Ranking in evolving complex networks

Hao Liao; Manuel Sebastian Mariani; Matus Medo; Yi-Cheng Zhang; Ming-Yang Zhou

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Ranking in evolving complex networks

Hao Liao, Manuel Sebastian Mariani, Matus Medo, Yi-Cheng Zhang, Ming-Yang Zhou

arXiv:1704.08027v1Apr 26, 2017physics.soc-phcs.DLcs.IRcs.SI

TL;DR

Ranking in evolving networks matters because rankings shape information access, evaluation, and resource allocation, while static metrics can be misleading as real networks change. This review synthesizes static and time-aware network-ranking algorithms, their applications, and validation concerns. Its central conclusion is that temporal information is essential: disregarding it can produce sub-optimal or misleading results, although metric performance remains task- and dataset-dependent.

Problem
Static ranking methods can be misleading for evolving networks, and existing reviews have only marginally addressed how network evolution affects ranking algorithms.
Method
The review surveys static and time-aware ranking algorithms, temporal-network representations, applications, validation procedures, and ranking biases across evolving social, economic, and information systems.
Results
The review concludes that disregarding temporal information can produce sub-optimal or misleading rankings, while time-aware methods address tasks including temporal-window ranking, non-Markovian diffusion, and future prediction.
Takeaways & Limitations
Ranking metrics should be assessed for the specific task and dataset, with temporal information included when network evolution is essential to the ranking problem.
Takeaways & Limitations
No single metric outperforms all others across the studied problems, and extensive evaluation of metric performance and bias remains a future research need.

Abstract

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Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Well-established ranking algorithms (such as the popular Google's PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. The recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of real network traffic, prediction of future links, and identification of highly-significant nodes.

I. INTRODUCTION

Ranking algorithms filter abundant information and influence decisions across online, scientific, economic, health, and political settings. This review surveys static and time-aware network-based metrics, emphasizing how temporal evolution affects rankings and why task-specific validation is necessary.

Motivation: Ranking algorithms filter large amounts of data to retrieve information relevant to users with limited attention.Their outputs influence purchasing, access to scientific knowledge and online content, recognition of success, funding, disease analysis, and voting.
Network-based ranking: Complex networks represent systems as nodes and relationships, reducing system complexity while enabling analysis of structure and dynamics.Network-based ranking algorithms use these representations to infer node value, relevance, or importance; ranking algorithms and centrality metrics are used interchangeably here.
Research gap: Existing reviews discuss network-based ranking, but the impact of network evolution is often marginal despite temporal effects strongly influencing ranking effectiveness.Real networks usually evolve in time, motivating a focused review of temporal aspects.
Review scope: The review surveys static and time-aware ranking algorithms, including methods based on random walks and diffusion, and covers applications to evolving networks.It discusses static metrics, growing networks, temporal-network representations, time-aware recommendation, and recommender-system effects on network evolution.
Validation and scope: No universal ranking algorithm can address all datasets and tasks, so centrality metrics must be evaluated according to the specific ranking task.The review highlights validation and bias suppression, including time-aware applications to significant-node identification, GDP prediction, and link prediction.
Static metrics: Static centrality metrics use only the adjacency matrix and can be limited because degree ignores neighbor centrality.The H-index incorporates neighborhood information and can bridge local degree-based and more global notions of centrality.

1. Closeness centrality

Closeness centrality measures proximity through geodesic distances, whereas betweenness measures shortest-path mediation; both rely on restrictive assumptions about network flow. Other metrics incorporate neighborhood or whole-network structure, but their effectiveness varies by task.

Closeness centrality: Closeness centrality defines a node’s score from its average geodesic distance to other nodes.Harmonic closeness avoids the zero-score problem that arises when a node cannot reach even one node in a disconnected network.
Closeness centrality: Closeness centrality assumes information or disease flows only along shortest paths, limiting its usefulness to settings with prior global knowledge of flow.This assumption concerns expected hitting time through the network.
Betweenness centrality: Betweenness centrality ranks a node highly when many shortest paths between node pairs pass through it.σ_st counts shortest paths between s and t, while σ_st^(i) counts those passing through node i.
Betweenness centrality: Betweenness centrality also assumes that only shortest paths carry information or traffic, and evidence does not show that it accurately reproduces real-network information flows.It performs poorly relative to other metrics for identifying influential nodes.
Coreness centrality: Coreness centrality uses k-shell decomposition to distinguish core nodes from peripheral nodes by iteratively removing nodes with one connection.The decomposition assigns removed nodes to shells, beginning with the 1-shell.
H-index and eigenvector metrics: Higher-order H-index values converge to coreness in arbitrary undirected networks, bridging degree-based local centrality and global coreness.In many real-world networks, H-index outperforms degree and coreness for identifying influential spreaders in classical SIR and SIS models, although other analyses find it a poor indicator compared with non-backtracking centrality.

