Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

Luciano da F. Costa; Osvaldo N. Oliveira; Gonzalo Travieso; Francisco A. Rodrigues; Paulino R. Villas Boas; Lucas Antiqueira; Matheus P. Viana; Luis E. C. da Rocha

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Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

Luciano da F. Costa, Osvaldo N. Oliveira, Gonzalo Travieso, Francisco A. Rodrigues, Paulino R. Villas Boas, Lucas Antiqueira, Matheus P. Viana, Luis E. C. da Rocha

arXiv:0711.3199v3Nov 20, 2007physics.soc-phphysics.comp-ph

TL;DR

Complex networks offer a way to represent, characterize, and model real-world complex systems beyond isolated, reductionist treatments. This survey reviews their applications across many phenomena and areas, finding broad application potential while identifying scope boundaries in existing linguistic-network studies.

Problem
Reductionist approaches isolate systems and control parameters, motivating broader approaches for studying real-world complex systems.
Method
The survey examines how complex networks represent, analyze, and model real-world problems and data across diverse application areas.
Results
Complex networks are applied across at least 22 real-world areas, with protein applications receiving 50 reviewed applications and Internet applications 42 articles.
Takeaways & Limitations
Complex networks are positioned to play a key role in an increasing number of areas through additional measurements and theoretical models.
Takeaways & Limitations
Linguistic-network studies have not yet used more sophisticated resources such as argument structure, as far as the survey authors know.

Abstract

from arXiv · show

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks.

1 Introduction

Complex networks extend scientific analysis beyond reductionist models by representing, measuring, and modeling nonlinear real-world systems. This survey introduces core concepts and reviews their applications across diverse phenomena.

Motivation: Reductionist approaches enable quantitative treatment of controlled systems but cannot incorporate the complexity inherent in many naturally occurring phenomena.The paper contrasts isolated, parameter-controlled analysis with the complexity of real-world systems.
Motivation: Complex networks support an integrationist scientific framework because they represent discrete systems and capture nonlinear organization, evolution, and dynamics.Their connectivity constrains and defines many aspects of system dynamics.
Survey scope: The survey reviews how complex networks are applied to real data for representation, analysis, and modeling, organized by major areas and subareas.It begins with basic concepts and measurements before surveying applications.
Network representation: Graphs represent systems through vertices and edges, with extensions for direction, connection weights, and geographical node positions.Weighted and directed graphs encode connection intensity and orientation, while geographical networks add coordinates in an embedding space.
Network measurements: Network analysis uses local and global measurements including degree, clustering, shortest paths, node strength, and degree distributions.Weighted networks extend these measurements using edge weights and weighted path lengths.
Network structure: Communities are densely internally connected node groups that are sparsely connected to the rest of the network, but identifying them is NP-complete.Consequently, many heuristic algorithms have been proposed for community detection.
Measurement limitations: Sampling bias makes it important to use measurements that are robust to noisy or incomplete network data while still distinguishing network structures.The paper identifies this robustness problem as a continuing research issue.

3 Social Networks

The survey applies complex-network methods to diverse social systems, examining structural properties, temporal evolution, and links between network structure and social phenomena. It also highlights measurement challenges arising from culturally and contextually variable relations.

Limitations: Personal-relation data are difficult to define consistently because feelings, trust, friendship, and acquaintance vary with culture, demographics, and context.The paper gives country-specific acquaintance conventions and disagreement over similarity between musical groups as examples.
Survey scope: Social-network analyses commonly examine degree distributions, community structure, and evolving topological measurements using real-world data.The survey relates these structural properties to social features when available.
Acquaintances: Weighted acquaintance networks indicate that weak intercommunity ties can be more consequential for global communication than strong intracommunity ties.Removing strong ties mainly affects local communities, whereas removing weak ties can disrupt communication between communities and collapse the network.
Acquaintances and communication: Email networks exhibit small-world structure, high clustering, exponential degree distributions, and self-similar community organization.The University at Rovira i Virgili email network had clustering 0.25 and exponential cutoff k*=9.2 for k > 2.
Sexual relations: Sexual networks show cumulative power-law partner distributions, with exponents 2.54 for women and 2.31 for men over 12 months.The survey reports smaller lifetime exponents, 2.1 for women and 1.6 for men, and notes that broad and targeted interventions were both effective.
Cross-domain applications: Social-network applications span sports, comics, music, collaborations, and non-human relations, revealing recurring small-world, clustering, assortativity, and resilience patterns.Examples include persistent small-world structure in a growing sports network, hierarchical modularity in comic dialogue, and targeted-attack sensitivity in dolphin networks.

