<PAGE>

                                                                   EXHIBIT 10.44
 
                                   EXHIBIT B


THIS WARRANT HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED (THE "ACT") OR ANY STATE SECURITIES LAWS.  NO SALE OR DISPOSITION MAY BE
EFFECTED WITHOUT (I) EFFECTIVE REGISTRATION STATEMENTS RELATED THERETO, (II) AN
OPINION OF COUNSEL OR OTHER EVIDENCE, REASONABLY SATISFACTORY TO THE COMPANY,
THAT SUCH REGISTRATIONS ARE NOT REQUIRED, (III) RECEIPT OF NO-ACTION LETTERS
FROM THE APPROPRIATE GOVERNMENTAL AUTHORITIES, OR (IV) OTHERWISE COMPLYING WITH
THE PROVISIONS OF SECTION 7 OF THIS WARRANT.


                                                             As of June 19, 1997
                                                                      No. CS-001

                         CONCENTRIC NETWORK CORPORATION

                          AMENDED AND RESTATED COMMON
                             STOCK PURCHASE WARRANT

     THIS CERTIFIES THAT, for value received, Williams Communications Group,
Inc., a Delaware corporation, is entitled to subscribe for and purchase, subject
to the provisions and upon the terms and conditions hereinafter set forth, that
number of shares of the fully paid and nonassessable Common Stock of Concentric
Network Corporation, a Florida corporation (the "Company") equal to the quotient
obtained by dividing:  (X) where X is the principal amount of the Note (as
defined below) held by the holder of this Warrant plus accrued interest thereon,
by (Y) where Y is the product of (i) 4 and (ii) (Z), where Z is the initial
price per share of the first to occur of the following:  (a) the initial public
offering of the Company's Common Stock having an aggregate price to the public
of at least $40 million (the "IPO") or (b), the price per share of the Company's
Preferred Stock in a private financing (the "Private Financing") having an
aggregate price of at least $40 million (including for purposes of determining
the aggregate price of the IPO or the Private Financing: (i) the principal
amount of the Note, (ii) an $11.95 million equity investment to be made by the
holder hereof in connection with the IPO or the Private Financing and (iii)
services to be provided by the holder hereof to the Company, after the IPO or
Private Financing as the case may be, valued for purposes of this Warrant at $2
million).  Each such Share (as defined below) shall be purchasable at a per
share purchase price equal to fifty percent of the initial Price to Public per
share or the Private Financing price per share, as the case may be, (such price
and such other price as shall result, from time to time, from the adjustments
specified in Section 6 hereof is herein referred to as the "Warrant Price").  As
used herein, (a) the term "Date of Grant" shall mean the date first set forth
above (b) the term "Other Warrants" shall mean any other warrants issued by the
Company in connection with the transaction with respect to which this Warrant
was issued, and any warrant issued upon transfer or partial exercise of this
Warrant, (c) the term "Shares" shall mean the Common Stock to be issued by the
Company hereunder and any stock into or for which any such Common 

                                       1
<PAGE>
 
Stock may hereafter be converted or exchanged, (d) the term "Warrant" as used
herein shall be deemed to include Other Warrants unless the context clearly
requires otherwise, (e) the term "Note" shall mean the note issued by the
Company to the holder of this Warrant pursuant to the Note and Warrant Purchase
Agreement dated June 19, 1997 (f) the term "Price to Public" shall mean the
price to public set forth on the cover page of the final prospectus prepared in
connection with the IPO, and (g) the term "Financing Event" shall mean either
the IPO or the Private Financing, as applicable..

     1.   Term.  The purchase right represented by this Warrant is exercisable,
          ----                                                                 
in whole or in part, at any time and from time to time from the closing of the
Financing Event through the earliest to occur of (i) five years after the Date
of Grant, or (ii) immediately prior to any consolidation or merger of the
Company with or into any entity, or any other corporate reorganization in which
the Company shall not be the continuing or surviving entity of such
consolidation, merger or reorganization or any transaction, any series of
related transactions in which in excess of 50% of Company's voting power is
transferred, or any sale of all or substantially all of the assets of the
Company, other than the proposed reincorporation of the Company into Delaware
through the merger of the Company with and into Concentric Network Corporation,
a Delaware Corporation; provided, however, that the Company shall provide prior
written notice of any proposed event referred to in subsection (ii) above (other
than the proposed reincorporation into Delaware) so as to allow sufficient time
for the parties to obtain Hart-Scott-Rodino compliance, if necessary, to
exercise the Warrant.

