<Page>

                                                                     EXHIBIT 4.4

                                                               EXECUTION VERSION

================================================================================



                    ALLIED RISER COMMUNICATIONS CORPORATION,

                                     ISSUER,


                       COGENT COMMUNICATIONS GROUP, INC.,

                                   CO-OBLIGOR,


                                       AND


                            WILMINGTON TRUST COMPANY,

                                     TRUSTEE


                                   ----------

                  7.50% CONVERTIBLE SUBORDINATED NOTES DUE 2007



                          FIRST SUPPLEMENTAL INDENTURE

                          Dated as of February 4, 2002


                                       TO


                                    INDENTURE

                            Dated as of June 28, 2000


                                   ----------




================================================================================


<Page>

         FIRST SUPPLEMENTAL INDENTURE ("First Supplemental Indenture"), dated as
of February 4, 2002, among ALLIED RISER COMMUNICATIONS CORPORATION, a Delaware
corporation having its principal office at 1700 Pacific Avenue, Suite 400,
Dallas, Texas 75201 (the "Company"), COGENT COMMUNICATIONS GROUP, INC., a
Delaware corporation having its principal office at 1015 Thirty-First Street,
N.W., Washington, D.C. 20007 ("Cogent"), and WILMINGTON TRUST COMPANY, a banking
corporation, not in its individual capacity, but solely as Trustee hereunder and
under the Indenture (as defined below) (the "Trustee"). Capitalized terms not
otherwise defined herein shall have the meanings set forth in the Indenture.

                                    RECITALS

         WHEREAS, the Company and the Trustee have heretofore executed and
delivered a certain Indenture, dated as of June 28, 2000 (the "Indenture"),
providing for the issuance of Securities;

         WHEREAS the Company, Cogent and a wholly owned subsidiary of Cogent
("Merger Sub"), have entered into an Agreement and Plan of Merger, dated as of
August 28, 2001, as amended by Amendment No. 1, dated as of October 13, 2001 (as
so amended, the "Merger Agreement"), which provides for the merger of Merger Sub
with and into the Company (the "Merger"), with the Company continuing its
corporate existence under the laws of the State of Delaware as a wholly owned
subsidiary of Cogent;

         WHEREAS, under the Merger Agreement and at the effective time of the
Merger, with certain exceptions, each share of common stock of the Company, par
value $0.0001 per share, will be converted into the right to receive 0.0321679
shares of common stock of Cogent, par value $0.001 per share ("Cogent Common
Stock");

         WHEREAS, Section 12.11 of the Indenture provides, among other things,
that in case of any merger of another Person into or with the Company, with
certain exceptions, the Person resulting from such merger shall execute and
deliver to the Trustee a supplemental indenture providing that the Holder of
each Outstanding Security shall have the right thereafter, during the period
such Security shall be convertible as specified in Section 12.1 of the
Indenture, to convert such Security only into the kind and amount of securities,
cash and other property receivable upon such merger by a holder of the number of
shares of Common Stock of the Company into which such Security might have been
converted immediately prior to such merger;

         WHEREAS, Section 14.5 of the Indenture provides, among other things,
that in certain cases where Section 12.11 applies, the Person resulting from a
merger shall execute and deliver to the Trustee a supplemental indenture
modifying the provisions of the Indenture including provisions of Article XIV
and the definitions of Common Stock and Change in Control, to make such
provisions apply in the event of a subsequent Change in Control to the common
stock and the issuer thereof if different from the Company and Common Stock of
the Company (in lieu of the Company and the Common Stock of the Company);

         WHEREAS, Cogent has agreed to become a co-obligor with respect to the
due and punctual payment of the principal of and premium, if any, and interest
on the Securities and to



                                      -1-
<Page>

confirm the rights of Holders to receive Cogent Common Stock upon conversion of
the Securities in accordance with Article XII of the Indenture and with respect
to the provisions of Section 14.5 of the Indenture;

         WHEREAS, Section 8.1 of the Indenture provides, among other things,
that, without the consent of any Holders of Securities, the Company, when
authorized by a Board Resolution of the Company, and the Trustee, at any time
and from time to time, may enter into one or more indentures supplemental to the
Indenture (i) under Section 8.1(4), to make provision with respect to the
conversion rights of Holders of Securities pursuant to Section 12.11 of the
Indenture or to make provision with respect to the repurchase rights of Holders
of Securities pursuant to Section 14.5, and (ii) under Section 8.1(8) to make
any other provisions with respect to matters or questions arising under the
Indenture as the Company and the Trustee may deem necessary or advisable and
which do not adversely affect the interests of the Holders of Securities in any
material respect;