4 Communication

Complex networks represent communication and social interactions at large scale, revealing recurring structural properties while supporting models of dynamics, spreading, mobility, and connectivity.

Email networks can be constructed from server logs or address books, with vertices representing email addresses and directed arcs representing messages or listed contacts.
Telephone call graphs encode completed calls as directed links and can reach more than 50 million vertices and 170 million edges in a single day.
Mobile call analyses found that neighbor overlap increases with connection weight, supporting the weak ties hypothesis.
Mobile-phone trajectories showed regular mobility patterns, including short trips and frequent returns to a small number of locations.
Wireless encounter networks are sparse but have short distances and high clustering because shared home access points create densely connected groups.Nodes connected to about 1.88% to 5.94% of all nodes, depending on the dataset.
Communication networks are often large and exhibit small-world, scale-free, and community-structure properties.University email networks ranged from 1,667 to 59,812 vertices, and their degree and betweenness can change dramatically from day to day.

5 Economy

Complex-network methods model economic relations among countries, firms, currencies, industrial components, wealth distributions, and tourism stakeholders, linking topology with economic structure and dynamics.

Trade networks represent countries as nodes and imports and exports as incoming and outgoing degree.
The world trade web showed strong in–out degree correlation, substantial reciprocity, a power-law partner distribution, small-world structure, and a wealth-related trade-channel correlation.The reported in–out degree correlation was r = 0.91, with 0.61 reciprocity and γ ∼2.6 for k > 20.
Currency networks can be modeled as bipartite country–currency graphs, which displayed scale-free behavior with exponent γ = 1.
Refinery networks are scale-free, small-world, and hierarchically organized, making topology useful for plant design and evaluation.
Network rewiring changed modeled wealth distributions across phases from log-normal to power-law forms, with an intermediate log-normal distribution having a power-law tail.
Tourism networks reveal product clusters, structural divides, central organizations, and stakeholder collaboration patterns, while simulations examine information and knowledge diffusion.
In a tourism destination network, company type and size strongly influenced activations and accessibilities.

6 Financial market

Financial markets provide accurate longitudinal data for network analysis, enabling representations based on stock correlations, ownership, and filtered market structure. These networks expose market taxonomies, crisis-dependent topology, and investment distributions.

Financial networks can represent stock-price relationships or stock ownership, using the market’s extensive and accurate data to reflect evolving economic structure.
Correlation-based stock networks organize assets into hierarchical taxonomies according to economic activity.
During Black Monday, the asset-tree exponent changed to γ = 1.8 from γ = 2.1 in the broader reported analysis.
Asset graphs were more robust and stable than asset trees across consecutive periods and extreme conditions, although they did not necessarily preserve hierarchical organization.
Firm ownership networks encode investment amounts as edge weights and showed power-law distributions for portfolio diversification and portfolio volume.
Filtered correlation matrices were used to construct networks representing intra-market interactions among stock sectors.

7 Computer Science

Complex networks are applied in computer science to model software, peer-to-peer systems, email contacts, electronic circuits, and images. These representations support analyses of structure, dynamics, filtering, segmentation, and shape characterization.

Software Networks: Complex-network methods represent software packages as component networks, enabling analysis of link asymmetry and bug propagation.Linux package networks showed scale-free incoming links with exponent γ = 2.0, while outgoing links did not; bug propagation was modeled epidemiologically.
Peer-to-Peer Networks: Peer-to-peer networks exhibit heterogeneous connectivity, including power-law degree distributions in Gnutella and eDonkey snapshots.The Gnutella distribution deviated from a pure power law in a later snapshot, showing that observed structure can change over time.
Spam Filtering: Email-contact networks support distributed spam filtering through neighboring-user queries and trust accumulated from previously identified spam.Simulations reported detection near 100% with almost no false positives.
Electronic Circuits: Circuit networks display small-world or scale-free organization, strong flux heterogeneity, and performance advantages for some self-assembled designs.Microprocessor edge fluxes varied by up to four orders of magnitude, while nano self-assembled circuits showed improved synchronization, latency, and classification density versus purely local circuits.
Image Processing: Image segmentation maps pixels to nodes and uses community identification because pixels within objects tend to connect densely, whereas pixels across objects connect sparsely.Related boundary-shape methods use small-world networks and degree measurements to produce descriptors robust to noise, scaling, and rotation.