     2.   Method of Exercise; Payment; Issuance of New Warrant.  During the term
          ----------------------------------------------------                  
of this Warrant and subject to Sections 3 and 4 below, the purchase right
represented by this Warrant may be exercised by the holder hereof, in whole or
in part and from time to time, at the election of the holder hereof, by (a) the
surrender of this Warrant (with the notice of exercise substantially in the form
attached hereto as Exhibit A-1 and the Investment Representation Statement
                   -----------                                            
attached hereto as Exhibit A-2 duly completed and executed) at the principal
                   -----------                                              
office of the Company and (b) by the payment to the Company, by certified or
bank check, or by wire transfer to an account designated by the Company (a "Wire
Transfer") of an amount equal to the then applicable Warrant Price multiplied by
the number of Shares then being purchased.  The person or persons in whose
name(s) any certificate(s) representing the Shares shall be issuable upon
exercise of this Warrant shall be deemed to have become the holder(s) of record
of, and shall be treated for all purposes as the record holder(s) of, the Shares
represented thereby (and such Shares shall be deemed to have been issued)
immediately prior to the close of business on the date or dates upon which this
Warrant is exercised.  In the event of any exercise of the rights represented by
this Warrant, certificates for the Shares of stock so purchased shall be
delivered to the holder hereof as soon as possible and in any event within
thirty (30) days after such exercise and, unless this Warrant has been fully
exercised or expired, a new Warrant representing the portion of the Shares, if
any, with respect to which this Warrant shall not then have been exercised shall
also be issued to the holder hereof as soon as possible and in any event within
such thirty-day period.

     3.   Right to Convert Warrant into Stock; Net Issuance.
          ------------------------------------------------- 

          (a) Right to Convert.  In lieu of exercising this Warrant in the
              ----------------                                            
manner provided above in Section 2, the holder hereof shall have the right to
convert this Warrant (the "Conversion 

                                      -2-
<PAGE>
 
Right"), in whole or in part, at any time and from time to time after the
closing of the Financing Event subject to the notice restrictions of Section 4
and prior to the expiration date of the Warrant, by the surrender of this
Warrant and the Notice of Exercise form and the Investment Representation
Statement attached hereto duly executed to the office of the Company at the
address set forth herein (or such other office or agency of the Company as it
may designate by notice in writing to the registered holder hereof at the
address of such holder appearing on the books of the Company), into Shares as
provided in this Section 3. Upon exercise of this Conversion Right, the holder
hereof shall be entitled to receive that number of Shares of the Company equal
to the quotient obtained by dividing [(A-B)(X)] by (A), where:
 
     A    =     the initial price per share in the Financing Event.
 
     B    =     the Warrant Price.
 
     X    =     the number of Shares as to which this Warrant is being
                converted.

     If the above calculation results in a negative number, then no Shares shall
be issued or issuable upon conversion of this Warrant.

     Upon conversion of this Warrant in accordance with this Section 3, the
registered holder hereof shall be entitled to receive a certificate for the
number of Shares determined in accordance with the foregoing, and a new Warrant
in substantially identical form and dated as of such conversion for the purchase
of that number of Shares equal to the difference, if any, between the number of
Shares subject to this Warrant and the number of Shares as to which this Warrant
is so converted.

     No fractional shares shall be issuable upon exercise of the Conversion
Right, and, if the number of shares to be issued determined in accordance with
the foregoing formula is other than a whole number, the Company shall pay to the
holder an amount in cash equal to the fair market value of the resulting
fractional share on the Conversion Date (as hereinafter defined).  Shares issued
pursuant to this Section 3 shall be treated as if they were issued upon the
exercise of this Warrant.

