arXiv subjects

Francesco Zigliotto

Publications and source records attributed to Francesco Zigliotto.

3 recordsLinked to original sources

arXiv2025

Past-aware game-theoretic centrality: a framework for cardinality-constrained set-function maximization on networks

We consider cardinality-constrained optimization of set functions over the nodes of a graph. The standard greedy algorithm selects each node according to its immediate marginal contribution, a local criterion that may fail to anticipate the synergies within the final set. We introduce past-aware game-theoretic centrality (PAGTC), which evaluates a candidate node through its expected marginal contribution over the possible completions of the current partial solution to the prescribed target size. This yields a sequential selection strategy that explicitly accounts for the final budget. For nonnegative monotone submodular objectives and a budget $r$, we prove an approximation guarantee of $r/(2r-1)$ and derive computable a posteriori bounds. Since direct PAGTC evaluation involves averaging over a large number of coalitions, we extend an exact computation framework for game-theoretic centrality and derive efficiently computable expressions for two classes of graph-optimization problems, namely facility location and influence in complex contagion, covering both submodular and non-submodular cases. The numerical results show that the benefits depend on the objective and are most pronounced for complex contagion, where submodularity does not hold.

cs.SI↗

arXiv2025

Optimization of geometric hypergraph embedding

We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with the generation of geometric random hypergraphs. We propose two new spectral algorithms; both of these exploit the connection between hypergraphs and bipartite graphs. The assumption of an underlying geometric structure allows us to define a concrete measure of success that can be used to optimize the embedding via gradient descent. Synthetic tests show that this approach accurately reveals geometric structure that is planted in the data, and tests on real hypergraphs show that the approach is also useful for the downstream tasks of detecting spurious or missing data and node clustering.

cs.SI↗

arXiv2024

Modeling advection on distance-weighted directed networks

In this paper we propose a model for describing advection dynamics on distance-weighted directed graphs. To this end we establish a set of key properties, or axioms, that a discrete advection operator should satisfy, and prove that there exists an essentially unique operator satisfying all such properties. Both infinite and finite networks are considered, as well as possible variants and extensions. We illustrate the proposed model through examples, both analytical and numerical, and we describe an application to the simulation of a traffic network.

cs.SI↗