Anales AFA Vol. 37 Nro. 3 (Septiembre 2026 - Diciembre 2026) 51 - 55
GRAFOS DE INTERCONEXIÓN DE REDES DE NANOHILOS A PARTIR DE SUS
FOTOMICROGRAFÍAS
NANOWIRE NETWORKS’ INTERCONNECTION GRAPHS FROM THEIR
PHOTOMICROGRAPHS
J. Tau Anzoátegui1,2, J. I. Diaz Schneider3, E. Martínez3, P. Levy3, O. Filevich4,5 y C. P.
Quinteros*2,5
1Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física. Ciudad Universitaria, C1428EHA
CABA, Argentina.
2Instituto de Ciencias Físicas (ICIFI, UNSAM-CONICET), Martín de Irigoyen 3100, San Martín (1650), Argentina.
3Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina. Instituto de Nanociencia y Nanotecnología
(CNEA - CONICET), Nodo Bariloche. Gerencia Física, Centro Atómico Bariloche, Comisión Nacional de Energía Atómica (CNEA),
Av. Bustillo 9500, (8400) S. C. de Bariloche, Río Negro, Argentina.
4Instituto de Tecnologías Emergentes y Ciencias Aplicadas (ITECA, UNSAM-CONICET), Martín de Irigoyen 3100, San Martín (1650),
Argentina.
5Escuela de Ciencia y Tecnología, Martín de Irigoyen 3100, San Martín (1650), Argentina.
Recibido: 26/06/2026 ; Aceptado: 19/09/2026
Los autoensamblados de unidades sintonizables son estudiados intensivamente como sistemas físicos con capacidades
de procesamiento de señales. En particular, las redes de nanohilos de plata (AgNWNs) han demostrado acumulación,
no-linealidad y retención de memoria en múltiples escalas temporales, características que permiten una amplia variedad
de implementaciones neuromórficas. En este estudio, se extrae el esquema de interconexión para analizar la arquitec-
tura experimental de la red y en un futuro poder usarla como entrada de una plataforma de simulación. Mediante el
post-procesado de fotomicrografías de AgNWN, se presenta un procedimiento optimizado para extraer el diagrama de
interconexión y determinar el grafo asociado a cada muestra física. Se estudian métricas de grafos como la distribución
de grado, el tamaño de comunidades, el coeficiente de aglomeración y la longitud de camino, comparando los ensam-
blados experimentales con modelos topológicos de referencia denominados: small-world,modular yscale-free. Los
ensambles experimentales revelan similitudes tanto con topologías small-world como modulares. Adicionalmente, se
estudia el impacto en el grafo de eliminar artificialmente junturas mediante la cuantificación del coeficiente de aglome-
ración ydelalongitud de camino.
Palabras Clave: redes de nanohilos, autoensamblados grafos, análisis topológico, neuromórfico, procesamiento de
imágenes.
Self-assemblies of tunable units are being intensively studied as physical systems with signal processing abilities. Spe-
cifically, silver nanowire networks (AgNWNs) have demonstrated accumulation, non-linearity, and memory retention
with multiple timescales, features that enable a wide variety of neuromorphic implementations. In this study, we aim to
extract the interconnection scheme to analyze the experimentally obtained network architecture and, eventually, use it as
the input of a previously developed simulation platform. By post-processing photomicrographs of AgNWN, we present
a pipeline optimized to extract the interconnection diagram, recognizing the intersections formed among the nanowires,
to determine the associated graph for each physical sample. Graph metrics such as degree distribution, community size,
clustering coefficient, and path-length are studied to compare the experimental assemblies’ attributes to topological mo-
dels of reference. Small-world,modular, and scale-free are well-known structures in the field of mathematical graphs.
The experimental assemblies reveal similarities to both small-world and modular topologies. This communication also
studies the impact of artificially removing junctions from the resulting graphs on the previously calculated clustering
coefficient and path-length.