8 Internet

Complex-network analysis of the Internet examines its measured structure, traffic, vulnerability, routing, and growth. Because complete mapping is difficult, studies commonly use coarse-grained AS- or router-level representations.

Representation: Internet studies commonly use incomplete maps containing Autonomous-System or router-level links because the Internet changes constantly and lacks central administration.These coarse-grained graphs nevertheless support findings about Internet structure and dynamics.
Structure: Power-law patterns were found across Internet snapshots for degree distributions, degree rank, hop counts, and graph eigenvalues.Later studies confirmed scale-free behavior across additional AS snapshots and more complete or traced-route datasets.
Structure: Internet AS maps contain characteristic motifs and a strongly connected core, including more pentagons than degree-matched random networks.The innermost k-core was described as an approximately 100-node cluster with diameter 2.
Dynamics: Scaling analyses distinguish Internet and Web fluctuation regimes: Internet flux dispersion followed σ ∼⟨f⟩^ξ with ξ ≃0.5, whereas WWW fluctuations had ξ ≃1.The Internet result was modeled using random-walker diffusion and shortest-path packet transfer; the Web result was associated with external driving forces.
Traffic and Routing: Internet traffic reaches congestion at lower traffic levels than a random network, with hubs proposed as one explanation because they participate in many transmissions.Routing simulations also found that accounting for router queue load and using clustered alternatives can improve efficiency by avoiding congested nodes.
Modeling: Internet models reproduce selected empirical properties through growth, preferential attachment, triad formation, or positive-feedback preference mechanisms.The PFP model produced a degree-distribution exponent γ = 2.2 ± 0.1 and reproduced shortest-path length, clustering, and k-core decomposition.

9 World Wide Web

The World Wide Web is studied as a large, directed, evolving network whose topology, dynamics, motifs, and data limitations affect how information can be understood and retrieved. Network models and measurements reveal scale-free structure alongside more specialized organization.

Representation: Web maps are usually directed page-level networks built by crawlers, but crawler access is limited by authorization, dynamic pages, broken links, and unreachable servers.Some analyses instead represent sites as nodes connected by hyperlinks between their pages.
Structure: A 325,729-page nd.edu map had power-law out- and in-degree distributions with γout = 2.45 and γin = 2.1.A 200-million-page map also yielded γin = 2.1, while category-specific subnetworks deviated from a pure power law at low in-degree.
Motifs: The nd.edu Web map contained far more quadrilaterals than its randomized counterpart, indicating grid-like regularity.The grid coefficient was introduced to quantify cycles of length n.
Dynamics: Web dynamics include stable pages with constant visit rates and news pages whose visits surge after creation and then decay as a power law.This distinguishes persistent portal structure from short-lived news attention.
Modeling: Web models combine growth, user-topic linking, preferential attachment, and link rearrangement to reproduce empirical degree or component-size distributions.The Simon model accurately predicted the observed in-degree exponent γin = 2.1.
Scope and Applications: More complete Web data would improve structural understanding but also increase computational complexity, while combining interconnectivity with metadata enables more detailed subnetwork analysis.The survey connects this approach to search-engine and crawler design and to web-page placement.

10 Citations

Citation networks represent scientific reports as nodes and citations as directed edges, allowing studies of information flow, impact, similarity, researcher mobility, and emerging fields. Their large databases remain subject to limited standardization and entry errors.

Representation: Citation networks quantify information flow through directed links between reports, with in-degree reflecting accumulated citations and out-degree fixed after publication.The network grows as new reports and citations are added.
Citation Patterns: Patent citation distributions followed power laws with exponent γ = 2.89 overall and γ = 2.31 within a specific basic-and-applied research field.The cited analysis also examined how funding acknowledgements related to citation frequency.
Similarity: Shared references provide a network-based measure of report similarity because related publications are expected to cite similar prior work.This similarity can be inferred from the neighborhood of a publication node or from citation-index networks.
Research Dynamics: Optimal percolation applied to self-citation evolution, co-authorship, and keywords was used to detect emerging fields and trace scientist mobility.The method was also used to identify critical moments in an academic career.
Limitations: Citation databases are large and interaction rules are generally reliable, but limited standardization and inconsistent manual entries introduce inaccuracies.Reported errors include incorrect page numbers, page-specific citations, and transcription errors; these were described as having minor effects on citation distributions.