          (b) Method of Exercise.  The Conversion Right may be exercised by the
              ------------------                                               
holder by the surrender of this Warrant at the principal office of the Company
together with a written statement specifying that the holder thereby intends to
exercise the Conversion Right and indicating the number of Shares subject to
this Warrant which are being surrendered in exercise of the Conversion Right.
Such conversion shall be effective upon receipt by the Company of this Warrant
together with the aforesaid written statement, or on such later date as is
specified therein (the "Conversion Date"). Certificates for the Shares issuable
upon exercise of the Conversion Right and, if applicable, a new warrant
evidencing the balance of the Shares remaining subject to this Warrant, shall be
issued as of the Conversion Date and shall be delivered to the holder within
thirty (30) days following the Conversion Date.

     4.   Hart-Scott-Rodino Compliance.  Notwithstanding anything else in this
          ----------------------------                                        
Warrant, if the exercise or conversion of this Warrant is subject to the
premerger notification requirements of the 

                                      -3-
<PAGE>
 
Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended (the "HSR
Act"), it shall be a condition to such exercise or conversion that any waiting
period under the HSR Act applicable to the issuance of the Shares shall have
expired or been terminated and any approvals required thereunder shall have been
obtained, and each of the parties hereby agree to cooperate in promptly filing
premerger reports and in taking all steps reasonably necessary to obtain early
termination of any applicable HSR Act waiting periods.

     5.   Stock Fully Paid; Reservation of Shares.  All Shares that may be
          ---------------------------------------                         
issued upon the exercise of the rights represented by this Warrant will, upon
issuance pursuant to the terms and conditions herein, be fully paid and
nonassessable, and free from all taxes, liens and charges with respect to the
issue thereof.  During the period within which the rights represented by this
Warrant may be exercised, the Company will at all times have authorized, and
reserved for the purpose of the issue upon exercise of the purchase rights
evidenced by this Warrant, a sufficient number of shares of its capital stock to
provide for the exercise of the rights represented by this Warrant.

     6.   Adjustment of Warrant Price and Number of Shares.  The number and kind
          ------------------------------------------------                      
of securities purchasable upon the exercise of this Warrant and the Warrant
Price shall be subject to adjustment from time to time upon the occurrence of
certain events, as follows:

          (a) Reclassification.  In case of any reclassification or change of
              ----------------                                               
securities of the class issuable upon exercise of this Warrant (other than a
change in par value, or from par value to no par value, or from no par value to
par value, or as a result of a subdivision or combination), the Company shall
duly execute and deliver to the holder of this Warrant a new Warrant (in form
and substance reasonably satisfactory to the holder of this Warrant), so that
the holder of this Warrant shall have the right to receive, at a total purchase
price not to exceed that payable upon the exercise of the unexercised portion of
this Warrant, and in lieu of the Shares theretofore issuable upon exercise of
this Warrant, the kind and amount of shares of stock, other securities, money
and property receivable upon such reclassification or change by a holder of the
number of Shares then purchasable under this Warrant.  Such new Warrant shall
provide for adjustments that shall be as nearly equivalent as may be practicable
to the adjustments provided for in this Section 6.  The provisions of this
subparagraph (a) shall similarly apply to successive reclassifications or
changes.

          (b) Subdivision or Combination of Shares.  If the Company at any time
              ------------------------------------                             
while this Warrant remains outstanding and unexpired shall subdivide or combine
its outstanding shares of capital stock into which this Warrant is exercisable,
the Warrant Price shall be proportionately decreased in the case of a
subdivision or increased in the case of a combination, effective at the close of
business on the date the subdivision or combination becomes effective.

          (c) Stock Dividends and Other Distributions.  If the Company at any
              ---------------------------------------                        
time while this Warrant is outstanding and unexpired shall (i) pay a dividend
with respect to its capital stock issuable hereunder payable in the same class
or series of capital stock, or (ii) make any other distribution of capital stock
with respect to its capital stock (except any distribution specifically provided
for in Sections 6(a) and 6(b)), then the Warrant Price shall be adjusted, from
and after the date of determination of shareholders entitled to receive such
dividend or distribution, to that price 

                                      -4-
<PAGE>
 
determined by multiplying the Warrant Price in effect immediately prior to such
date of determination by a fraction (i) the numerator of which shall be the
total number of shares of the applicable class or series of capital stock
outstanding immediately prior to such dividend or distribution, and (ii) the
denominator of which shall be the total number of shares of such class or series
of capital stock outstanding immediately after such dividend or distribution.

