Imperial College London


Faculty of Natural SciencesDepartment of Physics

Senior Lecturer



+44 (0)20 7594 7837t.evans Website




Mrs Graziela De Nadai-Sowrey +44 (0)20 7594 7843




609Huxley BuildingSouth Kensington Campus





Publication Type

103 results found

Evans T, Chen B, 2022, Linking the network centrality measures closeness and degree, Communications Physics, Vol: 5, Pages: 1-11, ISSN: 2399-3650

Measuring the importance of nodes in a network with a centrality measure is an core task in any network application. There many measures available and it is speculated that many encode similar information. We give an explicit non-linear relationship between two of the most popular measures of node centrality: degree and closeness. Based on a shortest-path tree approximation, we give an analytic derivation that shows the inverse ofcloseness is linearly dependent on the logarithm of degree. We show that our hypothesis works well for a range of networks produced from stochastic network models and for networks derived from 130 real-world data sets. We connect our results with previous results for other network distance scales such as average distance. Our results imply that measuring closeness is broadly redundant unless our relationship is used to remove the dependence on degree from closeness. The success of our relationship suggests that most networks can be approximated by shortest-path spanning trees which are all statistically similar two or more steps away from their root nodes.

Journal article

Evans TS, Chen B, 2022, Linking the network centrality measures closeness and degree, Publisher: ArXiv

We propose a non-linear relationship between two of the most importantmeasures of centrality in a network: degree and closeness. Based on ashortest-path tree approximation, we give an analytic derivation that shows theinverse of closeness is linearly dependent on the logarithm of degree. We showthat our hypothesis works well for a range of networks produced from stochasticnetwork models including the Erdos-Reyni and Barabasi-Albert models. We thentest our relation on networks derived from a wide range of real-world dataincluding social networks, communication networks, citation networks, co-authornetworks, and hyperlink networks. We find our relationship holds true within afew percent in most, but not all, cases. We suggest some ways that thisrelationship can be used to enhance network analysis.

Working paper

Vasiliauskaite V, Evans TS, Expert P, 2022, Cycle analysis of directed acyclic graphs, Physica A: Statistical Mechanics and its Applications, Vol: 596, Pages: 1-22, ISSN: 0378-4371

In this paper, we employ the decomposition of a directed network as an undirected graph plus its associated node meta-data to characterise the cyclic structure found in directed networks by finding a Minimal Cycle Basis of the undirected graph and augmenting its components with direction information. We show that only four classes of directed cycles exist, and that they can be fully distinguished by the organisation and number of source–sink node pairs and their antichain structure. We are particularly interested in Directed Acyclic Graphs and introduce a set of metrics that characterise the Minimal Cycle Basis using the Directed Acyclic Graphs meta-data information. In particular, we numerically show that transitive reduction stabilises the properties of Minimal Cycle Bases measured by the metrics we introduced while retaining key properties of the Directed Acyclic Graph. This makes the metrics a consistent characterisation of Directed Acyclic Graphs and the systems they represent. We measure the characteristics of the Minimal Cycle Bases of four models of transitively reduced Directed Acyclic Graphs and show that the metrics introduced are able to distinguish the models and are sensitive to their generating mechanisms.

Journal article

Yao Q, Evans T, Chen B, Christensen KIMet al., 2021, Higher-order temporal network effects through triplet evolution, Scientific Reports, Vol: 11, Pages: 1-17, ISSN: 2045-2322

We study the evolution of networks through ‘triplets’ — three-node graphlets. We develop a method to compute a transitionmatrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions inthe evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only.The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstratethat non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore,this also reveals that different patterns of higher-order interaction are involved in different real-world situations.To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate ouralgorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods.Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as wefind our method, along with two other methods based on non-local interactions, give the best overall performance. Theresults also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understandand predict the evolution of different real-world systems.