         WHEREAS, the execution and delivery of this First Supplemental
Indenture has been authorized by resolutions of the board of directors of the
Company and by resolutions of the board of directors of Cogent;

         NOW, THEREFORE, THIS FIRST SUPPLEMENTAL INDENTURE WITNESSETH:

         For and in consideration of the premises and intending to be legally
bound hereby, it is mutually covenanted and agreed, for the equal and
proportionate benefit of all Holders of the Securities, as follows:

                                    ARTICLE I
                    REPRESENTATIONS OF THE COMPANY AND COGENT

         Each of the Company and Cogent represents and warrants as of the date
hereof to the Trustee as follows:

         SECTION 1.1. It is a corporation duly organized, validly existing and
in good standing under the laws of the State of Delaware.

         SECTION 1.2. The execution, delivery and performance by it of this
First Supplemental Indenture have been authorized and approved by all necessary
corporate action on its part.

                                   ARTICLE II
               ASSUMPTION OF OBLIGATIONS; CONVERSION OF SECURITIES

         SECTION 2.1. Cogent hereby agrees, upon the effectiveness of this First
Supplemental Indenture, (i) to become jointly and severally liable with the
Company as a co-obligor with respect to the due and punctual payment of the
principal of and premium, if any, and interest on the Securities under Section
10.1 of the Indenture and in accordance with the terms of the Securities and the
Indenture, and (ii) to issue its Common Stock upon conversion of any Security
pursuant to Article XII of the Indenture as amended by this First Supplemental
Indenture. Notwithstanding such agreement by Cogent, the Company is not relieved
of any of its obligations and covenants under the Indenture and the Securities,
except for the obligation to



                                      -2-
<Page>

issue its common stock upon conversion of Securities pursuant to Article XII of
the Indenture.

         SECTION 2.2. The Indenture is hereby amended to provide that upon the
effectiveness of this First Supplemental Indenture, on the terms and subject to
the conditions set forth in the Indenture, the Holder of each Outstanding
Security shall have the right, during the period such Security shall be
convertible as specified in Section 12.1 of the Indenture, to convert such
Security only into the kind and amount of Cogent Common Stock receivable upon
the Merger by a holder of the number of shares of common stock of the Company
into which such Security might have been converted immediately prior to the
Merger, assuming such holder of common stock of the Company is not a Constituent
Person or an Affiliate of a Constituent Person. From and after the effectiveness
of the Merger, the Conversion Rate shall be subject to adjustments from time to
time which shall be as nearly equivalent as may be practicable to the
adjustments provided for in Article XII of the Indenture.

         SECTION 2.3. Upon the effectiveness of this First Supplemental
Indenture:

         (a)   the following definitions are hereby added in Section 1.1 of the
Indenture:

               "COGENT" means Cogent Communications Group, Inc., a Delaware
               corporation, or any successor thereto.

               "FIRST SUPPLEMENTAL INDENTURE" means the First Supplemental
               Indenture, dated as of February 4, 2002, among the Company,
               Cogent and the Trustee, to the Indenture.

               "MERGER" has the meaning specified in the recitals to the First
               Supplemental Indenture.

         (b)   the first sentence of the definition of "Common Stock" in
Section 1.1 of the Indenture is hereby amended to read as follows:

               "COMMON STOCK" means the Common Stock, par value $0.001 per
               share, of Cogent authorized as of the effective date of the First
               Supplemental Indenture.

         (c)   references in Article XII of the Indenture to the "Company," the
"Board of Directors" and the "Officers' Certificate" shall be deemed references
to Cogent, the board of directors of Cogent, and an officers' certificate of
Cogent, respectively, to the extent necessary and appropriate to effect the
intent of Section 2.2 of this Supplemental Indenture.

         (d)   references in Section 15.4 of the Indenture to the "Company"
shall be deemed to refer to each of the Company and Cogent.

         SECTION 2.4. Upon the effectiveness of this First Supplemental
Indenture, (i) the reference in Section 14.2(4) of the Indenture to "the
Company's authorized but unissued Common Stock" shall be amended to read
"Cogent's authorized but unissued Common Stock;" (ii) the reference in Section
14.3(6) of the Indenture to "the stock transfer books of the Company" shall be
amended to read "the stock transfer books of Cogent;" (iii) references in


                                      -3-
<Page>

Section 14.4 of the Indenture (A) to "capital stock of the Company" shall be
amended to read "capital stock of Cogent," and (B) to the "Company" shall be
amended to read "Cogent."

