The Matrix Market is

a visual repository of test data for use in comparative studies of algorithms
for numerical linear algebra, featuring nearly 500 sparse matrices
from a variety of applications, as well as matrix generation tools and services

proposed by the National Institute of Standards and Technology (NIST),
a branch of the US Department of Commerce. As the Matrix Market info page puts it,

The Matrix Market is a component of the NIST project on
Tools for Evaluation of Mathematical and Statistical Software
which has focus areas in linear algebra, special functions and statistics.

The `.mtx`

Matrix Market Exchange format is documented on the
NIST page on Matrix Market Exchange formats.

Having saved the following into a file called `adjacency.mtx`

:

```
%%MatrixMarket matrix coordinate real symmetric
%
% adjacency matrix for a graph
%
5 5 6
1 2 1.000e+00
1 3 1.000e+00
1 5 1.000e+00
2 4 1.000e+00
3 4 1.000e+00
4 5 1.000e+00
```

one can use input-output functionality in SciPy to read that file
into a SciPy sparse matrix:

```
sage: from scipy.io import mmread
sage: a = mmread('adjacency.mtx')
```

which is represented as follows:

```
sage: a
<5x5 sparse matrix of type '<type 'numpy.float64'>'
with 12 stored elements in COOrdinate format>
```

and, if one want the list of its entries, prints out as follows:

```
sage: print(a)
(0, 1) 1.0
(0, 2) 1.0
(0, 4) 1.0
(1, 3) 1.0
(2, 3) 1.0
(3, 4) 1.0
(1, 0) 1.0
(2, 0) 1.0
(4, 0) 1.0
(3, 1) 1.0
(3, 2) 1.0
(4, 3) 1.0
```

One can convert it to a SciPy dense matrix:

```
sage: b = a.todense()
sage: b
matrix([[ 0., 1., 1., 0., 1.],
[ 1., 0., 0., 1., 0.],
[ 1., 0., 0., 1., 0.],
[ 0., 1., 1., 0., 1.],
[ 1., 0., 0., 1., 0.]])
```

and then convert that to a Sage matrix:

```
sage: c = matrix(b)
sage: c
[0.0 1.0 1.0 0.0 1.0]
[1.0 0.0 0.0 1.0 0.0]
[1.0 0.0 0.0 1.0 0.0]
[0.0 1.0 1.0 0.0 1.0]
[1.0 0.0 0.0 1.0 0.0]
```

from which one can create a graph:

```
sage: g = Graph(c)
sage: g
Graph on 5 vertices
sage: g.plot()
Launched png viewer for Graphics object consisting of 12 graphics primitives
```

Alternatively, to call Octave or MATLAB from SageMath, one can use the
corresponding interfaces:

but for the needs of this question, that should not be necessary.

In summary:

```
sage: from scipy.io import mmread
sage: g = Graph(matrix(mmread('adjacency.mtx').todense()))
```

I forgot to mention that the matrix in .mtx in format is the adjacency matrix of the graph. The problem is I cannot read the matrix and generate the underlying graph in SAGE 8.2 (Jupyter).

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