Journal article

Rivers R, Evans T, 2020, How do we avoid imposing the present on the past when modelling spatial interactions?, Documenta Praehistorica, Vol: 47, Pages: 462-475, ISSN: 1318-6701

Theoretical archaeological modelling for describing spatial interactions often adopts contemporary socioeconomic ideas whose C20th language gets translated into historical behaviour with the simplest of lexicons. This can lead to the impression that the past is like the present. Our intention in this paper is that, when this happens, to strip out as much of the contemporary context as we can, to bring modelling back to basic epistemic propositions. We suggest that although the underlying ontology may be specific to contemporary society the epistemology has much greater generality, leading to essentially the same conclusions without the carapace of intricate economics.

Journal article

Hilton B, Sood AP, Evans TS, 2020, Predictive limitations of spatial interaction models: a non-Gaussian analysis, Scientific Reports, ISSN: 2045-2322

We present a method to compare spatial interaction models against data basedon well known statistical measures which are appropriate for such models anddata. We illustrate our approach using a widely used example: commuting data,specifically from the US Census 2000. We find that the radiation model performssignificantly worse than an appropriately chosen simple gravity model. Variousconclusions are made regarding the development and use of spatial interactionmodels, including: that spatial interaction models fit badly to data in anabsolute sense, that therefore the risk of over-fitting is small and addingadditional fitted parameters improves the predictive power of models, and thatappropriate choices of input data can improve model fit.

Journal article

Evans TS, Calmon L, Vasiliauskaite V, 2020, Longest path in the price model, Scientific Reports, Vol: 10, Pages: 1-9, ISSN: 2045-2322

The Price model, the directed version of the Barab\'{a}si-Albert model,produces a growing directed acyclic graph. We look at variants of the model inwhich directed edges are added to the new vertex in one of two ways: usingcumulative advantage (preferential attachment) choosing vertices in proportionto their degree, or with random attachment in which vertices are chosenuniformly at random. In such networks, the longest path is well defined and insome cases is known to be a better approximation to geodesics than the shortestpath. We define a reverse greedy path and show both analytically andnumerically that this scales with the logarithm of the size of the network witha coefficient given by the number of edges added using random attachment. Thisis a lower bound on the length of the longest path to any given vertex and weshow numerically that the longest path also scales with the logarithm of thesize of the network but with a larger coefficient that has some weak dependenceon the parameters of the model.

Journal article

Falkenberg M, Lee J-H, Amano S-I, Ogawa K-I, Yano K, Miyake Y, Evans TS, Christensen Ket al., 2020, Identifying time dependence in network growth, Physical Review & Research International, Vol: 2, Pages: 023352 – 1-023352 – 17, ISSN: 2231-1815

Identifying power-law scaling in real networks—indicative of preferential attachment—has proved controversial. Critics argue that measuring the temporal evolution of a network directly is better than measuring the degree distribution when looking for preferential attachment. However, many of the established methods do not account for any potential time dependence in the attachment kernels of growing networks, or methods assume that node degree is the key observable determining network evolution. In this paper, we argue that these assumptions may lead to misleading conclusions about the evolution of growing networks. We illustrate this by introducing a simple adaptation of the Barabási-Albert model, the “k2 model,” where new nodes attach to nodes in the existing network in proportion to the number of nodes one or two steps from the target node. The k2 model results in time dependent degree distributions and attachment kernels, despite initially appearing to grow as linear preferential attachment, and without the need to include explicit time dependence in key network parameters (such as the average out-degree). We show that similar effects are seen in several real world networks where constant network growth rules do not describe their evolution. This implies that measurements of specific degree distributions in real networks are likely to change over time.

