresponding to a child node of the expansion tree are obtained from the embeddings of the parent node through vertex addition and edge addition. Further, the proposed algorithm does not involve any graph isomorphism check and the time complexities of these processes are and , respectively. The proposed algorithm has been tested on Protein-Protein Interaction (PPI) network obtained from the MINT database. The computational efficiency of the proposed algorithm outperforms most of the existing network motif discovery algorithms.

Motif-aware diffusion network inference

Diffusion processes over networks are widely encountered in various real-world applications. In many scenarios, however, only the states of nodes can be observed while the underlying diffusion networks are unknown. Many methods have therefore been proposed to infer the underlying networks based on node observations. To enhance the inference performance, structural priors of the networks, such as sparsity, scale-free, and community structures, are often incorporated into the learning procedure. As the building blocks of complex networks, motifs occur frequently in many real-world networks and play a vital role in describing the network structures and functionalities. However, to the best of our knowledge, no existing work has attempted to infer the diffusion network through exploiting network motifs. In order to explore this uncharted yet important issue, in this paper, we propose a novel framework called motif-aware diffusion network inference (MADNI), which aims to mine the motif profile from the node observations and infer the underlying network based on the mined motif profile. The mined motif profile and the inferred network are alternately refined until the learning procedure converges. We derive two network inference models in our framework for inferring the individual-level diffusion network and the meta-population-level diffusion network, respectively. Extensive experiments on both synthetic and real-world datasets validate the effectiveness of the proposed framework. Moreover, we show the generality of MADNI by analyzing the relations between mesoscale motif prior in our framework and other high-level structural priors such as community and scale-free properties in the existing works.

Detection of Network Motif Based on a Novel Graph Canonization Algorithm from Transcriptional Regulation Networks.

Network motifs are patterns of complex networks occurring significantly more frequently than those in random networks. They have been considered as fundamental building blocks of complex networks. Therefore, the detection of network motifs in transcriptional regulation networks is a crucial step in understanding the mechanism of transcriptional regulation and network evolution. The search for network motifs is similar to solving subgraph searching problems, which has proven to be NP-complete. To quickly and effectively count subgraphs of a large biological network, we propose a novel graph canonization algorithm based on resolving sets. This method has been implemented in a command line interface (CLI) program sgip using the SeqAn library. Comparing to Babai’s algorithm, this approach has a tighter complexity bound, , on strongly regular graphs. Results on several simulated datasets and transcriptional regulation networks indicate that sgip outperforms nauty on many graph cases. The source code of sgip is freely accessible in https://github.com/seqan/seqan/tree/master/apps/sgip and the binary code in http://packages.seqan.de/sgip/.