2. Katz centrality

Katz centrality extends eigenvector centrality by assigning every node a baseline score and weighting contributions from all network paths. Its path-length attenuation connects local degree-like behavior with longer-range network structure, while applications and limitations depend on network form.

Definition: Katz centrality assumes that a node is important when connected to other important nodes, while assigning every node a minimum score.This distinguishes it from eigenvector centrality in disconnected networks and directed acyclic graphs.
Path contributions: Katz scores incorporate all paths through a node, with α controlling how strongly longer paths are attenuated.Small α makes scores mostly depend on length-one paths and degree; larger admissible α gives longer paths greater influence.
Applications: A Katz variant substantially outperforms other static centrality metrics in predicting neuronal activity.The review also describes network-based win-lose scoring systems that rank competitors through direct and indirect wins.
Limitation: Katz centrality can produce unsatisfactory rankings when outdegree is heterogeneous because highly connected nodes can manipulate target-node scores.PageRank addresses this limitation by weighting less the edges created by nodes with many outgoing connections.

4. PageRank

PageRank ranks nodes through a damped random walk that combines link following with teleportation. Its variants alter the transition matrix, teleportation parameter, or teleportation vector, while practical use requires handling dangling nodes and network-specific assumptions.

Definition and interpretation: PageRank was introduced to rank web pages and computes scores for directed networks using a transition matrix, teleportation parameter α, and teleportation vector v.Its score vector can also be interpreted through the Google matrix and as the stationary state of a stochastic process.
Practical limitation: PageRank requires a defined transition rule for dangling nodes, which have zero outdegree in many real-world directed networks.Possible treatments include removing dangling nodes, setting kout = 1, or replacing undefined transitions with uniform entries.
Path contributions: PageRank scores depend on all paths through a node, with α controlling exponential damping of longer paths.For small α, PageRank approximately reduces to indegree when outdegree fluctuations are sufficiently small.
Random-walk interpretation: At each step, the PageRank random walker follows an outgoing edge with probability α or teleports with probability 1 − α.For α = 0.85, the average path length before teleportation is 5.67, corresponding to about six followed edges.
Variants: PageRank variants modify one or more of the transition matrix, teleportation parameter, and teleportation vector.Examples include reverse PageRank, LeaderRank without teleportation, smart teleportation, and pseudo-PageRank.
Variants: Smart-teleportation PageRank is more stable than original PageRank when the teleportation parameter varies.It uses a degree-based teleportation vector and gives indegree as the zero-order contribution to node scores.

6. HITS algorithm

HITS ranks nodes in directed networks with two mutually reinforcing scores: hub-centrality for pointing to authoritative nodes and authority-centrality for being pointed to by hubs. The review also contrasts ranking metrics on the Zachary karate club network and introduces bipartite-network extensions.

6. HITS algorithm: HITS assigns each node a hub score for pointing to authoritative nodes and an authority score for being pointed to by hubs.
6. HITS algorithm: The HITS score vectors are eigenvectors of A A^T and A^T A, respectively, with λ = (αβ)^−1.
6. HITS algorithm: HITS has been used to rank publications in citation networks, where topical reviews can function as hubs linking to influential papers.
Case study: In the Zachary karate club network, most nodes receive similar rankings across metrics, but some nodes differ substantially.
Case study: Node 8 ranks high by k-shell but low by betweenness because high-degree neighbors raise its k-shell value while interconnected neighbors create shortest-path shortcuts.
Case study: Node 10 has low degree and PageRank but comparatively high closeness because it is centrally located; PageRank and eigenvector centrality correlate at Pearson’s 0.89.
Bipartite networks: Bipartite ranking methods score two node groups separately, while ignoring same-kind connections can lose information available in social or scholarly networks.
Bipartite networks: co-HITS transfers scores between the two node groups using transition matrices and baseline score vectors, with column normalization enabling iterative computation.