Journal article

Ciacci A, Falkenberg M, Manani KA, Evans TS, Peters NS, Christensen Ket al., 2020, Understanding the transition from paroxysmal to persistent atrial fibrillation, Physical Review Research, Vol: 2, Pages: 1-23, ISSN: 2643-1564

Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterisedby the chaotic motion of electrical wavefronts in the atria. In clinicalpractice, AF is classified under two primary categories: paroxysmal AF, shortintermittent episodes separated by periods of normal electrical activity, andpersistent AF, longer uninterrupted episodes of chaotic electrical activity.However, the precise reasons why AF in a given patient is paroxysmal orpersistent is poorly understood. Recently, we have introduced the percolationbased Christensen-Manani-Peters (CMP) model of AF which naturally exhibits bothparoxysmal and persistent AF, but precisely how these differences emerge in themodel is unclear. In this paper, we dissect the CMP model to identify the causeof these different AF classifications. Starting from a mean-field model wherewe describe AF as a simple birth-death process, we add layers of complexity tothe model and show that persistent AF arises from the formation of temporallystable structural re-entrant circuits that form from the interaction ofwavefront collisions during paroxysmal AF. These results are compatible withrecent findings suggesting that the formation of re-entrant drivers in fibroticborder zones perpetuates persistent AF.

Journal article

Vasiliauskaite V, Evans TS, 2020, Making communities show respect for order, Applied Network Science, Vol: 5, Pages: 1-24, ISSN: 2364-8228

In this work we give a community detection algorithm in which the communities both respects the intrinsic order of a directed acyclic graph and also finds similar nodes. We take inspiration from classic similarity measures of bibliometrics, used to assess how similar two publications are, based on their relative citation patterns. We study the algorithm’s performance and antichain properties in artificial models and in real networks, such as citation graphs and food webs. We show how well this partitioning algorithm distinguishes and groups together nodes of the same origin (in a citation network, the origin is a topic or a research field). We make the comparison between our partitioning algorithm and standard hierarchical layering tools as well as community detection methods. We show that our algorithm produces different communities from standard layering algorithms.

Journal article

Wilkinson J, Emms T, Evans TS, 2019, Dynamical analysis of spatial interaction models, Publisher: arXiv

We develop a novel dynamical method to examine spatial interaction models(SIMs). For each SIM, we use our dynamical framework to model emigrationpatterns. We look at the resulting population distributions to see if they arerealistic or not. We use the US census data from 2010 and various spatialstatistics to access the success or failure of each model. While we looked atover eighty different SIMs, we will focus here on two examples: the productionconstrained gravity model and the Radiation model. The results suggest that allthese models fail to produce realistic population distributions and we identifythe flaws within existing models. This leads us to suggest that we shoulddefine site attractiveness in terms of a second short range SIM leading to anew spatial interaction model - the Two-Trip model - which offers significantimprovements when examined via our method. We also note that our Two-Tripadaptation can be used in any spatial modelling contexts, not just emigration.

Working paper

Chen B, Lin Z, Evans T, 2019, The Wikipedia Network of Mathematicians

This is data used in the paper "Analysis of the Wikipedia Network of Mathematicians". The data is taken from three snapshots of Wikipedia, taken in 2013, 2017 and 2018. It contains the raw Wikipedia data used as our source as well the results of our processing. Includes are edgelists, networks of the largest comopnent in graphml format, and tables of data on the nodes (the mathematicians). We have also included an appendix for the EPJ version of the paper, mathematiciansEPJappendix.pdf. However a complete version of this work is also at arXiv:1902.07622

Working paper

Yao Q, Evans TS, Christensen K, 2019, How the network properties of shareholders vary with investor type and country, PLoS One, Vol: 14, Pages: 1-19, ISSN: 1932-6203

We construct two examples of shareholder networks in which shareholders are connected if they have shares in the same company. We do this for the shareholders in Turkish companies and we compare this against the network formed from the shareholdings in Dutch companies. We analyse the properties of these two networks in terms of the different types of shareholder. We create a suitable randomised version of these networks to enable us to find significant features in our networks. For that we find the roles played by different types of shareholder in these networks, and also show how these roles differ in the two countries we study.

