Scale-free Topology Research Articles

What Drives the Assembly of Plant-associated Protist Microbiomes? Investigating the Effects of Crop Species, Soil Type and Bacterial Microbiomes

In a field experiment we investigated the influence of the environmental filters soil type (i.e. three contrasting soils) and plant species (i.e. lettuce and potato) identity on rhizosphere community assembly of Cercozoa, a dominant group of mostly bacterivorous soil protists. Plant species (14%) and rhizosphere origin (vs bulk soil) with 13%, together explained four times more variation in cercozoan beta diversity than the three soil types (7% explained variation). Our results clearly confirm the existence of plant species-specific protist communities. Network analyses of bacteria-Cercozoa rhizosphere communities identified scale-free small world topologies, indicating mechanisms of self-organization. While the assembly of rhizosphere bacterial communities is bottom-up controlled through the resource supply from root (secondary) metabolites, our results support the hypothesis that the net effect may depend on the strength of top-down control by protist grazers. Since grazing of protists has a strong impact on the composition and functioning of bacteria communities, protists expand the repertoire of plant genes by functional traits, and should be considered as 'protist microbiomes' in analogy to 'bacterial microbiomes'.

Disassortative Mixing and Systemic Rational Behaviour: How System Rationality Is Influenced by Topology and Placement in Networked Systems

Interdependent decisionmaking of individuals in social systems can be modelled by games played on complex networks. Players in such systems have bounded rationality, which influences the computation of equilibrium solutions. It has been shown that the ‘system rationality’, which indicates the overall rationality of a network of players, may play a key role in the emergence of scale-free or core-periphery topologies in real-world networks. In this work, we identify optimal topologies and mixing patterns of players which can maximise system rationality. Based on simulation results, we show that irrespective of the placement of nodes with higher rationality, it is the disassortative mixing of node rationality that helps to maximize system rationality in a population. In other words, the findings of this work indicate that the overall rationality of a population may improve when more players with non-similar individual rationality levels interact with each other. We identify particular topologies such as the core-periphery topology, which facilitates the optimisation of system rationality. The findings presented in this work may have useful interpretations and applications in socio-economic systems for maximizing the utility of interactions in a population of strategic players.

Performance Analysis of Consensus Algorithms Over Prism Networks Using Laplacian Spectra

Prism networks belong to generalized petersen graph topologies with planar and polyhedral properties. These networks are extensively used to study the complex networks in the context of computer science, biological networks, brain networks, and social networks. In this letter, the performance analysis of consensus algorithms over prism networks is investigated in terms of convergence time, network coherence, and communication delay. Specifically, in this letter, we first derive the explicit expressions for eigenvalues of Laplacian matrix over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional prism networks using spectral graph theory. Subsequently, the study of consensus metrics such as convergence time, maximum communication time delay, first order network coherence, and second order network coherence is performed. Our results indicate that the effect of noise and communication time-delay on the consensus dynamics in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional prism networks is minimal. The obtained results illustrate that the scale-free topology of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional prism networks along with loopy structure is responsible for strong robustness with respect to consensus dynamics in prism networks.

Functional insights of antibiotic resistance mechanism in Helicobacter pylori: Driven by gene interaction network and centrality-based nodes essentiality analysis

Increased antibiotic resistance in Helicobacter pylori (H. pylori), a major human pathogen, constitutes a substantial threat to human health. Understanding the pathophysiology and development of antibiotic resistance can aid our battle with the infections caused by H. pylori. The aim of this study is to discover the high-impact key regulatory mechanisms and genes involved in antimicrobial drug resistance (AMR). In this study, we constructed a functional gene interaction network by integrating multiple sources of data related to antibiotic resistant genes (number-77) from H. pylori. The gene interaction network was assortative, with a hierarchical, scale-free topology enriched in a variety of gene ontology (GO) categories and KEGG pathways. Using an iterative clustering methodology, we identified a number of communities in the AMR gene network that comprised nine genes (sodB, groEL, gyrA, recA, polA, tuf, infB, rpsJ, and gyrB) that were present at the deepest level and hence were key regulators of AMR. Further, an antibiotic-resistant gene network-based centrality analysis revealed superoxide dismutase (sodB) as a bottleneck node in the network. Our findings suggested that sodB is critically enriched in the cellular response to oxidative stress, removal of superoxide radicals, cellular oxidant detoxification processes, cellular component biogenesis, response to reactive oxygen species, urea metabolic process, nitrogen cycle metabolic process and reactive oxygen species metabolic process. We demonstrated how the sodB, which are involved in the response to reactive oxygen species, urea metabolic process, nitrogen cycle metabolic process, reactive oxygen species metabolic process, regulated by Fur gene/proteins, claim a major authority over regulation and signal propagation in the AMR.

