arXiv subjects

Tim S. Evans

Publications and source records attributed to Tim S. Evans.

At least 19 recordsLinked to original sources

arXiv2026

People, Places & Things: Network topology & motifs of R&D missions

Challenge-led R and D programs increasingly assemble heterogeneous people, organizations, funders, projects, and technical outputs around defined missions. Yet program evaluation often describes these systems through project lists, output counts, or retrospective case narratives. This article develops a typed network framework for representing R and D program architecture directly. We model programs as networks of people, places, and things: researchers, program directors, institutions, funders, publications, patents, projects, and citations. Applied to ARPA-E project impact sheets from the agency's first decade, the framework reconstructs 23 program-induced networks and an agency-level composed network. We show that R and D programs have an analysable topology: a typed arrangement of people, institutions, funders, projects, publications, patents, and citations that can be reconstructed, compared, and monitored. The analysis shows that programs can be compared by their local structural patterns, that cross-program overlap is concentrated more in recurring institutions than in individual researchers, and that program fingerprints differ across thematic areas. The article contributes to network science by extending topological analysis to R and D program systems, a class of governed, typed, and output-generating networks that has not been systematically represented in existing innovation-network work.

physics.soc-ph↗

arXiv2025

From Signed Networks to Group Graphs

I define a group graph which encodes the symmetry in a dynamical process on a network. Group graphs extend signed networks, where links are labelled with plus or minus one, by allowing link labels from any group and generalising the standard notion of balance. I show that for processes on a balanced group graph the time evolution is completely determined by the network topology, not by the group structure. This unifies and extends recent findings on signed networks (Tian and Lambiotte, 2024a) and complex networks (Tian and Lambiotte, 2024b). I will also relate the results discussed here to existing work such as the ``group labelling'' of Edelman and Saks (1979), the ``group graph'' of Harary, Lindstr\"om and Zetterstr\"om (1982), a ``voltage graph'' (Gross, 1974), a ``gain graph'' (Zaslavsky 1989), and ``group synchronisation'' (Karp et al, 2003). I will work with a more general case where edges need not be reciprocated and the labels of reciprocated edges need not be inverses of each other. Finally, I will review some promising applications for network dynamics and symmetry-driven modelling including status, clusterability, edges with a zero label, weak balance, unbalanced group graphs and using monoids.

physics.soc-ph↗

arXiv2024

The Behavioural House Indicator: A faster and real time small-area indicative deprivation measure for England

Researchers have been long preoccupied with the measuring and monitoring of economic and social deprivation at small scales, neighbourhood, level in order to provide official government agencies and policy makers with more precise data insights. Whist valuable methodologies have been developed, the exercise of data collection associated with these methods tend to be expensive, time consuming, published infrequently with significant time delays, and subject to recurring changes to methodology. Here, we propose a novel method based on a straightforward methodology and data sources to generate a faster and real time indicator for deprivation at different scaling, small to larger areas. The results of our work show that our method provides a consistent view of deprivation across the regions of England and Wales, which are inline with the other indexes, but also highlight specific flash points of deep rural and highly dense urban deprivation areas that are not well captured by existing indexes. Our method is intended to aid researchers and policy makers by complementing existing but infrequent indexes.

physics.soc-ph↗

arXiv2022

Local dominance unveils clusters in networks

Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or subgraphs with few connections in-between, via concepts such as the cut, conductance, or modularity. Here we consider another perspective built on the notion of local dominance, where low-degree nodes are assigned to the basin of influence of high-degree nodes, and design an efficient algorithm based on local information. Local dominance gives rises to community centers, and uncovers local hierarchies in the network. Community centers have a larger degree than their neighbors and are sufficiently distant from other centers. The strength of our framework is demonstrated on synthesized and empirical networks with ground-truth community labels. The notion of local dominance and the associated asymmetric relations between nodes are not restricted to community detection, and can be utilised in clustering problems, as we illustrate on networks derived from vector data.

physics.soc-ph↗

arXiv2022

Emergence of community structures through biased random walks rewiring

Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the topological structures of the network. The current network generating or growing models can reproduce some properties, including degree distributions, large clustering coefficients and communities. However, the scaling behaviour of the community size lacks investigation, especially from the perspectives of local interactions. Based on the assumption that heterogeneous nodes behave differently and result in different topological positions of the networks, we propose a model of designed random walks in directed networks to explain the features in the observed networks. The model highlights that two different dynamics can mimic the local interactions, and a hidden layer is essential when reproducing the characteristics of real complex networks. The key features the model can explain include community size distribution, degree distribution, percolation properties, distribution of average path length and dependence of the above properties on the labels of nodes in the data.

physics.soc-ph↗

arXiv2022

Linking the Network Centrality Measures Closeness and Degree

Measuring the importance of nodes in a network with a centrality measure is a core task in any network application. There are 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 of closeness 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.

physics.soc-ph↗

arXiv2021

Cycle Analysis of Directed Acyclic Graphs

In this paper, we employ the decomposition of a directed network as an undirected graph plus its associated node metadata to characterise the cyclic structure found in directed networks by finding a Minimal Cycle Basis of the undirected graph and augment 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 metadata 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 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.