Vibrational resonance in feed-forward-loop neuronal network motifs

A neuron carries out its functions in networks receiving contacts from roughly 104 presynaptic neurons. Such a dense connectivity profile for a single neuron may give rise to enormous complex neuronal topologies, which might be very difficult to understand the underlying mechanisms of neurological functions and diseases. Extensive experimental data from neuroanatomical studies have uncovered that neural networks include some recurring topologies of microcircuits, known as network motifs which serve as characteristic building blocks of complex networks [1,2]. Therefore, it is widely assumed that a clear explanation on dynamical and functional features of these network motifs can be considered as the first step to understand large networks. Following this motivation, in this study, we investigate the Vibrational Resonance (VR) phenomenon in a triple-neuron feed-forward-loop (FFL) which is one of the most significant brain network motifs, shown in Figure ​Figure1.1. VR is a physical phenomenon found in nonlinear systems where a weak signal can be detected and processed by the system with the assistance of another high frequency signal. It is very similar to the well-known stochastic resonance phenomenon, where the role of noise is replaced in VR by a high frequency signal. In recent years, there exists a growing interest in applications of VR to neuroscience because two frequency signals are pervasive in neural systems, i.e. bursting neurons exhibit two widely different time scales, simultaneous arrival of vocal signals having distinct frequencies to auditory neurons. Due to the significance of its potential in neural signal processing, the VR phenomenon has already been studied with computational models of neurons and their networks [3,4]. However, a population of excitatory and inhibitory neurons has not been considered, yet. Here, we study the VR dynamics depending on whether the neurons in the FFL motifs are excitatory or inhibitory considering eight possible structural configurations of the considered microcircuit (Table ​(Table1).1). Such an approach provides us to test the functional influences of structural configuration on VR dynamics in neural populations. Figure 1 Schematic illustration of the considered feed-forward-loop motif. LF and HF refers to low and high frequency signals, respectively. Neuron 1 and 3 is considered as input and output neurons, respectively. Table 1 Eight possible FFL types. We found that the weak signal transmission in the network via the VR mechanism is possible depending on both the coupling strength between neurons and the network structure. For instance, when a weak coupling strength is present between connected neurons, weak signal injected to the input neuron can be transmitted to the output with only T8-FFL motif. In this case, signal transmission is impossible for other types of network motifs. For intermediate coupling strengths, signal transmission performance is high for all motifs and motif type does not change very much VR dynamics. Finally, for strong coupling strengths, the best VR performance is obtained with T1-FFL motif where all the neurons in the network are excitatory. We also clarify the mechanisms that underlies the differences in performance of network motifs.

Species’ roles in food webs show fidelity across a highly variable oak forest

Ecological communities are composed of many species and an intricate network of interactions between them. Because of their overall complexity, an intriguing approach to understanding network structure is by breaking it down into the structural roles of its constituent species. The structural role of a species can be directly measured based on how it appears in network motifs – the basic building blocks of complex networks. Here, we study the distribution of species’ roles at three distinct spatio‐temporal scales (i.e. species, network, and temporal) in host–parasitoid networks collected across 22 sites over two years within a fragmented landscape of oaks in southern Finland. We found that species’ roles for hosts and parasitoids were heterogeneously distributed across the study system but that roles are strongly conserved over spatial scales. In addition, we found that species’ roles were remarkably consistent between years even in the presence of disturbances (e.g. species turnover). Overall, our results suggest that species’ roles are an intrinsic property of species that may be predictable over spatial and temporal scales.

Motifs in triadic random graphs based on Steiner triple systems

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade, the overabundance of certain subnetwork patterns, i.e., the so-called motifs, has attracted much attention. It has been hypothesized that these motifs, instead of links, serve as the building blocks of network structures. Although the relation between a network's topology and the general properties of the system, such as its function, its robustness against perturbations, or its efficiency in spreading information, is the central theme of network science, there is still a lack of sound generative models needed for testing the functional role of subgraph motifs. Our work aims to overcome this limitation. We employ the framework of exponential random graph models (ERGMs) to define models based on triadic substructures. The fact that only a small portion of triads can actually be set independently poses a challenge for the formulation of such models. To overcome this obstacle, we use Steiner triple systems (STSs). These are partitions of sets of nodes into pair-disjoint triads, which thus can be specified independently. Combining the concepts of ERGMs and STSs, we suggest generative models capable of generating ensembles of networks with nontrivial triadic Z-score profiles. Further, we discover inevitable correlations between the abundance of triad patterns, which occur solely for statistical reasons and need to be taken into account when discussing the functional implications of motif statistics. Moreover, we calculate the degree distributions of our triadic random graphs analytically.