Enhancing Firefly Algorithm with Dual-Population Topology Coevolution

The firefly algorithm (FA) is a meta-heuristic swarm intelligence optimization algorithm. It simulates the social behavior of fireflies with their flash and attraction characteristics. Numerous researches showed that FA can successfully deal with some problems. However, too many attractions between the fireflies may result in high computational complexity, slow convergence, low solution accuracy and poor algorithm stability. To overcome these issues, this paper proposes an enhanced firefly algorithm with dual-population topology coevolution (DPTCFA). In DPTCFA, to maintain population diversity, a dual-population topology coevolution mechanism consisting of the scale-free and ring network topology is proposed. The scale-free network topology structure conforms to the distribution law between the optimal and potential individuals, and the ring network topology effectively reduces the attractions, and thereby has a low computational complexity. The Gauss map strategy is introduced in the scale-free network topology population to lower parameter sensitivity, and in the ring network topology population, a new distance strategy based on dimension difference is adopted to speed up the convergence. This paper improves a diversity neighborhood enhanced search strategy for firefly position update to increase the solution quality. In order to balance the exploration and exploitation, a staged balance mechanism is designed to enhance the algorithm stability. Finally, the performance of the proposed algorithm is verified via several well-known benchmark functions. Experiment results show that DPTCFA can efficiently improve the existing problems of FA to obtain better solutions.

Endothelial signalling operates on a small‐world network to control vascular function

The endothelium is the innermost layer of all blood vessels and it controls a host of cardiovascular functions including vascular contractility, hemostasis, inflammation and the exchange of nutrients and waste products between circulating blood and tissue. The importance of the endothelium is clear since changes in the behaviour of this single layer of cells underlies almost all cardiovascular disease. To control each cardiovascular function, the endothelium processes and responds to endless streams of information that originate from multiple sources (i.e. blood cells, hormones, neighboring endothelial cells or underlying smooth muscle cells). To process so much information, the endothelium utilises distributed sensing on spatially‐distinct populations of cells that are primed to detect specific activators. These spatially‐distinct populations communicate across the endothelial network to coordinate vascular responses. The nature of the endothelial network, and how communication is achieved, is currently not understood. Here, by examining the Ca2+ responses in thousands of endothelial cells in intact arteries, we show how the endothelial network operates.Network organization controls overall system behaviour by determining the signal propagation speed, the robustness of the system to failures and attack, and the degree of synchronizability in the system. To determine the endothelial network structure, we used network (graph) theory. Graph theory has gained much attention due to its ability to quantify social, technological and biological systems, especially the connectivity and synchronisation of the nervous system. However, no studies have examined the network structure employed by the endothelium in the control of cardiovascular function. We analysed muscarinic‐ and histaminergic‐evoked Ca2+ activity from ~1000 endothelial cells from intact resistance arteries. Ca2+ signals were separately analysed in each of the 1000 individual endothelial cells using a custom‐written Python algorithm.Ca2+ activity in active cells was cross‐correlated and compared to a stochastic model to statistically quantify network connections. We show highly‐correlated Ca2+ activities occurred in multiple, separate, cell clusters for each agonist. The network communication links between the clusters exhibited unexpectedly short path‐lengths, i.e. the number of links between active cells was significantly shorter than expected when active cells were randomly positioned. The number of connections between active cells (degree distribution) followed a power‐law relationship, revealing a scale‐free network topology. The path‐length and degree distribution reveal an endothelial network with a ‘small‐world’ configuration. The small‐world configuration confers particularly dynamic endothelial properties including high signal‐propagation speed, stability and a high degree of synchronizability.These findings show that endothelial network design is effective for local and global efficiency in the interaction of cells, and for rapid and robust communication to efficiently control cardiovascular activity. The network organization explains how coordinated cell activity occurs across large regions of endothelium, despite sensing being distributed on spatially‐distinct populations of cells.