3. Fitness-complexity metric

The fitness-complexity metric ranks countries and products from international trade relationships using nonlinear, iteratively normalized scores. Its interpretation emphasizes diversified countries and products exported primarily by high-fitness countries, while higher nonlinearity improves structural-importance ranking but increases noise sensitivity.

3. Fitness-complexity metric: Fitness-complexity simultaneously measures countries’ fitness and products’ complexity from international trade data.
3. Fitness-complexity metric: The metric assumes competitive countries diversify exports, whereas sophisticated products are exported mainly by diversified, high-fitness countries.
3. Fitness-complexity metric: Fitness and complexity scores are updated iteratively and normalized by their respective average values after each step.
3. Fitness-complexity metric: A product exported by countries with fitness 0.1 and 10 receives an unnormalized score of 0.099, whereas one exported only by the fitness-10 country receives 10.
3. Fitness-complexity metric: Increasing exponent γ makes rankings better reproduce structural importance but more sensitive to noisy data.
3. Fitness-complexity metric: Variants penalize products exported by low-fitness countries more heavily or improve algorithm convergence.
3. Fitness-complexity metric: Fitness-complexity outperforms degree, method of reflections, PageRank, and betweenness centrality for ranking structural importance in economic and ecological networks.
3. Fitness-complexity metric: In plant-pollinator networks, pollinator fitness represents importance and plant complexity represents vulnerability.

B. PageRank’s temporal bias and its suppression

PageRank can favor old or recent nodes in evolving networks, depending on the relative decay timescales of node relevance and activity. Rescaling scores against age-matched nodes suppresses this bias and often improves recovery of intrinsic node fitness.

Temporal bias: PageRank’s score is influenced by network evolution, causing recent nodes with insufficient accumulated links to receive lower scores.This produces a documented bias against recent nodes.
Temporal bias: In citation networks, the forward-only structure of citations makes recent nodes difficult for PageRank’s random walkers to reach, producing a strong bias toward old nodes.Teleportation is the only route by which the random walk can reach recent nodes in this setting.
Temporal bias: When relevance and activity decay on similar timescales, PageRank can uncover useful information, but when their timescales differ greatly, in-degree outperforms it.For ΘR ≫ΘA, PageRank favors old nodes; for ΘR ≪ΘA, it favors recent nodes.
Bias suppression: Rescaled PageRank compares each node’s score with scores of nodes published in a nearby age window to suppress temporal bias.The proposed rescaling uses neighboring papers or nodes as an age-matched reference group.
Bias suppression: Rescaled PageRank removes age bias across most tested model conditions and outperforms PageRank in uncovering node fitness where the original metric is strongly biased.Its advantage disappears near ΘR ≈ΘA, where PageRank is already not biased toward a specific age.
Empirical application: In APS citation data from 1893–2015, rescaled PageRank’s top-paper ranking remains approximately flat across publication years, unlike citation count and PageRank.The dataset contains 560,000 papers, and PageRank’s median rank increases throughout the displayed period.

IV. TIME-DEPENDENT NODE CENTRALITY METRICS

Time-dependent centrality metrics incorporate node or edge age directly, or rescale static scores to reduce age-related bias. These approaches include time-rescaled degree and PageRank, age-weighted degree, and temporal extensions of Katz and PageRank.

Overview: Time-dependent algorithms explicitly include time in their defining equations, unlike static metrics that use only the adjacency matrix.They are designed to address shortcomings of static metrics in evolving systems.
Node-based time-rescaled metrics: Rescaled indegree and PageRank normalize scores within temporal windows to reduce dependence on node age.Rescaled citation counts can use age-matched averages, while rescaled PageRank uses moving windows of scores.
Node-based time-rescaled metrics: Rescaled PageRank is not biased by paper age in APS data, whereas the appropriate temporal-window size remains unresolved.Too-large windows favor old nodes; too-small windows make rankings sensitive to statistical fluctuations.
Edge-weighted metrics: Age-weighted degree variants address degree’s failure to identify future popularity when preferences shift or attractiveness decays.Recent-degree scores combine current degree with degree growth over a parameterized time window, and λ selects between these components.
Edge-weighted metrics: Long-gap citation count predicts milestone-movie status, while Effective Contagion Matrix weights paths by link age and emphasizes recently pointing nodes.ECM outperformed degree, weighted indegree, PageRank, age-based PageRank, and CiteRank for future citation-count increase and future popularity.