          (d) Adjustment of Number of Shares.  Upon each adjustment in the
              ------------------------------                              
Warrant Price, the number of Shares purchasable hereunder shall be adjusted, to
the nearest whole share, to the product obtained by multiplying the number of
Shares purchasable immediately prior to such adjustment in the Warrant Price by
a fraction, the numerator of which shall be the Warrant Price immediately prior
to such adjustment and the denominator of which shall be the Warrant Price
immediately thereafter.

     7.   Notice of Adjustments.  Whenever the Warrant Price or the number of
          ---------------------                                              
Shares purchasable hereunder shall be adjusted pursuant to Section 6 hereof, the
Company shall make a certificate signed by its chief financial officer setting
forth, in reasonable detail, the event requiring the adjustment, the amount of
the adjustment, the method by which such adjustment was calculated, and the
Warrant Price and the number of Shares purchasable hereunder after giving effect
to such adjustment, and shall cause copies of such certificate to be mailed
(without regard to Section 13 hereof, by first class mail, postage prepaid) to
the holder of this Warrant at such holder's last known address.

     8.   Fractional Shares.  No fractional Shares will be issued in connection
          -----------------                                                    
with any exercise hereunder, but in lieu of such fractional shares the Company
shall make a cash payment therefor based on the fair market value of the Shares
on the date of exercise as reasonably determined in good faith by the Company's
Board of Directors.

     9.   Compliance with Act; Disposition of Warrant or Shares.
          ----------------------------------------------------- 

          (a) Compliance with Act.  The holder of this Warrant, by acceptance
              -------------------                                            
hereof, agrees that this Warrant, and the Shares to be issued upon exercise
hereof are being acquired for investment and that such holder will not offer,
sell or otherwise dispose of this Warrant, or any Shares except under
circumstances which will not result in a violation of the Act or any applicable
state securities laws.  Upon exercise of this Warrant, unless the Shares being
acquired are registered under the Act and any applicable state securities laws
or an exemption from such registration is available, the holder hereof shall
confirm in writing that the Shares so purchased are being acquired for
investment and not with a view toward distribution or resale in violation of the
Act and shall confirm such other matters related thereto as may be reasonably
requested by the Company.  This Warrant and all Shares issued upon exercise of
this Warrant (unless registered under the Act and any applicable state
securities laws) shall be stamped or imprinted with a legend in substantially
the following form:

     "THE SECURITIES EVIDENCED HEREBY HAVE NOT BEEN REGISTERED UNDER THE
     SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE 

                                      -5-
<PAGE>
 
     SECURITIES LAWS. NO SALE OR DISPOSITION MAY BE EFFECTED WITHOUT (i)
     EFFECTIVE REGISTRATION STATEMENTS RELATED THERETO, (ii) AN OPINION OF
     COUNSEL OR OTHER EVIDENCE, REASONABLY SATISFACTORY TO THE COMPANY, THAT
     SUCH REGISTRATIONS ARE NOT REQUIRED, (iii) RECEIPT OF NO-ACTION LETTERS
     FROM THE APPROPRIATE GOVERNMENTAL AUTHORITIES, OR (iv) OTHERWISE COMPLYING
     WITH THE PROVISIONS OF SECTION 9 OF THE WARRANT UNDER WHICH THESE
     SECURITIES WERE ISSUED, DIRECTLY OR INDIRECTLY."

     Said legend shall be removed by the Company, upon the request of a holder,
at such time as the restrictions on the transfer of the applicable security
shall have terminated.  In addition, in connection with the issuance of this
Warrant, the holder specifically represents to the Company by acceptance of this
Warrant as follows:

               1)  The holder is aware of the Company's business affairs and
     financial condition, and has acquired information about the Company
     sufficient to reach an informed and knowledgeable decision to acquire this
     Warrant.  The holder is acquiring this Warrant for its own account for
     investment purposes only and not with a view to, or for the resale in
     connection with, any "distribution" thereof in violation of the Act.

               2)  The holder understands that this Warrant has not been
     registered under the Act in reliance upon a specific exemption therefrom,
     which exemption depends upon, among other things, the bona fide nature of
     the holder's investment intent as expressed herein.

               3)  The holder further understands that this Warrant must be held
     indefinitely unless subsequently registered under the Act and qualified
     under any applicable state securities laws, or unless exemptions from
     registration and qualification are otherwise available.  The holder is
     aware of the provisions of Rule 144, promulgated under the Act.