Robustness of noisy quantum networks

Quantum networks allow us to harness networked quantum technologies and to develop a quantum internet. But how robust is a quantum network when its links and nodes start failing? We show that quantum complex networks based on typical noisy quantum-repeater nodes are prone to discontinuous phase transitions with respect to the random loss of operating links and nodes, abruptly compromising the connectivity of the network, and thus significantly limiting the reach of its operation. Furthermore, we determine the critical quantum-repeater efficiency necessary to avoid this catastrophic loss of connectivity as a function of the network topology, the network size, and the distribution of entanglement in the network. From all the network topologies tested, a scale-free network topology shows the best promise for a robust large-scale quantum internet.

Small-world connectivity dictates collective endothelial cell signaling

Every blood vessel is lined by a single layer of highly specialized, yet adaptable and multifunctional endothelial cells. These cells, the endothelium, control vascular contractility, hemostasis, and inflammation and regulate the exchange of oxygen, nutrients, and waste products between circulating blood and tissue. To control each function, the endothelium processes endlessly arriving requests from multiple sources using separate clusters of cells specialized to detect specific stimuli. A well-developed but poorly understood communication system operates between cells to integrate multiple lines of information and coordinate endothelial responses. Here, the nature of the communication network has been addressed using single-cell Ca2+ imaging across thousands of endothelial cells in intact blood vessels. Cell activities were cross-correlated and compared to a stochastic model to determine network connections. Highly correlated Ca2+ activities occurred in scattered cell clusters, and network communication links between them exhibited unexpectedly short path lengths. The number of connections between cells (degree distribution) followed a power-law relationship revealing a scale-free network topology. The path length and degree distribution revealed an endothelial network with a “small-world” configuration. The small-world configuration confers particularly dynamic endothelial properties including high signal-propagation speed, stability, and a high degree of synchronizability. Local activation of small clusters of cells revealed that the short path lengths and rapid signal transmission were achieved by shortcuts via connecting extensions to nonlocal cells. These findings reveal that the endothelial network design is effective for local and global efficiency in the interaction of the cells and rapid and robust communication between endothelial cells in order to efficiently control cardiovascular activity.

Network Theoretical Approach to Explore Factors Affecting Signal Propagation and Stability in Dementia's Protein-Protein Interaction Network.

Dementia—a syndrome affecting human cognition—is a major public health concern given to its rising prevalence worldwide. Though multiple research studies have analyzed disorders such as Alzheimer’s disease and Frontotemporal dementia using a systems biology approach, a similar approach to dementia syndrome as a whole is required. In this study, we try to find the high-impact core regulating processes and factors involved in dementia’s protein–protein interaction network. We also explore various aspects related to its stability and signal propagation. Using gene interaction databases such as STRING and GeneMANIA, a principal dementia network (PDN) consisting of 881 genes and 59,085 interactions was achieved. It was assortative in nature with hierarchical, scale-free topology enriched in various gene ontology (GO) categories and KEGG pathways, such as negative and positive regulation of apoptotic processes, macroautophagy, aging, response to drug, protein binding, etc. Using a clustering algorithm (Louvain method of modularity maximization) iteratively, we found a number of communities at different levels of hierarchy in PDN consisting of 95 “motif-localized hubs”, out of which, 7 were present at deepest level and hence were key regulators (KRs) of PDN (HSP90AA1, HSP90AB1, EGFR, FYN, JUN, CELF2 and CTNNA3). In order to explore aspects of network’s resilience, a knockout (of motif-localized hubs) experiment was carried out. It changed the network’s topology from a hierarchal scale-free topology to scale-free, where independent clusters exhibited greater control. Additionally, network experiments on interaction of druggable genome and motif-localized hubs were carried out where UBC, EGFR, APP, CTNNB1, NTRK1, FN1, HSP90AA1, MDM2, VCP, CTNNA1 and GRB2 were identified as hubs in the resultant network (RN). We finally concluded that stability and resilience of PDN highly relies on motif-localized hubs (especially those present at deeper levels), making them important therapeutic intervention candidates. HSP90AA1, involved in heat shock response (and its master regulator, i.e., HSF1), and EGFR are most important genes in pathology of dementia apart from KRs, given their presence as KRs as well as hubs in RN.