4. Focusing on a temporal window: T-Rank, SARA

Temporal-window and model-based methods focus ranking on recent activity or infer importance from evolving-network dynamics. Examples include T-Rank, SARA, CiteRank, reputation weighting, and fitness or relevance models.

4. Focusing on a temporal window: T-Rank, SARA: T-Rank favors pages receiving incoming links and frequent updates within a chosen temporal window of interest.Its freshness function weights timestamps by distance from that window, enabling analysis after unexpected events.
4. Focusing on a temporal window: T-Rank, SARA: SARA computes author-level rankings using only links within a specified temporal window and identifies Nobel Prize winners better than citation-count indices.The algorithm is a weighted PageRank variant applied to scientific-author citation networks.
5. PageRank with time-dependent teleportation: CiteRank: CiteRank uses time-dependent teleportation to suppress older papers’ advantage; parameters c = 0.5 and τ = 2.6 years best matched future indegree increase.Its score and future citation distribution both show a two-step exponential decay associated with two citation mechanisms.
6. Time-dependent reputation algorithms: Time-dependent reputation systems weight recent evaluations more heavily and can quickly lower reputation after a user begins fraudulent behavior.The generic formulation assigns evaluation weights according to evaluation time relative to the time reputation is computed.
C. Model-based ranking of nodes: Fitness and relevance models infer node importance from evolving degree patterns, with relevance models additionally representing node aging.Fitted paper fitness estimates have been used to predict future impact, while relevance decays toward zero or a small constant for older nodes.
C. Model-based ranking of nodes: Model-based ranking can estimate paper fitness and use it to predict future impact from fitted relevance dynamics.The relevance model compares observed link acquisition with preferential-attachment expectations and fits paper-specific temporal citation patterns.

V. RANKING NODES IN TEMPORAL NETWORKS

Temporal ordering and repeated interactions can materially change network flows and centrality, so evolving networks require representations that preserve memory and time-respecting paths.

Temporal ordering of interactions can affect diffusion, social influence, and evaluations based on static centrality metrics.
Temporal networks record time-stamped contacts, allowing repeated interactions and their timing to be represented explicitly.
Projecting a temporal network onto a static weighted network discards essential information and can yield misleading results.
Higher-order representations transform edge lists into time-respecting paths and preserve path statistics up to a chosen order.
Memory effects can substantially alter passenger and journal-citation flows compared with first-order Markovian representations.
Time-respecting paths require strictly increasing event times, while a maximum inter-event threshold δ can restrict paths to relevant timescales.

C. Ranking based on higher-order network representations

Higher-order network models relax the Markovian assumption by conditioning transitions on prior trajectory, preserving observed temporal-path frequencies while increasing model complexity.

Time-aggregated diffusion assumes the next move depends only on the current node, an assumption that can be unrealistic in real systems.
Second-order models condition a transition from j to i on the preceding node k, making the walk Markovian on directed edges rather than physical nodes.
The second-order transition probability preserves observed frequencies of time-respecting paths of length two, subject to the inter-event threshold δ.
Second-order random walks are more predictable than memoryless walks, but their representation requires E > N memory nodes.
The increased complexity associated with memory models requires particular attention in dense networks.

3. Second-order PageRank

Higher-order PageRank and related memory-aware random walks extend ranking and diffusion analysis beyond first-order representations, revealing substantially different rankings and improved predictive behavior.

Accounting for memory effects can slow or speed diffusion, with predictions based on the second-largest eigenvalue matching real-data simulations.
Including higher-order effects decreases the PageRank score of more than 90% of webpages in the WWW data.
More than two memory steps make random walks more predictable and improve out-of-sample prediction accuracy for real-world ship trajectories.
Higher-order PageRank assigns physical-node scores by summing PageRank scores of memory nodes representing that physical node.
Higher-order and standard PageRank scores are positively correlated but provide substantially different information about website importance.
TempoRank uses temporal layers directly, and its scores show little correlation with scores from time-aggregated networks.
A non-zero sojourn probability guarantees convergence of the TempoRank walk exactly when the time-aggregated network is connected.

2. Coupling between temporal layers

Temporal ranking methods extend multilayer, sport-scoring, and shortest-path centralities by coupling layers or respecting event order, improving correspondence with evolving-network behavior.