          (b) Disposition of Warrant or Shares.  With respect to any offer, sale
              --------------------------------                                  
or other disposition of this Warrant or any Shares acquired pursuant to the
exercise of this Warrant prior to registration of such Warrant or Shares, the
holder hereof agrees to give written notice to the Company prior thereto,
describing briefly the manner thereof, together with a written opinion of such
holder's counsel, or other evidence, if reasonably requested by the Company, to
the effect that such offer, sale or other disposition may be effected without
registration or qualification (under the Act as then in effect or any federal or
state securities law then in effect) of this Warrant or the Shares and
indicating whether or not under the Act certificates for this Warrant or the
Shares to be sold or otherwise disposed of require any restrictive legend as to
applicable restrictions on transferability in order to ensure compliance with
such law.  Promptly upon receiving such written notice and reasonably
satisfactory opinion or other evidence, if so requested, the Company, as
promptly as practicable but no later than fifteen (15) days after receipt of the
written notice, shall notify such holder that such holder may sell or otherwise
dispose of this Warrant or such Shares, all in accordance with the terms of the
notice delivered to the Company.  If a determination has been made pursuant to
this Section 9(b) that the opinion of counsel for the holder or other evidence
is not 

                                      -6-
<PAGE>
 
reasonably satisfactory to the Company, the Company shall so notify the holder
promptly with details thereof after such determination has been made.
Notwithstanding the foregoing, this Warrant or such Shares may, as to such
federal laws, be offered, sold or otherwise disposed of in accordance with Rule
144 or 144A under the Act, provided that the Company shall have been furnished
with such information as the Company may reasonably request to provide a
reasonable assurance that the provisions of Rule 144 or 144A have been
satisfied. Each certificate representing this Warrant or the Shares thus
transferred (except a transfer pursuant to Rule 144 or 144A) shall bear a legend
as to the applicable restrictions on transferability in order to ensure
compliance with such laws, unless in the aforesaid opinion of counsel for the
holder, such legend is not required in order to ensure compliance with such
laws. The Company may issue stop transfer instructions to its transfer agent in
connection with such restrictions.

          (c) Applicability of Restrictions.  Neither any restrictions of any
              -----------------------------                                  
legend described in this Warrant nor the requirements of Section 9(b) above
shall apply to any transfer or grant of a security interest in, this Warrant (or
the Shares obtainable upon exercise thereof) or any part hereof (i) to a partner
of the holder if the holder is a partnership, (ii) to a partnership of which the
holder is partner or (iii) to an affiliated company of the holder; provided,
                                                                   -------- 
however, in any such transfer, if applicable, the transferee shall agree in
-------                                                                    
writing to be bound by the terms of this Warrant as if an original signatory
hereto.

     10.  Rights as Shareholders; Information.  No holder of this Warrant, as
          -----------------------------------                                
such, shall be entitled to vote or receive dividends or be deemed the holder of
Shares, nor shall anything contained herein be construed to confer upon the
holder of this Warrant, as such, any of the rights of a shareholder of the
Company or any right to vote for the election of directors or upon any matter
submitted to shareholders at any meeting thereof, or to receive notice of
meetings, or to receive dividends or subscription rights or otherwise until this
Warrant shall have been exercised and the Shares purchasable upon the exercise
hereof shall have become deliverable, as provided herein. Notwithstanding the
foregoing, the Company will transmit to the holder of this Warrant such
information, documents and reports as are generally distributed to the holders
of any class or series of the securities of the Company concurrently with the
distribution thereof to the shareholders.

     11.  Representations and Warranties.  Except as set forth in the section
          ------------------------------                                     
captioned "Business--Legal Proceedings" of the Registration Statement on form S-
1 (File No. 333-27241) filed with the Securities and Exchange Commission by the
Company, the Company hereby represents and warrants to the holder of this
Warrant as follows:

          (a) This Warrant has been duly authorized and executed by the Company
and is a valid and binding obligation of the Company enforceable in accordance
with its terms, subject to laws of general application relating to bankruptcy,
insolvency and the relief of debtors and the rules of law or principles at
equity governing specific performance, injunctive relief and other equitable
remedies;

          (b) The Shares have been, or will be upon the closing of the IPO or
Private Financing, duly authorized and reserved for issuance by the Company and,
when issued in accordance with the terms hereof will be validly issued, fully
paid and non-assessable;

                                      -7-
<PAGE>
 
          (c) The rights, preferences, privileges and restrictions granted to or
imposed upon the Shares and the holders thereof are as set forth in the Amended
and Restated Articles of Incorporation of the Company as they have been and may
be amended from time to time.

