Maximum entropy temporal networks
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910130470125568 |
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| author | Barucca, Paolo |
| author_facet | Barucca, Paolo |
| contents | Temporal networks consist of timestamped directed interactions that may appear continuously in time, yet few studies have directly tackled the continuous-time modeling of networks. Here, we introduce a maximum-entropy approach to temporal networks and with basic assumptions on constraints, the corresponding network ensembles admit a modular and interpretable representation: a set of global time processes and a static maximum-entropy edge, e.g. node pair, probability. This time-edge labels factorization yields closed-form log-likelihoods, degree, clustering and motif expectations, and yields a whole class of effective generative models. We provide the maximum-entropy derivation for the non-homogeneous Poisson Process (NHPP) intensities governing the probability of directed edges in temporal networks via the functional optimization over path entropy, connecting NHPP modeling to maximum-entropy network ensembles. NHPPs consistently improve log-likelihood over generic Poisson processes, while the maximum-entropy edge labels recover strength constraints and reproduce expected unique-degree curves. We discuss the limitations of this framework and how it can be integrated with multivariate Hawkes calibration procedures, renewal theory, and neural kernel estimation in graph neural networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum entropy temporal networks Barucca, Paolo Social and Information Networks Data Analysis, Statistics and Probability 60G55, 60K35, 05C82 G.3; G.2.2 Temporal networks consist of timestamped directed interactions that may appear continuously in time, yet few studies have directly tackled the continuous-time modeling of networks. Here, we introduce a maximum-entropy approach to temporal networks and with basic assumptions on constraints, the corresponding network ensembles admit a modular and interpretable representation: a set of global time processes and a static maximum-entropy edge, e.g. node pair, probability. This time-edge labels factorization yields closed-form log-likelihoods, degree, clustering and motif expectations, and yields a whole class of effective generative models. We provide the maximum-entropy derivation for the non-homogeneous Poisson Process (NHPP) intensities governing the probability of directed edges in temporal networks via the functional optimization over path entropy, connecting NHPP modeling to maximum-entropy network ensembles. NHPPs consistently improve log-likelihood over generic Poisson processes, while the maximum-entropy edge labels recover strength constraints and reproduce expected unique-degree curves. We discuss the limitations of this framework and how it can be integrated with multivariate Hawkes calibration procedures, renewal theory, and neural kernel estimation in graph neural networks. |
| title | Maximum entropy temporal networks |
| topic | Social and Information Networks Data Analysis, Statistics and Probability 60G55, 60K35, 05C82 G.3; G.2.2 |
| url | https://arxiv.org/abs/2509.02098 |