Motif statistics and spike correlations in neuronal networks

Motifs are patterns of subgraphs that are the building blocks of complex networks. Recent experiments have characterized the frequencies with which different motifs occur in biological neural networks, and found remarkable deviations from what we would expect if the networks were randomly connected [1]. Here, we study the impact of such patterns of connectivity on the level of correlated, or synchronized, spiking activity among pairs of cells. Correlations in spiking activity have been shown to strongly impact the neural coding of information. We use a linear, stochastic model of recurrent networks. A cell’s time-dependent firing rate is perturbed from its baseline level by convolution of a response kernel and the input signal from presynaptic neurons. Each neuron generates spikes as an inhomogeneous Poisson process. Previous studies have shown that such models can capture pairwise correlations in integrate and fire networks [2,3], and they are closely related to spike response and Hawkes models [4,6]. For this model, there is an explicit expression for pairwise correlation in terms of the connectivity matrix. By expanding this expression in a series, one can relate each term to a different motif (with a different number of connections). Through a resumming technique, we show that the average correlation across the network can be closely approximated using the frequencies of only first and second order motifs. These are the diverging motif—two cells both receiving projections from another cell, its counterpart the converging motif—two cells projecting to a common cell, and the chain motif—three cells linked by two consecutive projections. Specifically, we show that the prevalence of diverging and chain motifs tends to increase correlation, while the converging motif makes no contribution to the average correlation. Moreover, we numerically show that variance of correlations across the network is largely determined by the frequency of the chain motif (see Figure ​Figure1)1) alone. Finally, we demonstrate potential effect of motif statistics on neural coding by showing how motif frequencies impact linear Fisher information. In particular, we find that the linear Fisher information is only affected by converging motif frequency (more information with given more converging motifs). Figure 1 Each dot represent one network sample plotted against its chain and diverging motif frequencies. Color shows the standard deviation of correlations in the network. Inset is the same plot with respect to diverging and converging motifs.

Biological network motif detection: principles and practice

Network motifs are statistically overrepresented sub-structures (sub-graphs) in a network, and have been recognized as 'the simple building blocks of complex networks'. Study of biological network motifs may reveal answers to many important biological questions. The main difficulty in detecting larger network motifs in biological networks lies in the facts that the number of possible sub-graphs increases exponentially with the network or motif size (node counts, in general), and that no known polynomial-time algorithm exists in deciding if two graphs are topologically equivalent. This article discusses the biological significance of network motifs, the motivation behind solving the motif-finding problem, and strategies to solve the various aspects of this problem. A simple classification scheme is designed to analyze the strengths and weaknesses of several existing algorithms. Experimental results derived from a few comparative studies in the literature are discussed, with conclusions that lead to future research directions.

8.1.2 Overrepresented and Underrepresented Patterns in System Architectures Across Diverse Engineering Systems

AbstractRecent years have witnessed new research interest in the study of complex systems architectures, in domains like biological systems, social networks etc. Seminal works covering each of these systems have appeared in high impact journals like Nature, Science, etc. Unifying principles have emerged and helped in gaining new understanding in a domain by extending the understanding gained in other domains. These developments in complex systems open up possibilities in the research into architectures of complex engineering systems. Complex engineering systems are synthesized from large number of components giving it a physical architecture. We abstract the physical architecture of different engineering systems as a network/graph, where the nodes/vertices correspond to components and edges correspond to interconnections between them. Complex systems research in biology defines motifs as recurring sub‐graphs from which the network is built. They also argue motifs as simple building blocks of complex networks, offering a way to understand the basic functionality of a system. In this paper, we explore 32 arbitrarily chosen engineering systems architectures for motifs. We discover motifs within each system and also interesting motif templates across systems.