11 Transportation

The survey presents transportation networks as tools for understanding mobility, economic development, infrastructure, and network dynamics. Across airports and roads, network structure, representation, geography, and community organization shape connectivity, navigation, resilience, and planning.

Transportation networks: Transportation networks encompass airports, railways, highways, subways, and public transport, supporting studies of mobility, disease spread, and infrastructure design.They are also treated as indicators of economic growth and tools for improving infrastructure.
11.1 Airports: Airport networks are directed and weighted by flight direction and passenger or flight counts, although worldwide airport connections are nearly symmetric.The network representation uses cities with airports as vertices and flights as arcs.
11.1 Airports: Airport networks vary by scale and location: China is small-world with an exponential degree distribution, while India is hierarchical, small-world, and truncated power-law with disassortative mixing.The Indian network’s mixing pattern differs from the worldwide airport network, potentially reflecting local versus global scale.
11.1 Airports: Worldwide airports form a scale-free, small-world network, but the most connected cities are not necessarily the most central because community structure gives hubs regional rather than global roles.Geopolitical constraints, not only geography, help explain the observed community organization.
11.1 Airports: Over 12 years, Brazil’s airport network lost airports and routes while betweenness centrality increased, consistent with concentrating operations on profitable routes.The reported dynamics indicate that airports can gain or lose importance as route use changes.
11.1 Airports: Airport capacity is efficiently distributed, French routes can be optimized through graph coloring, and networks tolerate random attacks but remain vulnerable to targeted hub attacks.The capacity result is linked to the high cost of air transportation.
11.2 Roads and urban streets: Road networks can use primal graphs, where intersections are nodes and roads edges, or dual graphs, where roads are nodes and intersections edges.Primal representations relate topology to geography, whereas dual representations better capture travel difficulty and road changes.
11.2 Roads and urban streets: Dual-graph search information measures navigation difficulty: lower values indicate easier travel, and Manhattan was reported as better planned than Stockholm by this measure.The approach also favors fewer road changes when connecting arbitrary points.

12 Electric power transmission systems

The survey describes electric power transmission systems as very large, structured networks whose topology and component roles determine blackout vulnerability. Modeling progressed from simple topologies and instantaneous cascades toward realistic stochastic failures and operator responses.

12 Electric power transmission systems: Power transmission systems contain generators, transmission substations, load centers, and transmission lines, with redundant paths routing power to consumers.The survey characterizes the power grid as one of the most complex human-made networks.
12 Electric power transmission systems: Early blackout models used simple rings, trees, or grids and treated line failures as instantaneous cascading events.These models simulated individual components to study whole-system blackout dynamics.
12 Electric power transmission systems: Real power networks have hundreds of thousands of vertices, small-world structure, high clustering, exponential degree distributions, and a bow-tie configuration.A cited complete network contained 314,123 nodes.
12 Electric power transmission systems: Removing highly connected transmission substations can cause regional blackouts, whereas highly connected generator removal does not necessarily do so because generator redundancy routes power to load centers.Other substations may fail through additional overload after critical transmission-substation removal.
12 Electric power transmission systems: A more realistic model represents random line or substation failures, overloads, and operator repair responses as stochastic events occurring at any time.The model was designed to predict blackouts and identify strategies that minimize their impact.

13 Biomolecular Networks

Complex networks are used to characterize, predict, and model biomolecular organization across protein interactions, domains, metabolism, and transcriptional regulation. These applications reveal recurring structural properties, functional modules, evolutionary conservation, and experimentally important limitations.

