Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix

Estrada, Ernesto

doi:10.1016/j.laa.2022.09.025

Cited by 7 publications

(1 citation statement)

References 30 publications

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“…Conceptually,

is a measure of the network resistance to a flow between

and

. Recently ( 43 ), it was proven that this communicability distance—and every spherical Euclidean distance—is the effective resistance between nodes in a network with given edge weights.…”

Section: Resultsmentioning

confidence: 99%

Network bypasses sustain complexity

Estrada

Gómez‐Gardeñes

Lacasa

2023

Proc. Natl. Acad. Sci. U.S.A.

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Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts–Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network’s connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes—making the networks fragile—and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.

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“…Conceptually,

is a measure of the network resistance to a flow between

and

. Recently ( 43 ), it was proven that this communicability distance—and every spherical Euclidean distance—is the effective resistance between nodes in a network with given edge weights.…”

Section: Resultsmentioning

confidence: 99%

Network bypasses sustain complexity

Estrada

Gómez‐Gardeñes

Lacasa

2023

Proc. Natl. Acad. Sci. U.S.A.

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Communicability cosine distance: similarity and symmetry in graphs/networks

Estrada

2024

Comp. Appl. Math.

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A distance based on the exponential kernel of the adjacency matrix of a graph and representing how well two vertices connect to each other in a graph is defined and studied. This communicability cosine distance (CCD) is a Euclidean spherical distance accounting for the cosine of the angles spanned by the position vectors of the graph vertices in this space. The Euclidean distance matrix (EDM) of CCD is used to quantify the similarity between vertices in graphs and networks as well as to define a local vertex invariant—a closeness centrality measure, which discriminate very well vertices in small graphs. It allows to distinguish all nonidentical vertices, also characterizing all identity (asymmetric) graphs–those having only the identity automorphism–among all connected graphs of up to 9 vertices. It also characterizes several other classes of identity graphs. We also study real-world networks in term of both the discriminating power of the new centrality on their vertices as well as in ranking their vertices. We analyze some dictionary networks as well as the network of copurshasing of political books, remarking some of the main advantages of the new approaches studied here.

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Resistance distance and Kirchhoff index of unbalanced blowups of graphs

Sun,

Yang,

2025

Discrete Mathematics

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Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix

Cited by 7 publications

References 30 publications

Network bypasses sustain complexity

Network bypasses sustain complexity

Communicability cosine distance: similarity and symmetry in graphs/networks

Resistance distance and Kirchhoff index of unbalanced blowups of graphs

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