GraphCrunch: A tool for large network analyses

BackgroundThe recent explosion in biological and other real-world network data has created the need for improved tools for large network analyses. In addition to well established global network properties, several new mathematical techniques for analyzing local structural properties of large networks have been developed. Small over-represented subgraphs, called network motifs, have been introduced to identify simple building blocks of complex networks. Small induced subgraphs, called graphlets, have been used to develop "network signatures" that summarize network topologies. Based on these network signatures, two new highly sensitive measures of network local structural similarities were designed: the relative graphlet frequency distance (RGF-distance) and the graphlet degree distribution agreement (GDD-agreement).Finding adequate null-models for biological networks is important in many research domains. Network properties are used to assess the fit of network models to the data. Various network models have been proposed. To date, there does not exist a software tool that measures the above mentioned local network properties. Moreover, none of the existing tools compare real-world networks against a series of network models with respect to these local as well as a multitude of global network properties.ResultsThus, we introduce GraphCrunch, a software tool that finds well-fitting network models by comparing large real-world networks against random graph models according to various network structural similarity measures. It has unique capabilities of finding computationally expensive RGF-distance and GDD-agreement measures. In addition, it computes several standard global network measures and thus supports the largest variety of network measures thus far. Also, it is the first software tool that compares real-world networks against a series of network models and that has built-in parallel computing capabilities allowing for a user specified list of machines on which to perform compute intensive searches for local network properties. Furthermore, GraphCrunch is easily extendible to include additional network measures and models.ConclusionGraphCrunch is a software tool that implements the latest research on biological network models and properties: it compares real-world networks against a series of random graph models with respect to a multitude of local and global network properties. We present GraphCrunch as a comprehensive, parallelizable, and easily extendible software tool for analyzing and modeling large biological networks. The software is open-source and freely available at . It runs under Linux, MacOS, and Windows Cygwin. In addition, it has an easy to use on-line web user interface that is available from the above web page.

Core transcriptional regulatory circuitry in human hepatocytes

We mapped the transcriptional regulatory circuitry for six master regulators in human hepatocytes using chromatin immunoprecipitation and high-resolution promoter microarrays. The results show that these regulators form a highly interconnected core circuitry, and reveal the local regulatory network motifs created by regulator–gene interactions. Autoregulation was a prominent theme among these regulators. We found that hepatocyte master regulators tend to bind promoter regions combinatorially and that the number of transcription factors bound to a promoter corresponds with observed gene expression. Our studies reveal portions of the core circuitry of human hepatocytes.

Response to Comment on "Network Motifs: Simple Building Blocks of Complex Networks" and "Superfamilies of Evolved and Designed Networks"

Our previous work (1) presented a phenomenological observation on real-world networks: They show distinct subgraph significance profiles (SP) when compared with randomized networks with the same degree sequence as the real networks. This observation calls for a theory—a model that prescribes evolutionary dynamics or constraints that, once used to evolve a network, yield the observed SPs. The SP method also provides a way to test whether a given theoretical model actually reproduces the local structure of the real network. Selection of network motifs for their function is one such possible theory, which, as we mention below, can and should be tested experimentally; it is certainly not the only possible theory (1, 2).

Transcriptional Networks and Their Relatives

Living cells are the product of gene expression programs involving regulated transcription of thousands of genes. Lee et al. used immunoprecipitation and microarray studies to build a global analysis of transcriptional regulatory networks in Saccharomyces cerevisiae . Patterns observed were characterized as motifs that were then combined by an automatic process into a network structure. Such transcriptional regulation represents a network of interactions, and similar networks underlie apparently unrelated systems, such as food webs and electronic circuits. To examine their fundamental design features, Milo et al. (see the Perspective by Oltvai and Barabási) looked at local organizing principles of networks, expressed as motifs of how different interactors are joined, that occurred at more than random frequencies. Motifs shared by food webs had features that were not shared by transcription networks from yeast and from Escherichia coli or by electronic circuits, although similarities were seen in information-processing circuits. T. I. Lee, N. J. Rinaldi, F. Robert, D. T. Odom, Z. Bar-Joseph, G. K. Gerber, N. M. Hannett, C. T. Harbison, C. M. Thompson, I. Simon, J. Zeitlinger, E. G. Jennings, H, L. Murray, D. B. Gordon, B. Ren, J. J. Wyrick, J.-B. Tagne, T. L. Volkert, E. Fraenkel, D. K. Gifford, R. A. Young, Transcriptional regulatory networks in Saccharomyces cerevisiae . Science 298 , 799-804 (2002). [Abstract] [Full Text] R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, U. Alon, Network motifs: Simple building blocks of complex networks. Science 298 , 824-827 (2002). [Abstract] [Full Text] Z. N. Oltvai, A.-L. Barabási, Life's complexity pyramid. Science 298 , 763-764 (2002). [Summary] [Full Text]