Generation of Realistic Gene Regulatory Networks by Enriching for Feed-Forward Loops.

The regulatory relationships between genes and proteins in a cell form a gene regulatory network (GRN) that controls the cellular response to changes in the environment. A number of inference methods to reverse engineer the original GRN from large-scale expression data have recently been developed. However, the absence of ground-truth GRNs when evaluating the performance makes realistic simulations of GRNs necessary. One aspect of this is that local network motif analysis of real GRNs indicates that the feed-forward loop (FFL) is significantly enriched. To simulate this properly, we developed a novel motif-based preferential attachment algorithm, FFLatt, which outperformed the popular GeneNetWeaver network generation tool in reproducing the FFL motif occurrence observed in literature-based biological GRNs. It also preserves important topological properties such as scale-free topology, sparsity, and average in/out-degree per node. We conclude that FFLatt is well-suited as a network generation module for a benchmarking framework with the aim to provide fair and robust performance evaluation of GRN inference methods.

An Adaptive Robustness Evolution Algorithm With Self-Competition and its 3D Deployment for Internet of Things

Internet of Things (IoT) includes numerous sensing nodes that constitute a large scale-free network. Optimizing the network topology to increase resistance against malicious attacks is a complex problem, especially on 3-dimension (3D) topological deployment. Heuristic algorithms, particularly genetic algorithms, can effectively cope with such problems. However, conventional genetic algorithms are prone to falling into premature convergence owing to the lack of global search ability caused by the loss of population diversity during evolution. Although this can be alleviated by increasing population size, the additional computational overhead will be incurred. Moreover, after crossover and mutation operations, individual changes in the population are mixed, and loss of optimal individuals may occur, which will slow down the population&#x2019;s evolution. Therefore, we combine the population state with the evolutionary process and propose an Adaptive Robustness Evolution Algorithm (AREA) with self-competition for scale-free IoT topologies. In AREA, the crossover and mutation operations are dynamically adjusted according to population diversity to ensure global search ability. A self-competitive mechanism is used to ensure convergence. We construct a 3D IoT topology that is optimized by AREA. The simulation results demonstrate that AREA is more effective in improving the robustness of scale-free IoT networks than several existing methods.

Small molecules for cell reprogramming: a systems biology analysis.

If somatic stem cells would be able to maintain their regenerative capacity over time, this might, to a great extent, resolve rejuvenation issues. Unfortunately, the pool of somatic stem cells is limited, and they undergo cell aging with a consequent loss of functionality. During the last decade, low molecular weight compounds that are able to induce or enhance cell reprogramming have been reported. They were named “Small Molecules” (SMs) and might present definite advantages compared to the exogenous introduction of stemness-related transcription factors (e.g. Yamanaka’s factors). Here, we undertook a systemic analysis of SMs and their potential gene targets. Data mining and curation lead to the identification of 92 SMs. The SM targets fall into three major functional categories: epigenetics, cell signaling, and metabolic “switchers”. All these categories appear to be required in each SM cocktail to induce cell reprogramming. Remarkably, many enriched pathways of SM targets are related to aging, longevity, and age-related diseases, thus connecting them with cell reprogramming. The network analysis indicates that SM targets are highly interconnected and form protein-protein networks of a scale-free topology. The extremely high contribution of hubs to network connectivity suggests that (i) cell reprogramming may require SM targets to act cooperatively, and (ii) their network organization might ensure robustness by resistance to random failures. All in all, further investigation of SMs and their relationship with longevity regulators will be helpful for developing optimal SM cocktails for cell reprogramming with a perspective for rejuvenation and life span extension.

Functional Complex Networks Based on Operational Architectonics: Application on EEG-based Brain–computer Interface for Imagined Speech

A new method for analyzing brain complex dynamics and states is presented. This method constructs functional brain graphs and is comprised of two pylons: (a) Operational architectonics (OA) concept of brain and mind functioning. (b) Network neuroscience. In particular, the algorithm utilizes OA framework for a non-parametric segmentation of EEG signals, which leads to the identification of change points, namely abrupt jumps in EEG amplitude, called Rapid Transition Processes (RTPs). Subsequently, the time coordinates of RTPs are used for the generation of undirected weighted complex networks fulfilling a scale-free topology criterion, from which various network metrics of brain connectivity are estimated. These metrics form feature vectors, which can be used in machine learning algorithms for classification and/or prediction. The method is tested in classification problems on an EEG-based BCI data set, acquired from individuals during imagery pronunciation tasks of various words/vowels. The classification results, based on a Naïve Bayes classifier, show that the overall accuracies were found to be above chance level in all tested cases. This method was also compared with other state-of-the-art computational approaches commonly used for functional network generation, exhibiting competitive performance. The method can be useful to neuroscientists wishing to enhance their repository of brain research algorithms.