cs.SI↗

arXiv2021

Higher-order temporal network effects through triplet evolution

We study the evolution of networks through `triplets' - three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the 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 demonstrate that 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 our algorithm'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 we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.

physics.soc-ph↗

arXiv2020

Identifying time dependence in network growth

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 Barab{á}si-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 also likely to change over time.

physics.soc-ph↗

arXiv2020

Understanding the transition from paroxysmal to persistent atrial fibrillation from micro-anatomical re-entry in a simple model

Atrial fibrillation (AF) is the most common cardiac arrhytmia, characterised by the chaotic motion of electrical wavefronts in the atria. In clinical practice, AF is classified under two primary categories: paroxysmal AF, short intermittent episodes separated by periods of normal electrical activity, and persistent AF, longer uninterrupted episodes of chaotic electrical activity. However, the precise reasons why AF in a given patient is paroxysmal or persistent is poorly understood. Recently, we have introduced the percolation based Christensen-Manani-Peters (CMP) model of AF which naturally exhibits both paroxysmal and persistent AF, but precisely how these differences emerge in the model is unclear. In this paper, we dissect the CMP model to identify the cause of these different AF classifications. Starting from a mean-field model where we describe AF as a simple birth-death process, we add layers of complexity to the model and show that persistent AF arises from re-entrant circuits which exhibit an asymmetry in their probability of activation relative to deactivation. As a result, different simulations generated at identical model parameters can exhibit fibrillatory episodes spanning several orders of magnitude from a few seconds to months. These findings demonstrate that diverse, complex fibrillatory dynamics can emerge from very simple dynamics in models of AF.

q-bio.TO↗

arXiv2020

Longest Path in the Price Model

The Price model, the directed version of the Barabási-Albert model, produces a growing directed acyclic graph. We look at variants of the model in which directed edges are added to the new vertex in one of two ways: using cumulative advantage (preferential attachment) choosing vertices in proportion to their degree, or with random attachment in which vertices are chosen uniformly at random. In such networks, the longest path is well defined and in some cases is known to be a better approximation to geodesics than the shortest path. We define a reverse greedy path and show both analytically and numerically that this scales with the logarithm of the size of the network with a coefficient given by the number of edges added using random attachment. This is a lower bound on the length of the longest path to any given vertex and we show numerically that the longest path also scales with the logarithm of the size of the network but with a larger coefficient that has some weak dependence on the parameters of the model.

physics.soc-ph↗

arXiv2020

Making Communities Show Respect for Order

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.

physics.soc-ph↗

arXiv2019

Dynamical Analysis of Spatial Interaction Models

We develop a novel dynamical method to examine spatial interaction models (SIMs). For each SIM, we use our dynamical framework to model emigration patterns. We look at the resulting population distributions to see if they are realistic or not. We use the US census data from 2010 and various spatial statistics to access the success or failure of each model. While we looked at over eighty different SIMs, we will focus here on two examples: the production constrained gravity model and the Radiation model. The results suggest that all these models fail to produce realistic population distributions and we identify the flaws within existing models. This leads us to suggest that we should define site attractiveness in terms of a second short range SIM leading to a new spatial interaction model - the Two-Trip model - which offers significant improvements when examined via our method. We also note that our Two-Trip adaptation can be used in any spatial modelling contexts, not just emigration.

physics.soc-ph↗

arXiv2019

Social Success of Perfumes

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.

physics.soc-ph↗

arXiv2019

Analysis of the Wikipedia Network of Mathematicians

We look at the network of mathematicians defined by the hyperlinks between their biographies on Wikipedia. We show how to extract this information using three snapshots of the Wikipedia data, taken in 2013, 2017 and 2018. We illustrate how such Wikipedia data can be used by performing a centrality analysis. These measures show that Hilbert and Newton are the most important mathematicians. We use our example to illustrate the strengths and weakness of centrality measures and to show how to provide estimates of the robustness of centrality measurements. In part, we do this by comparison to results from two other sources: an earlier study of biographies on the MacTutor website and a small informal survey of the opinion of mathematics and physics students at Imperial College London.

cs.DL↗

arXiv2018

Community Detection with Metadata in a Network of Biographies of Western Art Painters

In this work we look at the structure of the influences between Western art painters as revealed by their biographies on Wikipedia. We use a modified version of modularity maximisation with metadata to detect a partition of artists into communities based on their artistic genre and school in which they belong. We then use this community structure to discuss how influential artists reached beyond their own communities and had a lasting impact on others, by proposing modifications on standard centrality measures.

physics.soc-ph↗

arXiv2016

Was Thebes Necessary? Contingency in Spatial Modelling

When data is poor we resort to theory modelling. 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 paper, this not only involves choosing input parameter values such as site separations but also input functions which characterises the ease of travel between sites. Although the generic behaviour 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 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, whereas 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 modelling.

physics.soc-ph↗

arXiv2016

Embedding Graphs in Lorentzian Spacetime

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 into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Euclidean signature, to manifolds of any metric signature. We then use this general method to develop an algorithm to be used on networks which have causal structure allowing them to be embedded in Lorentzian manifolds. The method is demonstrated by calculating embeddings for both causal sets and citation networks in Minkowski spacetime. We finally 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.

physics.soc-ph↗