2. Coupling between temporal layers: Coupling consecutive temporal layers makes each node’s centrality depend on neighboring layers and constrains its temporal variation.
3. Dynamic network-based scoring systems for ranking in sport: Dynamic win-lose scoring discounts past wins exponentially and includes indirect wins occurring after the player’s direct win.
3. Dynamic network-based scoring systems for ranking in sport: Dynamic win-lose scores have better predictive power than Park and Newman’s static counterpart in tennis-player data.
Temporal path-based centralities: Temporal shortest-path methods distinguish paths with minimum edge count from fastest paths with minimum temporal duration.
Temporal path-based centralities: Temporal betweenness counts the fraction of shortest or fastest time-respecting paths passing through a node.
3. Temporal closeness centrality: Temporal closeness can be zero when nodes lack temporal paths during observation, motivating harmonic-average alternatives.
3. Temporal closeness centrality: Second-order time-aggregated networks better approximate temporal betweenness and closeness than first-order time-aggregated networks.

VI. TEMPORAL ASPECTS OF RECOMMENDER SYSTEMS

Temporal dynamics challenge static recommender assumptions because ratings and user or item effects can change over time. The review surveys time-aware extensions to matrix factorization and notes that combining diverse methods can improve prediction accuracy.

Matrix factorization: Matrix factorization represents users and items with latent vectors and factorizes the sparse rating matrix into user taste and item property matrices.The model estimates ratings from the match between user preferences and item properties.
Temporal dynamics: Static recommendation models weight ratings equally over time and assume constant parameters, but rating data generally violate this stationarity assumption.Observed effects include a sudden average-rating increase of approximately 0.3 in 2004 and ratings that generally increase with item age.
Temporal dynamics: The time-aware prediction extends the baseline by replacing constant user and item deviations with d_i(t) and d_α(t), alongside time-dependent user preferences when modeled.The complete form is ˆr_iα(t) = µ + d_i(t) + d_α(t) + p_i(t) · q_α.
Temporal dynamics: Time-aware matrix factorization allows user and item bias terms to vary with time, while deciding which temporal effects matter remains context-dependent.Candidate effects include changing movie appreciation and rapidly changing user mood; model components can be tested by measuring prediction precision.
Method combination: Combining diverse well-performing predictors through blending or bagging can further improve recommendation performance.Successful NetflixPrize teams employed some form of method combination, indicating that different methods capture different parts of user behavior.

B. Temporal dynamics in network-based recommendation

Network-based recommendation is biased toward older popular items because conventional evaluation and recommendation processes underrepresent recent links. Time-aware evaluation and ranking adjustments can improve recency, while repeated recommendations create a trade-off between precision and inequality.

Temporal evaluation: Network-based recommendation methods often favor popular items, but popularity requires time, making recommended items likely to be old.Recent items are therefore underrepresented when recommendations are compared with newly formed links.
Temporal evaluation: Removing links at random overestimates recommendation performance because random removal preferentially targets popular items; removing the latest links better reconstructs the near future.The latter procedure uses preceding links as input and differs fundamentally from random removal, which mixes past and future links.
Temporal bias: Time-based evaluation reduces measured performance because network growth depends on node age as well as popularity, allowing recent nodes to gain popularity.Preferential attachment is modulated by node age and other influences, so popularity alone poorly reproduces the newest links.
Temporal adjustment: Increasing the standing of recent items with their recent degree increase can improve recommendation recall and recommend less popular items than baseline methods.The review describes this as an elementary modification, while the best way to include time remains open.
Network growth: Iterating popularity-favoring recommendations can concentrate attention on a handful of items and produce a pathological stationary state.In the ProbS-HeatS hybrid, lower θ yields high precision but high inequality, whereas θ near one yields lower precision and lower inequality.
Scientific papers: Time-aware paper metrics can identify milestone papers better early after publication, while network-based metrics outperform citation-count counterparts in the reviewed comparison.Rescaled PageRank and CiteRank perform better than citation count and PageRank during the first 15 years after publication.
Scientific papers: Rescaled PageRank can rank recent seminal papers earlier than citation count and ordinary PageRank because it lacks age bias.In the cited example, a recent gravitational-wave paper ranked 17 of 593,443 by rescaled PageRank, versus 1,763 by citation count and 12,277 by PageRank.
Scientific papers: Rescaling can reward immediate impact, penalize sleeping beauties, and increase early false positives, so early results require caution.A few quickly obtained citations can produce high initial scores that later decrease substantially.