Quantifying the Robustness of Complex Networks with Heterogeneous Nodes

The robustness of a complex network measures its ability to withstand random or targeted attacks. Most network robustness measures operate under the assumption that the nodes in a network are homogeneous and abstract. However, most real-world networks consist of nodes that are heterogeneous in nature. In this work, we propose a robustness measure called fitness-incorporated average network efficiency, that attempts to capture the heterogeneity of nodes using the ‘fitness’ of nodes in measuring the robustness of a network. Further, we adopt the same measure to compare the robustness of networks with heterogeneous nodes under varying topologies, such as the scale-free topology or the Erdős–Rényi random topology. We apply the proposed robustness measure using a wireless sensor network simulator to show that it can be effectively used to measure the robustness of a network using a topological approach. We also apply the proposed robustness measure to two real-world networks; namely the CO2 exchange network and an air traffic network. We conclude that with the proposed measure, not only the topological structure, but also the fitness function and the fitness distribution among nodes, should be considered in evaluating the robustness of a complex network.

Toward robust and energy-efficient clustering wireless sensor networks: A double-stage scale-free topology evolution model

Establishing a scale-free topology is widely regarded as one of the effective methods that can significantly improve the fault tolerance performance of wireless sensor networks (WSNs). However, the scale-free topology is very vulnerable to malicious attacks in which the nodes with high importance are attacked first, and its energy efficiency is also unsatisfactory. Therefore, how to build a comprehensively robust and energy-efficient WSN becomes a challenging issue. To address this issue, the paper proposes a Robust and Energy-efficient Scale-free double stage Topology evolution model (REST). In the first stage of REST, a scale-free backbone topology is built to achieve good fault tolerance, and in the second stage, the backbone topology is optimized using a memetic evolutionary algorithm to achieve good intrusion tolerance and energy efficiency. The topology constructed by REST is organized in a clustering manner, which is applicable to most task scenarios. Analytical and simulation results have demonstrated that REST can obtain a more satisfactory topological structure spending less time than existing algorithms.

A cuckoo search algorithm with scale-free population topology

The scale-free network is an important type of complex network. The node degrees in a scale-free network follow the power-law distribution. In the skeleton of a scale-free network, there exists a few nodes which own huge neighborhood size and play an important role in information transmission of the entire network, while most of the network nodes have few connections whose influences of information exchange are limited to a relatively low level. In this paper, we introduce a scale-free population topology into the cuckoo search (CS) algorithm to propose a novel variant, which is termed the scale-free cuckoo search (SFCS) algorithm. Unlike other CS algorithms where the individuals exchange information randomly, two properties of the scale-free network can improve the SFCS algorithm in two aspects: the possibility that the information of competent individuals quickly floods the whole population is reduced significantly, which guarantees population diversity; and the corrupt individuals can learn from competent individuals with greater probability, which is beneficial for convergence. Thus, SFCS can obtain a better trade-off between exploitation and exploration during the search process. To evaluate the effectiveness of the proposed SFCS, 58 benchmark functions with different dimensions (10-D, 30-D, and 50-D), and 21 real-world optimization problems are employed in our experiment. We compare SFCS with the basic CS algorithm, two CS variants, and five state-of-the-art optimization algorithms, and the experimental results and statistical analysis verify the superiority of SFCS in terms of solution quality and convergence speed. Furthermore, we compare SFCS with a scale-free fully informed particle swarm optimization algorithm (SFIPSO) and the results prove our scale-free idea is effective despite its simplicity. We also introduce the scale-free population topology into the differential evolution (DE) and the firefly algorithm (FA) and the experimental results show that the scale-free population topology enhance the search ability of the DE and FA. These lead us to believe that the scale-free population topology may be a new technique for improving the performance of the population-based algorithms.