          (d) The execution and delivery of this Warrant are not, and the
issuance of the Shares upon exercise of this Warrant in accordance with the
terms hereof will not be, inconsistent with the Company's Second Amended and
Restated Articles of Incorporation or Bylaws, as they may be amended from time
to time do not and will not contravene any law, governmental rule or regulation,
judgment or order applicable to the Company, and do not and will not conflict
with or contravene any provision of, or constitute a default under, any
indenture, mortgage, contract or other instrument of which the Company is a
party or by which it is bound or require the consent or approval of, the giving
of notice to, the registration or filing with or the taking of any action in
respect of or by, any Federal, state or local government authority or agency or
other person, except for the filing of notices pursuant to federal and state
securities laws, which filings will be effected by the time required thereby;
and

          (e) There are no actions, suits, audits, investigations or proceedings
pending or, to the knowledge of the Company, threatened against the Company in
any court or before any governmental commission, board or authority which, if
adversely determined, will have a material adverse effect on the ability of the
Company to perform its obligations under this Warrant.

     12.  Modification and Waiver.  This Warrant and any provision hereof may be
          -----------------------                                               
changed, waived, discharged or terminated only by an instrument in writing
signed by the party against which enforcement of the same is sought.

     13.  Notices.  Any notice, request, communication or other document
          -------                                                       
required or permitted to be given or delivered to the holder hereof or the
Company shall be delivered, or shall be sent by certified or registered mail,
postage prepaid, to each such holder at its address as shown on the books of the
Company or to the Company at the address indicated therefor on the signature
page of this Warrant.

     14.  Lost Warrants or Stock Certificates.  The Company covenants to the
          -----------------------------------                               
holder hereof that, upon receipt of evidence reasonably satisfactory to the
Company of the loss, theft, destruction or mutilation of this Warrant or any
stock certificate and, in the case of any such loss, theft or destruction, upon
receipt of an indemnity reasonably satisfactory to the Company, or in the case
of any such mutilation upon surrender and cancellation of such Warrant or stock
certificate, the Company will make and deliver a new Warrant or stock
certificate, of like tenor, in lieu of the lost, stolen, destroyed or mutilated
Warrant or stock certificate.

     15.  Descriptive Headings. The descriptive headings of the several
          --------------------                                         
paragraphs of this Warrant are inserted for convenience only and do not
constitute a part of this Warrant.  The language in this Warrant shall be
construed as to its fair meaning without regard to which party drafted this
Warrant.

                                      -8-
<PAGE>
 
     16.  Governing Law.  This Warrant shall be construed and enforced in
          -------------                                                  
accordance with, and the rights of the parties shall be governed by, the laws of
the State of California.

     17.  Severability.  The invalidity or unenforceability of any provision of
          ------------                                                         
this Warrant in any jurisdiction shall not affect the validity or enforceability
of such provision in any other jurisdiction, or affect any other provision of
this Warrant, which shall remain in full force and effect.

     18.  Entire Agreement; Modification.  This Warrant constitutes the entire
          ------------------------------                                      
agreement between the parties pertaining to the subject matter contained in it
and supersedes all prior and contemporaneous agreements, representations, and
undertakings of the parties, whether oral or written, with respect to such
subject matter.


                                   CONCENTRIC NETWORK CORPORATION
                                   a Florida corporation
 

                                         /s/ Henry R. Nothhaft
                                   By:________________________________________
                                         Henry R. Nothhaft
                                         President and Chief Executive Officer

                                   Address:   10590 N. Tantau Avenue
                                              Cupertino, CA  94303

                                      -9-
<PAGE>
 
                                  EXHIBIT A-1

                              NOTICE OF EXERCISE
                              ------------------


To:  CONCENTRIC NETWORK CORPORATION  (the "Company")

    1.  The undersigned hereby:

        [_]  elects to purchase __________ shares of Common Stock of the Company
             pursuant to the terms of the attached Warrant, and tenders herewith
             payment of the purchase price of such shares in full; or

        [_]  elects to exercise its net issuance rights pursuant to Section 3 of
             the attached Warrant with respect to __________ shares of Common
             Stock.