Keywords: nanowire networks, self-assemblies, graphs, topological analysis, neuromorphic, image processing.
https://doi.org/10.31527/analesafa.2026.37.3.51-55 ISSN - 1850-1168 (online)
*cquinteros@unsam.edu.ar
J. Tau Anzoátegui et al. / Anales AFA Vol. 37 Nro. 3 (Septiembre 2026 - Diciembre 2026) 51 - 55 51
I. INTRODUCTION
The computational strategies implemented by modern computers stem from concepts derived from the neurophysio-
logy of biological brains[1]. The encoding of information as memory states or trapped charge in synthetic units is one
example (in hardware) of this[2]. The implementation of artificial neural networks composed of neuronal nodes and sy-
naptic weights constitutes another example (this time in software) of the same original inspiration[3]. However, the course
of technological progress has distanced synthetic implementations from their biological counterparts[4]. The power con-
sumption of current computing systems and the restrictions this may entail in the near future necessitate proposing an
alternative: exploiting synthetic systems radically different from the CMOS gates that are presently at the heart of the
hardware[2].
Self-assemblies of tunable units are being intensively studied as physical systems with signal-processing capabilities[2,
5-10]. Understood as complex networks of nanometric objects, these platforms (made of nanoparticles or nanowires,
among others) resemble morphological, topological, and functional aspects of neural tissues[4]. In that regard, the ex-
tremely high number of units, the spontaneous interconnection scheme among them, and the non-trivial architecture[11]
are desirable features for a new generation of neuromorphic hardware inspired by the collective attributes instead of the
detailed fidelity of the individual constituents[12].
In this framework, self-assemblies are being studied either experimentally[2,5-10,13] or with simulation schemes[9,
14,15]. Experimentally, synthesizing and measuring two or multi-electrode devices and subjecting them to a variety of
incoming signals allows for the identification of desirable properties such as accumulation, non-linearity, short- and long-
term memory, among others. Simulations performed on different platforms allow analysis of the impact of the properties
of individual components (which are experimentally inaccessible) on the macroscopic collective response[16]. Except
for a few cases[14,17], the interconnection schemes fed into the simulation platforms are not usually consistent with
the experimentally obtained geometry. As such, the obtained simulated responses are just qualitatively comparable to the
physical assemblies. In this study, we aim to bridge the gap between the two approaches by interpreting photomicrographs
of the real samples as graphs of interconnected nodes useful to configure the simulations. Additionally, the conversion of
the experimental information (optical images) into mathematical objects makes the latter suitable for network analysis in
terms of their topology and geometry-related metrics.
II. SYNTHESIS AND IMAGE ACQUISITION
The AgNWs assemblies were fabricated with a targeted geometry (∼170 nm in diameter and ∼70 µm in length),
then dispersed in a solvent (containing polymeric residues coming from the NWs growth), and finally deposited onto a
desired substrate to form the networks (AgNWNs)[18]. The desired areal density (∼2500 mm−2) is reached by sequential
deposition steps[18]. As depicted in Fig. 1, two millimetric-sized Ag electrodes (1 mm apart) were sputtered to access the
assembly electrically.
FIG. 1: Infograph of a typical nanowire network (NWN) depicting the constituent units. Each NWN comprises the network of nanowires
(NWs) intersecting each other, enclosed by two macroscopic electrodes placed 1 mm apart. A zoomed-in area is included as an inset
where individual NWs and their junctions can be spotted.
The resultant assemblies comprise metallic NWs, coated with a polymeric layer residual from the synthesis, which
intersect with each other, forming capacitor-like junctions (Ag-polymer-Ag). The electrical connection between the two
macroscopic electrodes is mediated by the conduction along the NWs themselves and across the tunable memristive
junctions. The electrical conductivity requires geometrical percolation of the assembly, but is also conditioned by the state
of the memristive intersections among the constituent NWs.
Dark-field optical images were taken with a Leica DM2700 M using a typical magnification of 10x. Samples of in-
termediate areal densities N
mm2(as reported in[9]) were characterized using this technique. While in-plane scanning the
sample, multiple images are taken to completely cover the assembly. These partial images are primarily stitched to obtain
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an image of the full active area. The image produced from this collection will be the input to the pipeline designed for the
following graph extraction.
III. PIPELINE FOR GRAPH GENERATION
The pipeline comprises a sequence of steps (schematically summarized in Fig. 2). First, the routine enables the iden-
tification of the macroscopic electrodes. This operation is of paramount importance since the graph objects contained
within it will present a preferential hierarchy in the electrical percolation. In the following, the NWN itself needs to be
interpreted.