Journal article

Vasiliauskaite V, Evans TS, 2019, Social success of perfumes, PLoS ONE, Vol: 14, ISSN: 1932-6203

We study data on perfumes and their odour descriptors-notes-to understand how note compositions, called accords, influence successful fragrance formulas. We obtain accords which tend to be present in perfumes that receive significantly more customer ratings. Our findings show that the most popular notes and the most over-represented accords are different to those that have the strongest effect to the perfume ratings. We also used network centrality to understand which notes have the highest potential to enhance note compositions. We find that large degree notes, such as musk and vanilla as well as generically-named notes, e.g. floral notes, are amongst the notes that enhance accords the most. This work presents a framework which would be a timely tool for perfumers to explore a multidimensional space of scent compositions.

Journal article

Patel VM, Panzarasa P, Ashrafian H, Evans TS, Kirresh A, Sevdalis N, Darzi A, Athanasiou Tet al., 2019, Collaborative patterns, authorship practices and scientific success in biomedical research: a network analysis., Journal of the Royal Society of Medicine, Vol: 112, Pages: 245-257, ISSN: 1758-1095

OBJECTIVE: To investigate the relationship between biomedical researchers' collaborative and authorship practices and scientific success. DESIGN: Longitudinal quantitative analysis of individual researchers' careers over a nine-year period. SETTING: A leading biomedical research institution in the United Kingdom. PARTICIPANTS: Five hundred and twenty-five biomedical researchers who were in employment on 31 December 2009. MAIN OUTCOME MEASURES: We constructed the co-authorship network in which nodes are the researchers, and links are established between any two researchers if they co-authored one or more articles. For each researcher, we recorded the position held in the co-authorship network and in the bylines of all articles published in each three-year interval and calculated the number of citations these articles accrued until January 2013. We estimated maximum likelihood negative binomial panel regression models. RESULTS: Our analysis suggests that collaboration sustained success, yet excessive co-authorship did not. Last positions in non-alphabetised bylines were beneficial for higher academic ranks but not for junior ones. A professor could witness a 20.57% increase in the expected citation count if last-listed non-alphabetically in one additional publication; yet, a lecturer suffered from a 13.04% reduction. First positions in alphabetised bylines were positively associated with performance for junior academics only. A lecturer could experience a 8.78% increase in the expected citation count if first-listed alphabetically in one additional publication. While junior researchers amplified success when brokering among otherwise disconnected collaborators, senior researchers prospered from socially cohesive networks, rich in third-party relationships. CONCLUSIONS: These results help biomedical scientists shape successful careers and research institutions develop effective assessment and recruitment policies that will ultimately sustain the quality of biomedical r

Journal article

Chen B, Lin Z, Evans TS, 2019, Analysis of the Wikipedia network of mathematicians, Publisher: arXiv

We look at the network of mathematicians defined by the hyperlinks betweentheir biographies on Wikipedia. We show how to extract this information usingthree snapshots of the Wikipedia data, taken in 2013, 2017 and 2018. Weillustrate how such Wikipedia data can be used by performing a centralityanalysis. These measures show that Hilbert and Newton are the most importantmathematicians. We use our example to illustrate the strengths and weakness ofcentrality measures and to show how to provide estimates of the robustness ofcentrality measurements. In part, we do this by comparison to results from twoother sources: an earlier study of biographies on the MacTutor website and asmall informal survey of the opinion of mathematics and physics students atImperial College London.

Working paper

Kitromilidis M, Evans TS, 2018, Community detection with metadata in a network of biographies of western art painters, Publisher: arXiv

In this work we look at the structure of the influences between Western artpainters as revealed by their biographies on Wikipedia. We use a modifiedversion of modularity maximisation with metadata to detect a partition ofartists into communities based on their artistic genre and school in which theybelong. We then use this community structure to discuss how influential artistsreached beyond their own communities and had a lasting impact on others, byproposing modifications on standard centrality measures.