         SECTION 2.5. Upon the effectiveness of this First Supplemental
Indenture, Section 14.5 of the Indenture is hereby amended to read in its
entirety as follows:

               SECTION 14.5 CONSOLIDATION, MERGER, ETC. In the case of any
          merger, consolidation, conveyance, sale, transfer or lease of all or
          substantially all of the assets of Cogent to which Section 12.11
          applies, in which the Common Stock is changed or exchanged as a result
          into the right to receive shares of stock and other securities or
          property or assets (including cash) which includes shares of Common
          Stock or common stock of another Person that are, or upon issuance
          will be, traded on a United States national securities exchange or
          approved for trading on an established automated over-the-counter
          trading market in the United States and such shares constitute at the
          time such change or exchange becomes effective in excess of 50% of the
          aggregate fair market value of such shares of stock and other
          securities, property and assets (including cash) (as determined by the
          Company, which determination shall be conclusive and binding), then
          the Person formed by such consolidation or resulting from such merger
          or combination or which acquires the properties or assets (including
          cash) of Cogent, as the case may be, shall execute and deliver to the
          Trustee a supplemental indenture (which shall comply with the Trust
          Indenture Act as in force at the date of execution of such
          supplemental indenture) modifying the provisions of this Indenture
          relating to the right of Holders to cause the Company to repurchase
          the Securities following a Change in Control, including without
          limitation the applicable provisions of this Article XIV and the
          definitions of Common Stock and Change in Control, as appropriate, and
          such other related definitions set forth herein as determined in good
          faith by the Company (which determination shall be conclusive and
          binding), to make such provisions apply in the event of a subsequent
          Change in Control to the common stock and the issuer thereof if
          different from Cogent and Common Stock of Cogent (in lieu of Cogent
          and the Common Stock of Cogent).

                                   ARTICLE III
                                  MISCELLANEOUS

         SECTION 3.1. This First Supplemental Indenture constitutes an integral
part of the Indenture, which, as supplemented and amended by this First
Supplemental Indenture, is in all respects hereby adopted, ratified and
confirmed.

         SECTION 3.2. Securities authenticated and delivered after the execution
of this First Supplemental Indenture may, and shall if required by the Trustee,
bear a notation in form approved by the Trustee as to any matter provided for in
this First Supplemental Indenture.

         SECTION 3.3. Notice of the execution of this First Supplemental
Indenture shall be given by the Company to the Holder of each Security as
provided in Sections 1.6 and 12.11 of the Indenture promptly upon such execution
hereof.



                                      -4-
<Page>

         SECTION 3.4. The recitals contained herein shall be taken as the
statements of the Company and Cogent, and the Trustee does not assume any
responsibility for their correctness. The Trustee makes no representations as to
the validity or sufficiency of this First Supplemental Indenture.

         SECTION 3.5. If any provision of this First Supplemental Indenture
limits, qualifies or conflicts with the duties imposed by any of Sections 310 to
317, inclusive, of the Trust Indenture Act through operation of Section 318(c)
thereof, such imposed duties shall control.

         SECTION 3.6. Nothing in this First Supplemental Indenture, express or
implied, shall give to any Person, other than the parties hereto and their
successors and assigns, any benefit or any legal or equitable right, remedy or
claim under this First Supplemental Indenture.

         SECTION 3.7. THIS FIRST SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY THE
LAWS OF THE STATE OF NEW YORK.

         SECTION 3.8. This First Supplemental Indenture may be executed in any
number of counterparts, each of which so executed shall be deemed to be an
original, but all such counterparts shall together constitute but one and the
same instrument.

         SECTION 3.9. This First Supplemental Indenture shall become effective
on the day and year first above written, at the time of effectiveness of the
Merger.



         [The balance of this page has intentionally been left blank.]




                                      -5-
<Page>


         IN WITNESS WHEREOF, the parties hereto have caused this First
Supplemental Indenture to be duly executed all as of the day and year first
above written.

                                  ALLIED RISER COMMUNICATIONS
                                  CORPORATION


                                  By:
                                     -------------------------------------------
                                     Name:  David Schaffer
                                     Title: Chief Executive Officer



                                  COGENT COMMUNICATIONS GROUP, INC.


                                  By:
                                     -------------------------------------------
                                     Name:  David Schaeffer
                                     Title: Chairman and Chief Executive Officer



                                  WILMINGTON TRUST COMPANY,
                                  not in its individual capacity but solely as
                                  Trustee hereunder and under the Indenture


                                  By:
                                     -------------------------------------------
                                     Name:
                                     Title:





                                      -6-