Protein-protein interaction networks: Protein interaction networks are heterogeneous and commonly exhibit power-law connectivity, small-world structure, and highly connected modular organization.Yeast connectivity follows a power law with an exponential cutoff and exponent about 2.5; similar dependence appears in H. pylori and D. melanogaster.
Protein-protein interaction networks: Highly connected proteins are associated with network integrity and lethality, while high-betweenness proteins can also be functionally important despite low connectivity.Removing highly connected proteins fragments the network, and lethal proteins correlate positively with betweenness centrality.
Protein-protein interaction networks: Yeast protein-interaction motifs can be more frequent than in degree-preserving random networks and may be conserved across evolution.Motif conservation is examined among 678 yeast proteins with orthologs in five eukaryotic organisms.
Protein-protein interaction networks: The yeast two-hybrid method enables global interaction analysis without antibodies or protein purification but produces many false positives.Its estimated reliability is about 50%, motivating biochemical and computational alternatives for assessing interaction databases.
Protein-protein interaction networks: Protein-interaction analyses support four main applications: structural characterization, protein-function prediction, interactome modeling, and protein-domain interaction modeling.These applications combine network measurements, neighborhood-based inference, empirical interaction data, and evolutionary modeling.
Metabolic and regulatory networks: Metabolic networks across 43 organisms are nonrandom, scale-free, small-world, modular, and hierarchically organized.Their degree exponent is γ ≃2.2 and their average shortest path is ℓ≈ 3.2; links connecting modules can be more evolutionarily conserved than hubs.
Genetic networks: Transcriptional regulatory networks contain functional modules assembled from motifs such as multiple-input and feed-forward loops.E. coli regulatory networks include 39 well-defined-function modules, and regulatory motifs can share transcription factors rather than occurring in isolation.

14 Medicine

Complex networks are applied in medicine to represent biomolecular systems, disease relationships, and anatomical structures. They are also used to study infection spreading and characterize cortical bone networks.

Disease networks: Medical network models represent cellular biomolecular systems, relationships among diseases, and broader disease-associated biological organization.The framework spans metabolic, protein-protein interaction, and genetic networks alongside networks of diseases.
Epidemiology: Network dynamics are used to study the spread of infections caused by viruses or bacteria.Epidemiological applications treat infection spreading as a dynamical process on networks.
Anatomical networks: Complex-network measurements can characterize the channel network of cortical bone structures.Bone channels are represented with intersections as vertices and interconnecting channels as edges.

15 Ecology

Complex networks represent ecological interactions and support static, dynamical, assembly, and evolutionary modeling of ecological systems. Applications include food-web robustness, extinction analysis, and mutualistic relationships.

Ecological interaction networks: Ecological communities can be represented as networks of competition, parasitism, mutualism, and predator-prey interactions.Food-web modeling is organized into static, dynamical, and species-assembly or evolutionary approaches.
Ecological dynamics: Ecological network dynamics include metapopulation processes, epidemic spreading, and food-web robustness analysis.Robustness analysis is used to quantify species extinction under habitat modification and global warming.
Mutualism: Mutualistic networks describe beneficial interactions in which both participating species obtain fitness benefits.The algae-coral relationship illustrates shelter and nutrient exchange alongside photosynthetic benefits.

16 Neuroscience

Complex networks provide a framework for studying brain structure, dynamics, disease, language, and cognition. Across these applications, network topology is linked to propagation, synchrony, pathology, linguistic structure, and text-analysis tasks, while spatial and temporal resolution remain important constraints.

Brain-network representation: Brain networks can be modeled across scales from individual neurons to large brain regions, using directed, unweighted, or weighted representations.The appropriate representation depends on whether connections are synaptic, pathway-based, or functional.
Brain-network representation: A central neuroscience question is how brain function relates to the structure of neural connectivity.Anatomical, functional, and effective connectivity capture physical links, temporal correlations, and directed influence, respectively.
Brain dynamics: Small-world topology supports faster information propagation and can combine rapid responses with coherent oscillations in neural models.Small-world networks may provide both advantages observed separately in regular and random networks; phase synchrony also depends on rewiring.
Brain dynamics: Functional brain networks displayed scale-free and small-world structure across task types, with clustering near 0.15 and power-law coefficient near 2.2.Reported path lengths were ℓ= 11.4 for N = 31, 503, ℓ= 12.9 for N = 17, 174, and ℓ= 6.0 for N = 4, 891.
Brain disease: MEG and EGG network analyses compared Alzheimer patients with healthy controls to investigate topology associated with brain pathology.The cited study analyzed 15 Alzheimer patients and 13 healthy controls using thresholded synchronization-likelihood networks.
Linguistic networks: Semantic and linguistic networks frequently show small-world or scale-free properties and support models of lexical development and language structure.Representations include synonym, consonant, word-adjacency, and other network types, with preferential attachment used in lexical-growth modeling.
Language applications: Word-adjacency networks have been applied to synonym selection, essay-quality assessment, machine-translation evaluation, and authorship characterization.These applications relate network measurements or structural changes to human-assigned quality, translation quality, or authorship.
Open challenges: Linguistic-network research remains limited for argument structure, individual language development, and several applied tasks because relevant data and cognitive mechanisms are difficult to obtain or specify.The survey identifies unexplored possibilities including improved parsers and machine-translation systems.