FIG. 2: Sketch of the pipeline flow. Starting from the stitched picture, the procedure identifies the electrodes and binarizes the RGB-
format image to facilitate the skeletonization conversion. Once the network has been converted to a set of one-pixel-wide contours,
network extraction is performed. The wires and their mutual intersections (zenithal view) are interpreted as a graph comprised of
nodes and edges, respectively, depicted in the zoomed-in area. The right panel displays a section of the skeletonized image overlaid
with the extracted graph.
Recognizing the nanowires and the intersections among them requires image processing strategies. Binarization of the
image facilitates posterior identification of the constituents. Additionally, an image cleaning procedure is implemented,
where spurious pixels are filtered, removing both small black holes and isolated white noise. Once cleaned, the image
undergoes a skeletonization[19] process to reduce the NWs to a single-pixel-wide line. The image obtained from the
previous step allows for the intersection identification as the cross-points between lines. Initially, the skeleton is converted
into a graph by mapping junctions to nodes and NW segments to edges. Subsequently, this graph is transformed into its
corresponding line graph, effectively reversing the roles of nodes and edges.
It is important to emphasize that a cross-point does not imply an intersection. From a zenithal view, it is not possible
to determine whether two NWs occupying the same area and forming an angle between them are actually in contact
or if there is some vertical space between them. After building the corresponding graphs, this will be accounted for by
introducing a removal probability. This probability ranges from p=0, where all cross-points are assumed to be physical
junctions, to p=1, where all cross-points are eliminated.
The result is a collection of segments and intersections. Since the segments are just portions of the original NWs
(conductive and not tunable), while the intersections are the electrically active components, the segments will be coded
as nodes and the junctions as edges. Together, the number of nodes, ‘N’ (formerly segments of NWs), and of edges, ‘e’
(the intersections among NWs from the zenithal point of view) and their interconnectivity map will determine the type of
structure associated with each experimental assembly. The number of links each node possesses is referred to as its degree
(k).
Three samples (A, B, and C) were optically imaged and translated into graphs using the developed pipeline, more details
on the algorithms and their parameters can be consulted in the referenced GitHub repository [20]. The characteristics of
the obtained graphs are summarized in Table 1. Samples A and B possess similar densities, while C is sparser.
TABLA 1: Graph features of the experimental samples.
Attribute ↓/Sample →A B C
Nodes (N) 66435 77477 26222
Edges (e) 121217 139293 41941
Degree (average) 3.65 3.60 3.20
IV. TOPOLOGICAL ANALYSIS
Graph generation from experimentally-acquired optical images enables geometrical considerations. Multiple metrics
are defined as indicators of the network segregation and/or integration and are related to some archetypal interconnection
schemes. Among them, we could mention: small-world,modular, and scale-free networks.
Small-world networks[21] are typically formed by clusters, within which the connectivity is high, and hubs linking
nodes belonging to different clusters. Two metrics are defined: clustering coefficient (CC) and path length (PL).
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The clustering coefficient defines the likelihood that a graph is formed by subgroups. Specifically, the local clustering
coefficient of a node uis the fraction of possible triangles through that node that exist[22,23]:
CC =1
N∑
u
cu=1
N∑
u
T(u)
deg(u)(deg(u)−1)(1)
where T(u)is the number of triangles through node uand deg(u)is the degree of u. We evaluate the average clustering
coefficient, defined as the mean of cuover all Nnodes in the graph.
The path length is defined as the mean of the minimum distance (in number of edges) between all pairs of nodes in the
network:
PL =1
N(N−1)∑
u=v
d(u,v)(2)
where d(u,v)is the shortest distance between node uand v. A statistical approximation was implemented to handle the
prohibitive computational cost for large-scale graphs: a representative subset of m=1000 random seed nodes was sampled
within the largest connected component, and the shortest paths from these seed nodes to all other nodes were evaluated.
Small-world networks, early proposed by Watts-Strogatz[21], possess a short average path-length and a high cluste-
ring coefficient.Modular networks[24] are characterized by presenting communities that determine a coexisting structure
of sparse and dense connectivity zones. Finally, scale-free networks[25] have a highly heterogeneous connectivity dis-
tribution, with most nodes having very few links and a few nodes (hubs) linking to an exceptionally high number of
nodes.