Working paper

Vasiliauskaite V, Evans TS, 2018, Diversity from the Topology of Citation Networks

We study transitivity in directed acyclic graphs and its usefulness incapturing nodes that act as bridges between more densely interconnected partsin such type of network. In transitively reduced citation networks degreecentrality could be used as a measure of interdisciplinarity or diversity. Westudy the measure's ability to capture "diverse" nodes in random directedacyclic graphs and citation networks. We show that transitively reduced degreecentrality is capable of capturing "diverse" nodes, thus this measure could bea timely alternative to text analysis techniques for retrieving papers,influential in a variety of research fields.

Working paper

Clough JR, Evans TS, 2017, Embedding graphs in Lorentzian spacetime, PLOS ONE, Vol: 12, ISSN: 1932-6203

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG) into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.

Journal article

Evans TS, Rivers RJ, 2017, Was Thebes necessary? Contingency in spatial modeling, Frontiers in Digital Humanities, Vol: 4, ISSN: 2297-2668

When data are poor, we resort to theory modeling. This is a two-step process. We have first to identify the appropriate type of model for the system under consideration and then to tailor it to the specifics of the case. To understand settlement formation, which is the concern of this article, this involves choosing not only input parameter values such as site separations but also input functions that characterizes the ease of travel between sites. Although the generic behavior of the model is understood, the details are not. Different choices will necessarily lead to different outputs (for identical inputs). We can only proceed if choices that are “close” give outcomes that are similar. Where there are local differences, it suggests that there was no compelling reason for one outcome rather than the other. If these differences are important for the historic record, we may interpret this as sensitivity to contingency. We re-examine the rise of Greek city-states as first formulated by Rihll and Wilson in 1979, initially using the same “retail” gravity model. We suggest that, although cities like Athens owe their position to a combination of geography and proximity to other sites, the rise of Thebes is the most contingent, whose success reflects social forces outside the grasp of simple network modeling.

Journal article

Clough JR, Evans TS, 2015, What is the dimension of citation space?, Physica A, 448 (2016) 235-247

Citation networks represent the flow of information between agents. They areconstrained in time and so form directed acyclic graphs which have a causalstructure. Here we provide novel quantitative methods to characterise thatstructure by adapting methods used in the causal set approach to quantumgravity by considering the networks to be embedded in a Minkowski spacetime andmeasuring its dimension using Myrheim-Meyer and Midpoint-scaling estimates. Weillustrate these methods on citation networks from the arXiv, supreme courtjudgements from the USA, and patents and find that otherwise similar citationnetworks have measurably different dimensions. We suggest that thesedifferences can be interpreted in terms of the level of diversity or narrownessin citation behaviour.

Journal article

Goldberg SR, Anthony H, Evans TS, 2015, Modelling citation networks, SCIENTOMETRICS, Vol: 105, Pages: 1577-1604, ISSN: 0138-9130

Journal article

Goldberg SR, Anthony H, Evans TS, 2015, Modelling citation networks, Scientometrics, ISSN: 1588-2861

Journal article

Clough JR, Gollings J, Loach TV, Evans TSet al., 2015, Transitive reduction of citation networks, Journal of Complex Networks, Vol: 3, Pages: 189-203, ISSN: 2051-1310

In many complex networks, the vertices are ordered in time, and edges represent causal connections. We propose methods of analysing such directed acyclic graphs taking into account the constraints of causality and highlighting the causal structure. We illustrate our approach using citation networks formed from academic papers, patents and US Supreme Court verdicts. We show how transitive reduction (TR) reveals fundamental differences in the citation practices of different areas, how it highlights particularly interesting work, and how it can correct for the effect that the age of a document has on its citation count. Finally, we transitively reduce null models of citation networks with similar degree distributions and show the difference in degree distributions after TR to illustrate the lack of causal structure in such models.