2. Predicting the future success of scientific papers

The review covers methods for predicting the future success of scientific papers and researchers, emphasizing citation dynamics, popularity profiles, and author-network position. It also highlights age bias and the difficulty of forecasting research success with slowly changing metrics.

Scientific papers: Citation-growth models calibrate preferential attachment with aging on citation data to predict papers’ long-term citation counts.The aging component was found to decay log-normally with time.
Scientific papers: Cao et al.’s popularity-profile method outperforms Wang et al.’s model by matching papers to empirical popularity profiles.Its model-free use of observed profiles avoids relying on a specific paper-popularity growth model.
Scientific papers: Rescaled in-degree, combining citation count with appearance time, identifies papers likely to become highly successful in the future.Later evaluation found the identified papers significantly outperformed random papers, including citation-matched random papers.
Scientific papers: Author position in co-authorship networks is another basis for predicting paper success, alongside citation-network indicators.Sarigol et al. studied more than 100,000 computer science papers published from 1996 to 2007.
Researchers: The h-index was reported to predict researchers’ future success better than total citations, citations per paper, and total paper count.Later work introduced the age-unbiased Q metric, which was empirically stable over time and suitable for predicting future h-index.
Researchers: Predicting future h-index values is difficult to evaluate because the metric changes slowly and can only increase, making unchanged-h-index baselines strong.This issue was among the criticisms directed at a multifeature linear-regression approach.

1. Prediction of GDP through linear regression

The review compares linear regression and analogue-based approaches for predicting countries’ future GDP using network-derived scores. It finds strongly heterogeneous country dynamics, with fitness and degree more predictive than the Method of Reflections in the reported analysis.

Prediction of GDP through linear regression: Linear regression predicts future log GDP from current log GDP and network-based metrics, including the Method-of-Reflections score.The approach estimates shared regression coefficients across countries.
Prediction of GDP through linear regression: The Method-of-Reflections score contributes more to economic-growth variance than governance, institutions, education, and standard competitiveness measures.This is reported for the regression analyses by Hidalgo and Hausmann and subsequent work.
Prediction of GDP through linear regression: Linear regression can miss heterogeneous country responses because it assumes a uniform trend and common coefficients.Cristelli et al. instead analyze country dynamics in the Fitness-GDP plane.
Prediction of GDP through the method of analogues: The method of analogues predicts future country dynamics from past trajectories without requiring known evolution laws.Countries are compared through their positions in score-GDP planes over a ten-year interval.
Prediction of GDP through the method of analogues: Low dispersion indicates more predictable future evolution, while high dispersion indicates less predictable evolution for countries sharing a score-GDP box.The dispersion measure counts how many boxes are occupied after ten years by countries originating from a given box.
Prediction of GDP through the method of analogues: The weighted mean dispersions are 0.41 for degree, 0.71 for Method of Reflections, and 0.35 for Fitness.These values imply that Fitness performs best, followed by degree, while Method of Reflections is not reliable for this analogue-based prediction.

VIII. PERSPECTIVES AND CONCLUSIONS

The review argues that ranking metrics require task-specific, thorough validation because no single metric performs best across all problems. It concludes that temporal information is essential, while ranking systems also raise unresolved bias and societal-impact concerns.

Perspectives and conclusions: Qualitative and anecdotal validation is insufficient, motivating extensive performance evaluation of static and time-aware ranking metrics.The appropriate evaluation depends on the task targeted by the metric.
Perspectives and conclusions: Future-edge prediction, external information, and model data are proposed as complementary validation strategies.External benchmarks include expert-selected significant nodes, known regional income, and known neuronal activity.
Perspectives and conclusions: Results across datasets show that no metric outperforms all others in every studied ranking problem.The review calls for analysis of which network properties make metrics succeed or fail in particular tasks.
Perspectives and conclusions: Ranking metrics can carry age and field biases, while social effects may produce filter bubbles, echo chambers, and exposure to unreliable information.The review emphasizes detecting and, where possible, suppressing such biases.
Perspectives and conclusions: Predicting ranking systems’ effects on network evolution remains difficult because homogeneous growth models oversimplify heterogeneous node behavior.The review states that clear guidelines for predicting a metric’s impact on a given network are still lacking.
Perspectives and conclusions: The review’s main conclusion is that disregarding temporal information can produce sub-optimal or misleading ranking results.It surveys multiple ways to incorporate time into ranking algorithms for evolving networks.