    2.  Please issue a certificate or certificates representing said shares in
the name of the undersigned or in such other name or names as are specified
below:


                    ________________________________________
                                     (Name)

                    ________________________________________
                                   (Address)

                    ________________________________________
                                   (Address)
<PAGE>
 
                                  EXHIBIT A-2
                                  -----------

                      INVESTMENT REPRESENTATION STATEMENT

                            Shares of the Securities
                    (as defined in the attached Warrant) of
                         CONCENTRIC NETWORK CORPORATION

    In connection with the purchase of the above listed securities, the
undersigned hereby represents to Concentric Network Corporation (the "Company")
as follows:

    (1)   The securities to be received upon the exercise of the Warrant (the
        "Securities") will be acquired for investment for its own account, not
        as a nominee or agent, and not with a view to the sale or distribution
        of any part thereof, and the undersigned has no present intention of
        selling, granting participation in or otherwise distributing the same,
        but subject, nevertheless, to any requirement of law that the
        disposition of its property shall at all times be within its control.
        By executing this Statement, the undersigned further represents that it
        does not have any contract, undertaking, agreement or arrangement with
        any person to sell, transfer, or grant participations to such person or
        to any third person, with respect to any Securities issuable upon
        exercise of the Warrant.

    (2)   The undersigned understands that the Securities issuable upon exercise
        of the Warrant at the time of issuance may not be registered under the
        Securities Act of 1933, as amended (the "Act"), and applicable state
        securities laws, on the ground that the issuance of such securities is
        exempt pursuant to Section 4(2) of the Act and state law exemptions
        relating to offers and sales not by means of a public offering and that
        the Company's reliance on such exemptions is predicated on the
        undersigned's representation set forth herein.

    (3)   The undersigned agrees that in no event will it make a disposition of
        any Securities acquired upon the exercise of the Warrant unless and
        until (i) it shall have notified the Company of the proposed disposition
        and shall have furnished the Company with a statement of the
        circumstances surrounding the proposed disposition, and (ii) it shall
        have furnished the Company with an opinion of counsel satisfactory to
        the Company and Company's counsel to the effect that (A) appropriate
        action necessary for compliance with the Act and any applicable state
        securities laws has been taken or an exemption from the registration
        requirements of the Act and such laws is available, and (B) the proposed
        transfer will not violate any of said laws.

    (4)   The undersigned acknowledges that an investment in the Company is
        highly speculative and represents that it is able to fend for itself in
        the transactions contemplated by this Statement, has such knowledge and
        experience in financial and business matters as to be capable of
        evaluating the merits and risks of its investments, and has the ability
        to bear the economic risks (including the risk of a total loss) of its
        investment. The 
<PAGE>
 
        undersigned represents that it has had the opportunity to ask questions
        of the Company concerning the Company's business and assets and to
        obtain any additional information which it considered necessary to
        verify the accuracy of or to amplify the Company's Disclosures, and has
        had all questions which have been asked by it satisfactorily answered to
        the Company.

    (5)   The undersigned acknowledges that the Securities issuable upon
        exercise of the Warrant must be held indefinitely unless subsequently
        registered under the Act or an exemption from such registration is
        available. The undersigned is aware of the provisions of Rule 144
        promulgated under the Act which permit limited resale of shares
        purchased in a private placement subject to the satisfaction of certain
        conditions, including, among other things, the existence of a public
        market for the shares, the availability of certain current public
        information about the Company, the resale occurring not less than one
        year after a party has purchased and paid for the security to be sold,
        the sale being through a "broker's transaction" or in transactions
        directly with a "market makers" (as provided by Rule 144(f)) and the
        number of shares being sold during any three-month period not exceeding
        specified limitations.

Dated:___________

                                     WILLIAMS COMMUNICATIONS GROUP, INC.


                                     By:_______________________________
                                          (Signature)

                                        _______________________________
                                          (Title)

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