18 Earthquakes

Complex-network models represent earthquakes through spatial-temporal event connections and reveal scale-free organization. Related network models also describe physical systems, including reaction landscapes and phase transitions under non-regular topologies.

Earthquake networks: Earthquake networks connect grid cells where successive shocks occur, and Japanese and Californian data showed scale-free structure.A second construction links each earthquake to its most correlated predecessor, with outgoing links representing aftershocks and exponent γ = 2.
Earthquake networks: Seismology networks contain about 10^2–10^3 nodes, and their analysis may help characterize collective behavior and potentially predict natural events.
Physical systems: Reaction graphs represent potential-energy minima as nodes and direct transitions as links, producing scale-free, small-world topology.Low-energy minima act as hubs, indicating a negative correlation between node degree and potential energy.
Physical systems: In small-world Ising models, long-range connections produce ferromagnetic phase transitions, while rewiring changes critical behavior across dimensions.In 1D, Tc ∝ |log p|^-1; in 2D and 3D, Tc − Tc^0 ∝ p^(1/νd), and the geometry changes the universality class.
Physical systems: Scale-free and arbitrary-degree topologies alter spin-system transitions, including size-dependent critical temperature and continuous infinite-order Potts transitions when the degree-distribution second moment diverges.

20 Chemistry

Complex networks are applied across chemical plants, reaction systems, mathematics, climate, security, and epidemic spreading. These applications use network topology and connectivity to characterize systems and identify structural or intervention-relevant patterns.

Chemical systems: Ammonia-plant networks exhibit small-world, weakly self-similar, modular structure, with communities corresponding to plant sections and allometric scaling supporting fluid flow.
Chemical systems: Astrochemical reaction networks use reactants and products as nodes and reveal two basic topologies associated with the presence or absence of life.
Chemical systems: Chemical-network applications span industrial processes, polymers, reactions, and astrochemistry, including rapid phase-space mapping through small-world topology.
Mathematics and climate: Prime-factor networks connect numbers sharing a factor and are nonsparse, small-world, and approximately size-invariant in degree distribution.
Mathematics and climate: Climate networks connect global grid cells whose time-series correlations exceed a threshold, enabling representations of climate dynamics and global change.
Security and epidemics: Network efficiency identifies critical nodes through the efficiency loss caused by node removal; in a terrorist network, the most critical node had the largest direct degree.
Security and epidemics: Epidemic studies also model computer viruses and diseases using random graphs, cellular automata, real infection data, percolation, delayed recovery, and geographic immunization.
Security and epidemics: Scale-free networks can lack epidemic thresholds, so disease spread may occur at any transmission rate and hub immunization becomes a proposed control strategy.For uncorrelated scale-free networks, traditional threshold behavior appears only for γ > 2.

25 Collaboration Network of the Papers Cited in this Review

The survey constructs global collaboration and research-area networks to examine how its cited literature and application domains are connected. Its review-wide analysis shows broad application coverage, heterogeneous measurement practices, and differing levels of theoretical-model use.

Collaboration network: The citation collaboration network maps authors to nodes and co-authorship to edges, containing 1,028 nodes and 4,707 edges.
Research-area connections: Research-area networks encode authors as vertex size and shared researchers as link strength, with biomolecular research concentrating many authors.
Global survey analysis: The survey covers at least 22 real-world areas, and reviewed studies commonly quantify topology and compare networks with scale-free or small-world models.
Global survey analysis: Table 7 covers 27 application areas; protein applications receive 50 reviewed studies, while Internet applications receive 42.The authors note that the table remains a representative snapshot despite bias from article selection.
Global survey analysis: Application areas differ in measurement practices, with organizational management using up to 20 measurements while most applications use 4 or 5.Internet application articles included 12 theoretical models, and several other areas considered 8 or more.
Conclusions and perspectives: The survey concludes that complex networks’ capacity to represent, characterize, and model real-world systems supports their expanding application across scientific areas.