Journal article

Goldberg SR, Anthony H, Evans TS, 2015, Do We Need Global and Local Knowledge of the Citation Network?, 15th International Conference of the International-Society-for-Scientometrics-and-Informetrics (ISSI) on Scientometrics and Informetrics, Publisher: INT SOC SCIENTOMETRICS & INFORMETRICS-ISSI, Pages: 282-283, ISSN: 2175-1935

Conference paper

Clough JR, Evans TS, 2015, Time & Citation Networks, 15th International Conference of the International-Society-for-Scientometrics-and-Informetrics (ISSI) on Scientometrics and Informetrics, Publisher: INT SOC SCIENTOMETRICS & INFORMETRICS-ISSI, Pages: 1073-1078, ISSN: 2175-1935

Conference paper

Loach TV, Evans TS, 2015, Ranking Journals Using Altmetrics, 15th International Conference of the International-Society-for-Scientometrics-and-Informetrics (ISSI) on Scientometrics and Informetrics, Publisher: INT SOC SCIENTOMETRICS & INFORMETRICS-ISSI, Pages: 89-94, ISSN: 2175-1935

Conference paper

Rivers R, Evans T, Knappett C, 2015, From oar to sail: The role of technology and geography in the evolution of Bronze Age Mediterranean networks, Maritime Networks: Spatial structures and time dynamics, Pages: 63-76, ISBN: 9781138911253

Throughout port and maritime studies, the link between flows and the socio-economic characteristics of localities has been investigated mostly qualitatively. While systematic international quantitative investigations remain scarce and dispersed, their reliance upon port tonnage statistics tends to ignore maritime linkages. In the maritime network, the so-called industrial centres as well as the agri-bulk hubs are essential for feeding the more urbanized port regions concentrating populations and services along the main trunk line. This chapter provides an analysis of the Pacific Rim area based on the comparison of vessel movement data and regional socio-economic data collected at the level of subnational entities or port regions. The analysis of the socio-economic determinants of port and maritime traffic across the Pacific Rim region is fruitful in many ways. Even though the analysis only focuses on the Pacific Rim area, California stands out as the largest traffic region to which multiple commodity flows of various natures converge, mostly containers.

Book chapter

Evans T, Lambiotte R, 2014, LineGraphCreator

This is code to implement our weighted line graphs, i.e. graphs whose nodes are the edges of the original graph which aslo capture the correct dynamical features of the original network. Weighted line graphs provide an alternative, valuable representation of the system's topology, and have important applications in community detection. The usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities.Here we provide our simple C++ line graph code which takes in a graph as an edge list and outputs different types of line graph as another edge list. An executable suitable for most Windows machines is included as is basic documentation. This code been used successfully on a graph which produced 5.5e8 stubs in its line graph, though a special machine was used for this as it needs more than 4Gb of RAM memory. On a 4Gb machine a line graph with 4.5e7 stubs was created.We also have java based code which is part of a much bigger package.Discussions, papers and slides from talks:-Paper: Line Graphs, Link Partitions and Overlapping Communities, Phys.Rev.E 80 (2009) 016105 [arXiv:0903.2181].Conference Paper: Overlapping Communities, Link Partitions and Line Graphs, a very slightly altered version forECCS09.Slides from talk What am I? Finding Communities in Networks Using Line Graphs given at University of Warwick Complexity Forum, 28thOctober 2009.Slides from talk Overlapping Communities, Edge Partitions and Line Graphs given at ECCS09 (University of Warwick, 22nd September 2009).Paper: Edge Partitions and Overlapping Communities in Complex Networks, Eur. Phys. J. B 2010, 77, 265–272 [arXiv:0912.4389]. This covers in more detail the case where one is interested in the different line graphs of a weighted graph.Input used for the Les Miserable network and the correpsonding outputs


Evans T, 2014, The Connected Past London 2014

A collection of material associated with The Connected Past London 2014, a one and a half day multi-disciplinary meeting held at Imperial College on the 8th and 9th of September, 2014 and attended by nearly fifty researchers.  It aims to explore how concepts and techniques from network- and complexity science can be used to study archaeological and historical data. It is part of a series of meetings organised by The Connected Past team.Slides from most (but not all) talks are provided. Most talks were also recorded but the videos are yet to be made available.

Scholarly edition

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