FIG. 3: Different network schemes used as a reference: small-world, modular, and scale-free. The top row, (a), (b), and (c), comprises
a degree histogram including an inset with sketches. On the second row, (d), (e), and (f) show the adjacency matrix, while the bottom
row, (g), (h), and (i), displays the distribution of community sizes for each case. Networks of size N = 70000 and average degree k = 4.
Fig. 3represents some salient features of the three archetypal networks, quantified in artificially built networks genera-
ted with size N = 70000 and average degree k = 4, comparable to the experimental cases.
Fig. 4depicts the degree distribution and adjacency matrix obtained from three different samples. Comparison of the
obtained graph characteristics allows for identifying a moderate range of available connectivity degrees, compatible with
small-world-like schemes. However, adjacency matrices show a modular arrangement as indicated by the presence and
sustainable size of the squares forming around the matrices’ diagonals.
As mentioned in the Introduction, the experimentally available zenithal view does not enable distinguishing real jun-
ctions from concurrent NWs that may not be in physical contact. Here we explore the graph variability by quantifying
some of the previous metrics as a function of an arbitrary edge-removal probability (per).
Clustering coefficient and path length are displayed as a function of per (Fig. 5). Starting from the clustering coefficient
determined for the whole network, removing edges produces a reduction of the agglomeration capability. The same analy-
sis was conducted with the three networks of reference, showing that despite the initial condition being different for each
case, the overall evolution as a function of per is the same (inset of Fig. 5(d)).
The path length (Fig. 5(e)) has been calculated in three different ways, averaged over 20 independent runs. The base
graph considers the interconnection scheme identified regardless of the electrodes. The effective graph considers that
the nodes located within the electrodes’ areas are equivalent to each other. The effective electrode graph redefines the
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FIG. 4: Network metrics of graphs generated from experimental images. Degree distributions with optical images as insets with a
scale bar of 100 µm ((a), (b), and (c)), adjacency matrices ((d), (e), and (f)), and community distributions ((g), (h), and (i)) for three
experimental cases (samples A, B, and C, respectively).
FIG. 5: Clustering coefficient and path length as a function of the edge-removal probability. (a), (b) and (c) depict schematics of the
different graphs used to measure the path length. (d) shows the clustering coefficient as a function of per for the samples and the
reference networks. (e) displays the path length as a function of per for Sample A in the three different cases shown above.
path length considering only paths of electrical validity (origin nodes in Vin electrode and destination nodes in Vout). The
topological analysis indicates that the experimental assemblies do not strictly correspond to just one type of archetypal
network architecture, but hints of the three types could be found.
V. CONCLUSIONS
This work presents a pipeline developed to build a graph or network as a mathematical object associated with the optical
images of experimental samples. Graphs’ attributes, such as the number of obtained nodes and edges, reflecting NWs’
segments and intersections, respectively, were compared among three experimental samples. Topological metrics and
means of representation derived from three networks chosen as references were used to relate the obtained graphs to well-
known structures. Considering that all the identified intersections reflect real junctions, all the resulting graphs displayed
a degree distribution similar to a small-world distribution. Adjacency matrices showed the presence of communities of
different sizes, which are not mutually isolated but interconnected.
Topological metrics such as the path length and clustering coefficient were calculated as a function of an artificially in-
troduced edge-removal probability. This artificial insert, aimed at accounting for the realistic status of the NWN, allowed
us to test the impact of the effective density on the metrics. Future work will be devoted to further exploring the im-
pact of the electrodes’ definition on the topology, and to testing multiple electrical protocols using previously developed
simulation platforms.
J. Tau Anzoátegui et al. / Anales AFA Vol. 37 Nro. 3 (Septiembre 2026 - Diciembre 2026) 51 - 55 55
Acknowledgments
The authors kindly acknowledge Prof. Zdenka Kuncic, Mr. Teo Ibar, Dr. Victoria Rosato Siri, Dr. Federico Golmar, Dr.
Lucas Finazzi, and the members of the LINE group and IA-CoNSoFi consortium for their insightful comments and the
fruitful discussions. This work was partly supported by CONICET PIP 2023-2025 11220220100508CO and CONICET
PIET-R 2025 29820250100057CO.
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