EDGE DOMINATION NUMBER AND THE NUMBER OF MINIMUM EDGE DOMINATING SETS IN PSEUDOFRACTAL SCALE-FREE WEB AND SIERPIŃSKI GASKET

As a fundamental research object, the minimum edge dominating set (MEDS) problem is of both theoretical and practical interest. However, determining the size of a MEDS and the number of all MEDSs in a general graph is NP-hard, and it thus makes sense to find special graphs for which the MEDS problem can be exactly solved. In this paper, we study analytically the MEDS problem in the pseudofractal scale-free web and the Sierpiński gasket with the same number of vertices and edges. For both graphs, we obtain exact expressions for the edge domination number, as well as recursive solutions to the number of distinct MEDSs. In the pseudofractal scale-free web, the edge domination number is one-ninth of the number of edges, which is three-fifths of the edge domination number of the Sierpiński gasket. Moreover, the number of all MEDSs in the pseudofractal scale-free web is also less than that corresponding to the Sierpiński gasket. We argue that the difference of the size and number of MEDSs between the two studied graphs lies in the scale-free topology.

Analysis on cascading robustness of energy-balanced scale-free wireless sensor networks

Existing studies on cascading failure of scale-free wireless sensor networks (WSNs) fail to take into consideration the impact of the sink node. On the one hand, this limitation makes the generated scale-free topology cannot meet the performance requirements of WSNs in terms of energy balance; on the other hand, it makes the cascading model cannot reasonably characterize the cascading process of WSNs. Therefore, this paper presents a novel scale-free topology evolution model, which introduces a new influencing factor “route-oriented path load” into the preferential attachment mechanism to improve the network load balancing. On this basis, we develop a practical cascading model for WSNs. The experimental results have shown that the proposed scale-free evolution model can obtain promising performance in both energy balancing and network robustness; increasing the average path length of the network or deploying the sink node in close proximity to the network center can improve the robustness of WSNs against cascading failure. The obtained results can help designers construct a more energy-balanced and cascade-robust WSN.

Anti-injury function of complex spiking neural networks under targeted attack

Brain-like intelligence is to simulate the structure and function of the biological brain as much as possible based on the latest findings in brain science. The biological brain has strong robustness under external attacks. In this study, two complex spiking neural networks (CSNNs) are constructed: a spiking neural network (SNN) with small-world topology and a SNN with scale-free topology, in which the nodes are Izhikevich neuron model, and the edges are the synaptic plasticity model including excitatory and inhibitory synapses. For the targeted attack, the anti-injury function of two CSNNs is comparatively analyzed. On this basis, the anti-injury mechanism of CSNN is explored. The experimental results show that: (1) Small-world SNN (SWSNN) has better performance than scale-free SNN (SFSNN) in the anti-injury ability under targeted attack on high-degree nodes, and they are similar in the anti-injury ability under targeted attack on intermediate and low-degree nodes; the results of the robustness of topology are consistent with the results of anti-injury function of CSNNs, which indicates that the anti-injury ability of two kinds of CSNNs is affected by topology. (2) The dynamic evolutions of neuron firing, synaptic weight, and topological characteristic in the information processing of CSNN have a linkage effect under targeted attack; the dynamic evolution of synaptic weight is significantly related to the anti-injury ability of CSNNs, which clues synaptic plasticity is the intrinsic factor of the anti-injury function of CSNNs.

Stability of inverter-interfaced power systems with multi-scale-free properties

Scale-free networks are proven to have many distinct properties and numerous statistical studies have shown that most large power systems have the scale-free topology. However, the overall system behavior is also constrained by node dynamics, of which the interaction effects with network topology remain unknown. Here, we investigate the individual and mutual effects of network degree distribution, with two system dynamic parameters, on system small-disturbance angle stability. We show that network degree distribution and active power injection distribution are critical in determining system small-disturbance angle stability while frequency coefficient shows relatively less significant influence. Further, the scale-free level for degree distribution positively interacts with active power injection distribution on the overall system behavior. Consequently, not only network topology but also system dynamic parameters and, importantly, their synergistic effects matter in determining system behavior. Based on the results, we further provide guidance for the coordination of the various parameters to improve system small-disturbance angle stability.